# Brain Teasers



## schielrn

Thought maybe we could see if we could start a thread of brain teasers:

You are in a room with a bathtub full of water. You have a teaspoon, a coffee mug and a mop bucket. There is a window in this room. What would be the quickest way to empty the tub and have no water left in there?


----------



## TinaP

Pull the plug.


----------



## schielrn

Yes. I was surprised that many people in my office missed that. About 25% of the people I have asked said they would use the bucket. I even had one guy say he would use the teaspoon to fill the coffee mug and then fill the bucket with the coffee mug to use all resources, but they didn't even think about the plug.


----------



## TinaP

I used to help my college roommate with one of her psych classes.  It was all about how people think and learn.  There were a mess of questions like this, I guess to help learn not to overlook the obvious.


----------



## jgthtrotih

HI,

i have one...

WET WET WET WET 
 WET WET WET WET 
 WET WET WET WET
  WET WET WET WET 
  WET WET WET WET 
  WET WET WET WET
 WET WET WET WET
      SPILL SPILL      
 WET WET WET WET
WET WET WET WET
  WET WET WET WET 
  WET WET WET WET
   WET WET WET WET 
   WET WET WET WET 
   WET WET WET WET
  WET WET WET WET
  WET WET  WET WET 
  WET WET WET WET


Thanks!


----------



## schielrn

Ever since I have left work yesterday I have been trying to figure this out and still haven't?  Maybe by Monday it will come to me.


----------



## Oorang

<deleted>


----------



## jgthtrotih

Schierln, 

It's a toughy! 

Oorang,

Your post didn't come through?

Thanks!


----------



## Misca

Thinking outside the box the absolutely quickest way would be to flip the tub over. If that's not possible, then pull the plug and use the bucket to empty it even faster.


----------



## Expiry

Surely the quickest way would be to pull the plug out, then use the bucket and the mug to continually bail out until it was empty.

Oh, and drinking some of it, too. Probably.


----------



## Sandeep Warrier

A couple of easy ones.... i guess

*[FONT=&quot]A man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "Twelve." The member replied, "Six" and was let in. A second member came to the door and the doorman said, "Six." The member replied, "Three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said, "Ten" and the man replied, "Five". But he was not let in. What should he have said and why?[/FONT]*

<link rel="File-List" href="file:///C:%5CDOCUME%7E1%5Csandeepw%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml"><!--[if gte mso 9]><xml>  <w:WordDocument>   <w:View>Normal</w:View>   <w:Zoom>0</w:Zoom>   <w:PunctuationKerning/>   <w:ValidateAgainstSchemas/>   <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>   <w:IgnoreMixedContent>false</w:IgnoreMixedContent>   <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>   <w:Compatibility>    <w:BreakWrappedTables/>    <w:SnapToGridInCell/>    <w:WrapTextWithPunct/>    <w:UseAsianBreakRules/>    <w:DontGrowAutofit/>   </w:Compatibility>   <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>  </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml>  <w:LatentStyles DefLockedState="false" LatentStyleCount="156">  </w:LatentStyles> </xml><![endif]--><style> <!--  /* Font Definitions */  @font-face     {font-family:"Lucida Sans";     panose-1:2 11 6 2 3 5 4 2 2 4;     mso-font-charset:0;     mso-generic-font-family:swiss;     mso-font-pitch:variable;     mso-font-signature:3 0 0 0 1 0;}  /* Style Definitions */  p.MsoNormal, li.MsoNormal, div.MsoNormal     {mso-style-parent:"";     margin:0in;     margin-bottom:.0001pt;     mso-pagination:widow-orphan;     font-size:12.0pt;     font-family:"Times New Roman";     mso-fareast-font-family:"Times New Roman";} @page Section1     {size:8.5in 11.0in;     margin:1.0in 1.25in 1.0in 1.25in;     mso-header-margin:.5in;     mso-footer-margin:.5in;     mso-paper-source:0;} div.Section1     {page:Section1;} --> </style><!--[if gte mso 10]> <style>  /* Style Definitions */  table.MsoNormalTable     {mso-style-name:"Table Normal";     mso-tstyle-rowband-size:0;     mso-tstyle-colband-size:0;     mso-style-noshow:yes;     mso-style-parent:"";     mso-padding-alt:0in 5.4pt 0in 5.4pt;     mso-para-margin:0in;     mso-para-margin-bottom:.0001pt;     mso-pagination:widow-orphan;     font-size:10.0pt;     font-family:"Times New Roman";     mso-ansi-language:#0400;     mso-fareast-language:#0400;     mso-bidi-language:#0400;} </style> <![endif]-->*[FONT=&quot]You have to measure exactly 4 liters of water, but you only have a 3-liter bottle and a 5-liter bottle. How do you do it?[/FONT]*



> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> SPILL SPILL
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET  WET WET
> WET WET WET WET


I looked at this without my glasses ... from some distance and it looked like a 3-d "C".... I'm sure that I'm way off though 
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Gerald Higgins

sandeep.warrier said:


> <LINK href="file:///C:%5CDOCUME%7E1%5Csandeepw%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel=File-List><STYLE> <!--  /* Font Definitions */  @font-face     {font-family:"Lucida Sans";     panose-1:2 11 6 2 3 5 4 2 2 4;     mso-font-charset:0;     mso-generic-font-family:swiss;     mso-font-pitch:variable;     mso-font-signature:3 0 0 0 1 0;}  /* Style Definitions */  p.MsoNormal, li.MsoNormal, div.MsoNormal     {mso-style-parent:"";     margin:0in;     margin-bottom:.0001pt;     mso-pagination:widow-orphan;     font-size:12.0pt;     font-family:"Times New Roman";     mso-fareast-font-family:"Times New Roman";} @page Section1     {size:8.5in 11.0in;     margin:1.0in 1.25in 1.0in 1.25in;     mso-header-margin:.5in;     mso-footer-margin:.5in;     mso-paper-source:0;} div.Section1     {page:Section1;} --> </STYLE>*[FONT=&quot]You have to measure exactly 4 liters of water, but you only have a 3-liter bottle and a 5-liter bottle. How do you do it?[/FONT]*


 
Can we give the answer to this one yet ?
By the way, I think you also mean, you have a supply of water, and also something that you can pour water into to get rid of it, even it's just the ground.


----------



## Sandeep Warrier

Gerald Higgins said:


> Can we give the answer to this one yet ?
> By the way, I think you also mean, you have a supply of water, and also something that you can pour water into to get rid of it, even it's just the ground.



Yup 
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## TinaP

sandeep.warrier said:


> *[FONT=&quot]A man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "Twelve." The member replied, "Six" and was let in. A second member came to the door and the doorman said, "Six." The member replied, "Three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said, "Ten" and the man replied, "Five". But he was not let in. What should he have said and why?[/FONT]*


 
Three, but I'm not saying why since I'm the first to reply to this one.  Unlike the very first brain teaser, when I blurted out the answer.


----------



## Lewiy

I agree with "three" but I'll keep that quiet too!!


----------



## schielrn

TinaP said:


> Three, but I'm not saying why since I'm the first to reply to this one. Unlike the very first brain teaser, when I blurted out the answer.


Ah I get it, but it took me about 5 minutes or so to figure it out. 

I'm still trying to figure out the 2nd one and even google hasn't been any help at this point.


----------



## Bruno_x

sandeep.warrier said:


> A man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "Twelve." The member replied, "Six" and was let in. A second member came to the door and the doorman said, "Six." The member replied, "Three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said, "Ten" and the man replied, "Five". But he was not let in. What should he have said and why?



definitely three, and if the doorman said three, the answer had to be five... 



sandeep.warrier said:


> You have to measure exactly 4 liters of water, but you only have a 3-liter bottle and a 5-liter bottle. How do you do it?


@schielrn : look at the formula below and "translate" it in handling the bottles...
= 3+ ((3+3)-5)

the answer for the brain teaser of tgthtrotih (the one with WET and SPILL) : i don't know 

There are nine identical-looking balls, but one is either heavier or lighter than the other eight. How can you determine which is the odd ball and find out whether this ball is heavier or lighter than the others using only two weighings with a balance?


----------



## schielrn

Bruno said:


> the answer for the brain teaser of tgthtrotih (the one with WET and SPILL) : i don't know


 Thats the one I meant I still didn't know the answer to.


----------



## Oorang

Fill up the 5 liter bottle. Use the 5 liter bottle to fill up the 3 liter bottle. What is left in the 5 liter bottle is  2 liters. Dump out the the 3 liter bottle and pour the 2 liters into the 3 liter bottle. Now fill up the 3 liter bottle. Use the 3 liter bottle to finish filling up the 3 liter bottle. As it will only take 1 liter to finish filling up the 3 liter bottle what will remain in the 5 liter bottle will be 4 liters.


----------



## Excelestial

My first thought was pull the plug as well.  But...I do know that bailing out water with a bucket is likely to empty the tub quicker than the little 1" diameter drain hole.  

Liken that to the story of the semi truck getting stuck under a bridge.  All the town's engineer's couldn't figure a way to get the truck unstuck.  Along comes a little 7-year old girl who simply offers..."let the air out the tires."  

It was so appointed.


----------



## jgthtrotih

Hi to Everyone,

Sandeep to your answer of a 3-D "C" you actually you are partially correct..i will post the answer at 3pm (PST) about 2 hours from now..i just want to get more people to guess with mine. Sandeep is the first so i just need 2 more people...P.M me if you want hints.

Thanks!


----------



## Excelestial

Use the 3 liter bottle to finish filling up the 3 liter bottle?  hmmmm...


----------



## Excelestial

1. Fill up 5-liter
2. empty into 3-liter...leaves 2-liters in 5L bottle
3. Pour out 5L...half the 2Liter is measured.
4. Repeat steps 1-3...the other half of 2Liter is measured...4 liters measured.

Measured in what?  You didn't ask.  lol


----------



## Excelestial

Oh and the answer is 3 for the answer to the doorman.  Twelve = 6 letters, Six = 3 letters...Ten = 3 letters.


----------



## RobMatthews

Two spills make a sea/"C" of wet?
28 WET TO SPILL 40 WET...
I got nothin. 



jgthtrotih said:


> HI,
> 
> i have one...
> 
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> SPILL SPILL
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> WET WET WET WET
> 
> 
> Thanks!


----------



## jgthtrotih

Hi All,

I know i said i would post the answer at 3pm..for mine (sorry i havent)...but you guys are soo close!!..i WILL post the answer at 9pm (PST) 2 1/2 hours from now...someone gotta know it!

RobMatthews yours is the closest.

Thanks!


----------



## Sandeep Warrier

Oorang said:


> ... Now fill up the 3 liter bottle. Use the 3 liter bottle to finish filling up the 3 liter bottle. .....



I think u mean fill the 5 liter bottle and use that to fill the 3 liter bottle.... 
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Scott Huish

> You have to measure exactly 4 liters of water, but you only have a 3-liter bottle and a 5-liter bottle. How do you do it?



Fill both bottles 1/2 full.


----------



## Sandeep Warrier

HOTPEPPER said:


> Fill both bottles 1/2 full.



No markings on the bottles 
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Excelestial

Got it...at nearly 2 in the morning...when the brain is lazy.

1.  fill up 3L bottle....empty into 5L bottle
2.  refill 3L bottle...empty into 5L bottle again...will leave 1L in 3L bottle
3.  empty 5L bottle
4.  Pour the 1L left in the 3L bottle into the 5L bottle...1L is now in the 5L bottle
5.  refill 3L bottle...pour the 3Liters into the 5L bottle which already has 1L in it
6.  3L + 1L = 4L

Say it ain't so!


----------



## Excelestial

Two...something...in the sea (c)....


----------



## Sandeep Warrier

Bruno said:


> .............
> There are nine identical-looking balls, but one is either heavier or lighter than the other eight. How can you determine which is the odd ball and find out whether this ball is heavier or lighter than the others using only two weighings with a balance?



Divide the nine balls into 3 sets of 3 balls each. Lets call them A, B & C.

Using the weighing scale compare the weights of A & B.

Two outcomes are possible:

1. The heavier ball is present in one of the sets and hence that set will tip. Once we have identified the set which contains the heavier ball, compare 2 balls from the set. Either one of the 2 is the heavier one... or the 3rd one is.

2. Both A & B have the same weight and hence the scales don't tip. So now we know that the heavier ball is in the 3rd set (C). Compare two balls from C like we did in point 1 and either one of the 2 is heavy or the remaining one is heavy.


<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Sandeep Warrier

A set of very simple - but at times confusing - questions.

<!--[if !supportLists]-->1.Some months have 30 days, some months have 31 days. How many months have 28 days?<!--[endif]-->
  <!--[if !supportLists]-->2.If a doctor gives you 3 pills and tells you to take one pill every half hour, how long would it be before all the pills had been taken?<!--[endif]-->
  <!--[if !supportLists]-->3.I went to bed at eight 8 o’clock in the evening and wound up my clock and set the alarm to sound at nine 9 o’clock in the morning. How many hours sleep would I get before being awoken by the alarm?<!--[endif]-->
  <!--[if !supportLists]-->4.Divide 30 by half and add ten. What do you get?<!--[endif]-->
  <!--[if !supportLists]-->5.A farmer had 17 sheep. All but 9 died. How many live sheep were left?<!--[endif]-->
  <!--[if !supportLists]-->6.If you had only one match and entered a COLD and DARK room, where there was an oil heater, an oil lamp and a candle, which would you light first?<!--[endif]-->
  <!--[if !supportLists]-->7.Take 2 apples from 3 apples. What do you have?<!--[endif]-->
  <!--[if !supportLists]-->8.How many animals of each species did Moses take with him in the Ark ?<!--[endif]-->
  <!--[if !supportLists]-->9.If you drove a bus with 43 people on board from Chicago and stopped at Pittsburgh to pick up 7more people and drop off 5 passengers and at Cleveland to drop off 8 passengers and pick up 4 more and eventually arrive at Philadelphia 20 hours later,What is the name of the driver?<!--[endif]-->
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Excelestial

1. all months have 28 days
2. 1.5 hours seems tooooooo...logical
3. 13 hours
4. 12
5. 9
6. the match
7. 2 apples
8. 2
9. <insert my name here>


----------



## Excelestial

9. --insert my name here--


----------



## Bruno_x

two spills changes wet into a sea  ?


----------



## Excelestial

Some...blank...in a big wet sea?

i see "a big wet c."  lol

two spills in a big wet sea?

I give already.


----------



## Sandeep Warrier

Excelestial said:


> 1. all months have 28 days
> 2. 1.5 hours seems tooooooo...logical
> 3. 13 hours
> 4. 12
> 5. 9
> 6. the match
> 7. 2 apples
> 8. 2
> 9. <insert my="" name="" here="">



You got 5 correct and 4 wrong... 
</insert><input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Andrew Fergus

sandeep.warrier said:


> You got 5 correct and 4 wrong...
> <input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


2 = 1 hour
3 = not possible to set a wind up clock for '9 in the morning' - so would be woken after 1 hour if you went to sleep at 8.
4 = 70
8 = trick question, none


----------



## Excelestial

hahahaha...ooooooohhhhh...it wasn't Moses.  Yanno...I think I heard that one before.


----------



## Excelestial

OOoohhhh.,....30/(1/2)...multiply by 2 to cancel the fraction = 30*2 = 60 + 10 = 70.  What kind of math did I do originally???  lol


----------



## Excelestial

My wind-up clock says there's a 9am!  0900!!


----------



## Excelestial

Okay...#2 question was lame.  Throw that one out.


----------



## Gerald Higgins

sandeep.warrier said:


> Divide the nine balls into 3 sets of 3 balls each. Lets call them A, B & C.
> 
> Using the weighing scale compare the weights of A & B.
> 
> Two outcomes are possible:
> 
> 1. The heavier ball is present in one of the sets and hence that set will tip. Once we have identified the set which contains the heavier ball, compare 2 balls from the set. Either one of the 2 is the heavier one... or the 3rd one is.
> 
> 2. Both A & B have the same weight and hence the scales don't tip. So now we know that the heavier ball is in the 3rd set (C). Compare two balls from C like we did in point 1 and either one of the 2 is heavy or the remaining one is heavy.


 
I THINK this approach is only guaranteed to work if you know the odd ball is heavier. But the original question says it COULD be lighter.
So three outcomes are possible from the first task.
1) Both A and B have the same weight, and therefore the odd ball is in C.
2) The odd ball is heavier, and in A or B
3) The odd ball is lighter, and in A or B.
I don't see how you can resolve this with a single additional weighing.
I suspect the question has been asked wrongly, it should have said, one ball is definitely heavier.

There is a similar problem about 10 balls, one of which is heavier OR lighter, and you have 3 weighings to find it. This is do-able.


----------



## Sandeep Warrier

Excelestial said:


> Okay...#2 question was lame.  Throw that one out.



Lame yes... but perfectly logical 



Gerald Higgins said:


> I THINK this approach is only guaranteed to work if you know the odd ball is heavier. But the original question says it COULD be lighter.



lol... once again I attempt to solve stuff without reading it completely


----------



## Scott Huish

7. 3 apples (presumably you still have the other apple)


----------



## jgthtrotih

Hi,

Originally Posted (#25) By RobMatthews:


> Two spills make a sea/"C" of wet?
> 28 WET TO SPILL 40 WET...
> I got nothin.


You Are Correct!..Well there are many different answers for this one...

Mine Was: "Its Wet Around The Spill"

Thanks!


----------



## steve case

If my rooster lays an egg in your back yard, whose egg is it?


----------



## barry houdini

Who cares, call the papers, you've got an egg-laying rooster.......


----------



## jgthtrotih

What are the next two letters in this sequence?


         O T T F F S S E ==?== ==?== 


Thanks!​


----------



## Andrew Fergus

E & o......?


----------



## barry houdini

jgthtrotih said:


> What are the next two letters in this sequence?​
> 
> 
> O T T F F S S E ==?== ==?==​
> 
> Thanks!​


 
N and T


----------



## jgthtrotih

Barry,

Your Good lol......where were you on my other teaser?

Thanks!


----------



## Sandeep Warrier

1) 54 C in a P (I J)
2) 2 F in a M
3) 2 F M in a M is a B M


----------



## Greg Truby

For Sandeep's latest, I believe that's
54 cards in a pack (or deck in America) (including jokers)
2 fortnights in a month, and
2 full moons in a month is a blue moon.


----------



## jgthtrotih

Read each line aloud without making any mistakes. If you make a mistake you MUST start again without going any further.

This is this puzzle
This is is puzzle
This is how puzzle
This is to puzzle
This is keep puzzle
This is an puzzle
This is idiot puzzle
This is busy puzzle
This is for puzzle
This is forty puzzle
This is seconds! puzzle

Thanks!


----------



## RobMatthews

i got emailed a huge list of things like Sandeep's the other day... (in an excel sheet, of course...)

<TABLE style="WIDTH: 150pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=200 border=0 x:str><COLGROUP><COL style="WIDTH: 150pt; mso-width-source: userset; mso-width-alt: 7314" width=200><TBODY><TR style="HEIGHT: 12.75pt" height=17><TD class=xl25 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: #d4d0c8; BORDER-LEFT: windowtext 0.5pt solid; WIDTH: 150pt; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" width=200 height=17>24 H in a D</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>26 L of the A</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>7 D of the W</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>7 W of the W</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>12 S of the Z</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>66 B of the B</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>52 C in a P (WJs)</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>13 S in the USF</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>18 H on a G C</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>39 B of the O T</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>5 T on a F</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>90 D in a R A</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>3 B M (S H T R)</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>32 is the T in D F at which W F</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>15 P in a R T</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>3 W on a T</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>100 C in a R</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>11 P in a F (S) T</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>12 M in a Y</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>13=UFS</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>8 T on a O</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>29 D in F in a L Y</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>27 B in the N T</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>365 D in a Y</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>13 L in a B D</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>52 W in a Y</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>9 L of a C</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>60 M in a H</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>23 P of C in the H B</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>64 S on a C B</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>9 P in S A</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>6 B to an O in C</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>1000 Y in a M</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl24 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>15 M on a D M C</TD></TR></TBODY></TABLE>


----------



## Sandeep Warrier

Excel WorkbookAB124 H in a D24 Hours in a Day226 L of the A26 Letters of the Alphabet37 D of the W7 Days of the Week47 W of the W7 Wonders of the World512 S of the Z12 Signs of the Zodiac666 B of the B752 C in a P (WJs)52 Cards in a Pack (Without Jokers)813 S in the USF13 Stripes in the United States Flag918 H on a G C1039 B of the O T39 Books of the Old Testament115 T on a F5 Toes on a Foot1290 D in a R A90 Degrees in a Right Angle133 B M (S H T R)1432 is the T in D F at which W F1515 P in a R T163 W on a T17100 C in a R1811 P in a F (S) T1912 M in a Y12 Months in a Year2013=UFS218 T on a O2229 D in F in a L Y29 Days in February in a Leap Year2327 B in the N T27 Books in the New Testament24365 D in a Y365 Days in a Year2513 L in a B D2652 W in a Y52 Weeks in a Year279 L of a C9 Lives of a Cat2860 M in a H60 Minutes in a Hour2923 P of C in the H B3064 S on a C B319 P in S A326 B to an O in C331000 Y in a M1000 Years in a Millennium3415 M on a D M CSheet1*Excel 2003*


----------



## Scott Huish

Got a few more of them:

Excel WorkbookAB124 H in a D24 Hours in a Day226 L of the A26 Letters of the Alphabet37 D of the W7 Days of the Week47 W of the W7 Wonders of the World512 S of the Z12 Signs of the Zodiac666 B of the B66 Books of the Bible752 C in a P (WJs)52 Cards in a Pack (Without Jokers)813 S in the USF13 Stripes in the US Flag918 H on a G C18 Holes on a Golf Course1039 B of the O T39 Books of the Old Testament115 T on a F5 Toes on a foot1290 D in a R A90 Degrees in a Right Angle133 B M (S H T R)3 Blind Mice (See How They Run)1432 is the T in D F at which W F32 is the Temperature in Degrees Fahrenheit at which Water Freezes1515 P in a R T163 W on a T17100 C in a R1811 P in a F (S) T1912 M in a Y12 Months in a Year2013=UFS218 T on a O8 Tentacles on a Octopus2229 D in F in a L Y29 Days in February in a Leap Year2327 B in the N T27 Books in the New Testament24365 D in a Y365 Days in a Year2513 L in a B D13 Loaves in a Bakers Dozen2652 W in a Y52 Weeks in a Year279 L of a C9 Lives of a Cat2860 M in a H60 Minutes in a Hour2923 P of C in the H B3064 S on a C B319 P in S A326 B to an O in C331000 Y in a M1000 Years in a Millenium3415 M on a D M C15 Men on a Dead Man's ChestSheet1


----------



## Sandeep Warrier

Some More....Excel WorkbookAB124 H in a D24 Hours in a Day226 L of the A26 Letters of the Alphabet37 D of the W7 Days of the Week47 W of the W7 Wonders of the World512 S of the Z12 Signs of the Zodiac666 B of the B66 Books of the Bible752 C in a P (WJs)52 Cards in a Pack (Without Jokers)813 S in the USF13 Stripes in the US Flag918 H on a G C18 Holes on a Golf Course1039 B of the O T39 Books of the Old Testament115 T on a F5 Toes on a Foot1290 D in a R A90 Degrees in a Right Angle133 B M (S H T R)3 Blind Mice (See How They Run)1432 is the T in D F at which W F32 is the Temperature in Degree Farenheit at which Water Freezes1515 P in a R T163 W on a T17100 C in a R1811 P in a F (S) T1912 M in a Y12 Months in a Year2013=UFS13 Unlucky For Some218 T on a O8 Tentacles on a Octopus2229 D in F in a L Y29 Days in February in a Leap Year2327 B in the N T27 Books in the New Testament24365 D in a Y365 Days in a Year2513 L in a B D13 Loaves in a Bakers Dozen2652 W in a Y52 Weeks in a Year279 L of a C9 Lives of a Cat2860 M in a H60 Minutes in an Hour2923 P of C in the H B23 Pairs of Chromosomes in the Human Body3064 S on a C B64 Squares on a Chess Board319 P in S A9 Provinces in South Africa326 B to an O in C6 Balls to an Over in Cricket331000 Y in a M1000 Years in a Millennium3415 M on a D M C15 Men on a Dead Man's ChestSheet1*Excel 2003*<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## litrelord

Nearly There...Excel WorkbookAB124 H in a D24 Hours in a Day226 L of the A26 Letters of the Alphabet37 D of the W7 Days of the Week47 W of the W7 Wonders of the World512 S of the Z12 Signs of the Zodiac666 B of the B66 Books of the Bible752 C in a P (WJs)52 Cards in a Pack (Without Jokers)813 S in the USF13 Stripes in the US Flag918 H on a G C18 Holes on a Golf Course1039 B of the O T39 Books of the Old Testament115 T on a F5 Toes on a Foot1290 D in a R A90 Degrees in a Right Angle133 B M (S H T R)3 Blind Mice (See How They Run)1432 is the T in D F at which W F32 is the Temperature in Degree Farenheit at which Water Freezes1515 P in a R T15 Players In A Rugby Team163 W on a T3 Wheels On A Trike17100 C in a R1811 P in a F (S) T11 Players In A Football (Soccer) Team1912 M in a Y12 Months in a Year2013=UFS13 Unlucky For Some218 T on a O8 Tentacles on a Octopus2229 D in F in a L Y29 Days in February in a Leap Year2327 B in the N T27 Books in the New Testament24365 D in a Y365 Days in a Year2513 L in a B D13 Loaves in a Bakers Dozen2652 W in a Y52 Weeks in a Year279 L of a C9 Lives of a Cat2860 M in a H60 Minutes in an Hour2923 P of C in the H B23 Pairs of Chromosomes in the Human Body3064 S on a C B64 Squares on a Chess Board319 P in S A9 Provinces in South Africa326 B to an O in C6 Balls to an Over in Cricket331000 Y in a M1000 Years in a Millennium3415 M on a D M C15 Men on a Dead Man's ChestSheet



Nick


----------



## Scott Huish

I looked the last one up:

It means 100 Cents in a Rand

A Rand is South African money and 1 Rand is equal to 100 cents.

I also saw answers of 100 cents in a row but this doesn't make any sense to me. I think the first answer is correct.

http://www.google.com/search?q=define%3Arand


----------



## sanrv1f

sandeep.warrier said:


> A set of very simple - but at times confusing - questions.
> 
> <!--[if !supportLists]-->1.Some months have 30 days, some months have 31 days. How many months have 28 days?<!--[endif]-->
> <!--[if !supportLists]-->2.If a doctor gives you 3 pills and tells you to take one pill every half hour, how long would it be before all the pills had been taken?<!--[endif]-->
> <!--[if !supportLists]-->3.I went to bed at eight 8 o’clock in the evening and wound up my clock and set the alarm to sound at nine 9 o’clock in the morning. How many hours sleep would I get before being awoken by the alarm?<!--[endif]-->
> <!--[if !supportLists]-->4.Divide 30 by half and add ten. What do you get?<!--[endif]-->
> <!--[if !supportLists]-->5.A farmer had 17 sheep. All but 9 died. How many live sheep were left?<!--[endif]-->
> <!--[if !supportLists]-->6.If you had only one match and entered a COLD and DARK room, where there was an oil heater, an oil lamp and a candle, which would you light first?<!--[endif]-->
> <!--[if !supportLists]-->7.Take 2 apples from 3 apples. What do you have?<!--[endif]-->
> <!--[if !supportLists]-->8.How many animals of each species did Moses take with him in the Ark ?<!--[endif]-->
> <!--[if !supportLists]-->9.If you drove a bus with 43 people on board from Chicago and stopped at Pittsburgh to pick up 7more people and drop off 5 passengers and at Cleveland to drop off 8 passengers and pick up 4 more and eventually arrive at Philadelphia 20 hours later,What is the name of the driver?<!--[endif]-->
> <input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">



1. 12
2. 1 Hr
3. 1 Hr
4. 70
5. 9
6. The Match
7. 2
8. None
9. Sankar


----------



## Sandeep Warrier

This may not be in the category of a brain teaser..... but one of the worst questions/jokes you'll ever hear.... 

Why did the scientist remove the bell from his home?


----------



## jgthtrotih

Sandeep?

to win the no-bell prize? lol

Thanks!


----------



## Sandeep Warrier

jgthtrotih said:


> Sandeep?
> 
> to win the no-bell prize? lol
> 
> Thanks!


----------



## Nalani

This riddle must be done *IN YOUR HEAD* and *NOT* using paper and a pen.

Take 1000 and add 40 to it. Now add another 1000.

Now add 30. And another 1000.

Now add 20. Now add another 1000. Now add 10.

What is the total?


----------



## Excelestial

Wow.  Brainiac sense of humor.  I stand outside...and look at myself.

And smh.  lol


----------



## Scott Huish

4100


----------



## Nalani

HOTPEPPER said:


> 4100


 
Was that on the first attempt?

Most people get 5000


----------



## Excelestial

I was waiting for the punch line myself.  Thought  maybe there was a mystery number in there or something.  I got 4100 also.


----------



## Scott Huish

Yes, that was on the first attempt and did it 4x in my head again in case I was missing something.


----------



## Scott Huish

What are the next two lines in this sequence:

Excel WorkbookFGHIJK111221312114111221Sheet1


----------



## schielrn

I just saw this one in an e-mail the other day and it took me a minute to figure it out, but I finally saw the pattern, but I will wait to answer.


----------



## Oaktree

Erik solved that 2 years ago 

(spoiler alert)

http://www.mrexcel.com/forum/showthread.php?t=256047&page=2


----------



## Scott Huish

OK, how about this one?

A man is trapped in a room. The room has only two possible exits: two doors. Through the first door there is a room constructed from magnifying glass. The blazing hot sun instantly fries anything or anyone that enters. Through the second door there is a fire-breathing dragon. How does the man escape?


----------



## PaddyD

Wait until nightfall, leave via first door whilst muttering to oneself that jailers aren't what they used to be.


----------



## Marbles

Leave at night?


----------



## Marbles

Another two doors.

Stuck in a room with two doors, each with a guard.  One door leads to freedom, one to death.  You're allowed to ask one question only, to find the right door.  One guard will always tell the truth to your question, the other will always lie.  What do you ask?


----------



## TinaP

Yoo hoo, Guard...  Are you a liar?


----------



## Scott Huish

Bill bets Craig $100 that he can predict the score of the hockey game before it starts. Craig agrees, but loses the bet. Why did Craig lose the bet?


----------



## Oorang

Because Bill was able to predict the score of the hockey game.

Alas Craig shouldn't be betting on tivo'd games.


----------



## Scott Huish

Um.. no


----------



## Oorang

TinaP said:


> Yoo hoo, Guard...  Are you a liar?


That won't work, the lying guard is a liar and will lie, so he/she will say "No I am not a liar." The truth telling guard is not a liar and will tell the truth, so he/she will say "No I am not a liar." This doesn't tell you anything. 

When you boil this problem down, the trick is to come up with a question that you know the answer to. Try this: "Pardon me, but are you a guard?"

http://en.wikipedia.org/wiki/Liar_paradox


----------



## Oorang

@HP. Did I make any statement that was contradicted by the question?


----------



## Scott Huish

Yes. If the game was Tivo'd, the game would've already been played and therefore started.


----------



## PaddyD

re the guards, ask either guard which door the other would suggest you walk through, then pick the other one.


----------



## Oorang

@PaddyD That's more in the spirit of the question (and I think the "Classical" answer). The funny thing is, the question lets you live but you never know who's lying. My way tells you whose lying, but you still have to take your chances with the doors (only 1 question). So I have to admit, my answer is inferior. *sigh*

@HP I was just joking about the Tivo bit. But the way the question is phrased it sounds like a literal answer is what you were looking for. Are you actually asking, "How was Bill able to make the prediction?"


----------



## schielrn

HOTPEPPER said:


> Bill bets Craig $100 that he can predict the score of the hockey game before it starts. Craig agrees, but loses the bet. Why did Craig lose the bet?


Bill predicts 0 to 0, because the score of the hockey game is 0 to 0 before it starts.


----------



## PaddyD

"Bill predicts 0 to 0, because the score of the hockey game is 0 to 0 before it starts"

If this is the 'right' answer, then I object on existential grounds  Before the game starts, there is no score.  0:0  is, as it were, the positive absence of any goals during the game.


----------



## Oorang

lol I also object... On the grounds that 0 ≠ Null


----------



## schielrn

PaddyD said:


> "Bill predicts 0 to 0, because the score of the hockey game is 0 to 0 before it starts"
> 
> If this is the 'right' answer, then I object on existential grounds  Before the game starts, there is no score. 0:0 is, as it were, the positive absence of any goals during the game.


But before the game what score do they show on the scoreboard.   I don't typically see Null to Null in the scoreboard.


----------



## Scott Huish

"Bill predicts 0 to 0, because the score of the hockey game is 0 to 0 before it starts"

That is the correct answer.


----------



## GorD

You have a room with one light and 3 switches outside the room - one of which operates the light.

You can't see into the room at all and the door is closed. You are only allowed to enter/look into the room once.

How can you tell (without any doubt) which switch operates the light?


----------



## schielrn

You close your eyes and open the door. You have not entered or looked in the room at this point. Then you leave the door open. You then look into the room and flip each of the switches to see which one turns on the light.


----------



## mattrx731

> You have a room with one light and 3 switches outside the room - one of which operates the light.
> 
> You can't see into the room at all and the door is closed. You are only allowed to enter/look into the room once.
> 
> How can you tell (without any doubt) which switch operates the light?


 
Leave switch 1 off, turn the other two on.  Wait 5 minutes, turn off switch 2, enter room.  If the light is on, it's switch 3, if the bulb is hot, but not on, it's switch 2, if the bulb is cold, it's switch 1.


----------



## Scott Huish

Why is half of 5 equal to 4?


----------



## GorD

mattrx731 said:


> Leave switch 1 off, turn the other two on.  Wait 5 minutes, turn off switch 2, enter room.  If the light is on, it's switch 3, if the bulb is hot, but not on, it's switch 2, if the bulb is cold, it's switch 1.



Correct - or you can do it with switching on one switch and waiting a few minutes also


----------



## GorD

schielrn said:


> You close your eyes and open the door. You have not entered or looked in the room at this point. Then you leave the door open. You then look into the room and flip each of the switches to see which one turns on the light.




Good try- but no


----------



## schielrn

GorD said:


> Correct - or you can do it with switching on one switch and waiting a few minutes also


What was wrong with my answer, I followed the rules?   How can you do it by only switching on one switch?


----------



## GorD

I meant switching on one switch ( rather than 2 initially) then waiting a few minutes - then turn that switch off and switch 2 on - same result

"You can't see into the room at all" - it was that bit you fouled up on


----------



## Sandeep Warrier

HOTPEPPER said:


> Why is half of 5 equal to 4?



5 => FIVE => 4 Letters

Half of 5 => Half of 4 Letters => 2 Letters.

Removing 2 Letters from FIVE => IV => 4 in Roman Numerals..
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Sandeep Warrier

1. What does a 6'3" butcher weigh?
2. I live above a star but never burn I have 11 neighbours they dont turn. My initials are P, Q, R and sometimes S Who am i 
3. How will you remove a crumpled paper inside an empty glass without holding the glass and the crumpled paper inside the empty glass?
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## schielrn

1. Meat
2. The 7 key on a phone
3. Add water to make the paper overflow or disintegrate or drop a match in the glass???


----------



## Sandeep Warrier

schielrn said:


> 3. Add water to make the paper overflow or disintegrate or drop a match in the glass???



Crumpled paper in _*empty glass*_.... kinda contradictory, don't you think 
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## schielrn

sandeep.warrier said:


> Crumpled paper in _*empty glass*_.... kinda contradictory, don't you think


 I didn't even pick that up.  Many, I guess that is what I get for trying to look at Brain Teasers at 630 in the morning.


----------



## Expiry

Surely having a crumpled paper in an empty glass in the first place is contradictory.

You could get someone else to pull it out.


----------



## Gettingbetter

Since we all love Excel on here I thought I would put a brain teaser on that involves grids (you will probably end up drawing it in Excel anyway ha ha)

You have a 5 by 5 grid

You have to fit 5 Dogs and 3 cats into this grid

Imagine that the Dogs can move like a queen on a chess board,

Heres the puzzle, you have to position all 8 (5 Dogs and 3 Cats) onto the 5 by 5 grid so that all of the Cats are safe.

No tricks or anything like that, just pure logic! and it can be done many diff ways but is remarkably difficult.


----------



## schielrn

I figured it out.  Took me a couple minutes, but was able to get it on the 2nd try.


----------



## schielrn

This was one way I went about it, but as stated it could be done a number of ways:

<TABLE style="WIDTH: 115pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=150 border=0><COLGROUP><COL style="WIDTH: 23pt" span=5 width=30><TBODY><TR style="HEIGHT: 15pt" height=20><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; WIDTH: 23pt; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" width=30 height=20>dog</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 23pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" width=30></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 23pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" width=30></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 23pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" width=30></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 23pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" width=30></TD></TR><TR style="HEIGHT: 15pt" height=20><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" height=20>dog</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">dog</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" height=20></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">cat</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">cat</TD></TR><TR style="HEIGHT: 15pt" height=20><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" height=20></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">cat</TD></TR><TR style="HEIGHT: 15pt" height=20><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" height=20>dog</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">dog</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD></TR></TBODY></TABLE>

Actually I just realized that is wrong.  Back to the spreadhseet.


----------



## Gettingbetter

Second try....!! That impresive, it took me ages, I became very adapt at drawing 5 by 5 grids and almost ran out of post-its..

Well Done !!


----------



## schielrn

Actually see my new post.   I'm up to attempt 6 right now.


----------



## Scott Huish

You put more than 1 dog in the same cell:

Excel WorkbookABCDE1dog/dogdog23catcat4cat5dogdogSheet1


----------



## Oaktree

Nice puzzle!  Took a few attempts:

Book3ABCDE1dogdog2cat3dog4dogdog5catcatSheet1


----------



## jgthtrotih

Hi,

Pronounced differently      but spelled the same
I have many meanings      from obscure to mundane 
In a trip across water      I get there before you
In precipitation      amazing, a marvel to awe you
One naming of me means      to acknowledge the praise
I move fastest in music      as the violin maestro plays
Taught to children of      all ages , or trip up they would
                                   I was also much      favoured by a notorious Hood.

Thanks!


----------



## Sandeep Warrier

jgthtrotih said:


> Hi,
> 
> Pronounced differently      but spelled the same
> I have many meanings      from obscure to mundane
> In a trip across water      I get there before you
> In precipitation      amazing, a marvel to awe you
> One naming of me means      to acknowledge the praise
> I move fastest in music      as the violin maestro plays
> Taught to children of      all ages , or trip up they would
> I was also much      favoured by a notorious Hood.
> 
> Thanks!



I guess Bow.... the only thing i felt matched 

 Pronounced differently      but spelled the same - Bow (as in cow) and Bow (as in toe),
I move fastest in music      as the violin maestro plays
and
I was also much      favoured by a notorious Hood. 

Not very sure on how it fits the others....
 <input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## jgthtrotih

sandeep.warrier said:


> I guess Bow.... the only thing i felt matched
> 
> Pronounced differently      but spelled the same - Bow (as in cow) and Bow (as in toe),
> I move fastest in music      as the violin maestro plays
> and
> I was also much      favoured by a notorious Hood.
> 
> Not very sure on how it fits the others....
> <input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">



Bow is right.


----------



## Gettingbetter

Well done OakTree!!! Unlucky Hotpepper (I did mention no tricks etc..just logic).

I will add another,

Two guys are sat at a table both with apples in front of them.

The first guy turns to the second and says
  "If you give me one of your apples I will have twice as many apples as you"
The second guy replies, 
  "yeah but if you give me one of your apples we will have the same amount of apples"


How many apples did they both originally have??

Once again no tricks or half apples or bites of apples or anything daft like that (Apples is just a variant and so could have been pins/dogs/unbrellas doesnt mean anything)

Just logic (for those who used to like difficult simultaneous equations)


----------



## Sandeep Warrier

Gettingbetter said:


> Well done OakTree!!! Unlucky Hotpepper (I did mention no tricks etc..just logic).
> 
> I will add another,
> 
> Two guys are sat at a table both with apples in front of them.
> 
> The first guy turns to the second and says
> "If you give me one of your apples I will have twice as many apples as you"
> The second guy replies,
> "yeah but if you give me one of your apples we will have the same amount of apples"
> 
> 
> How many apples did they both originally have??
> 
> Once again no tricks or half apples or bites of apples or anything daft like that (Apples is just a variant and so could have been pins/dogs/unbrellas doesnt mean anything)
> 
> Just logic (for those who used to like difficult simultaneous equations)



1st guy has 3 apples and the 2nd has 2.

If the 1st guy had 1 apple from the 2nd then his total would be 4 which is double of what the 2nd guy has. Similarly if the 2nd guy got 1 from the 1st, his total would be 3 which is the same as the 1st guy...
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Sandeep Warrier

Another possible answer....

Guy1: 7
Guy2: 5

Guy1 gets 1 apple from Guy2 =>
Guy1: 8
Guy2: 4
=> Guy1's total is twice Guy2's remaining apples.

Guy2 gets 1 apple from Guy1 =>
Guy1: 6
Guy2: 6
=> Guy2's total is same as Guy1's remaining apples.
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Gettingbetter

Sandeep your first answer was well off but congrats with your second. Well Done!!!

You guys are too good on here!!


----------



## Gettingbetter

Last one from me,

what comes next

F, E, V, I, F, T, D, W


ha ha you should all get this!!!


----------



## Sandeep Warrier

Gettingbetter said:


> Sandeep your first answer was well off but congrats with your second. Well Done!!!
> 
> You guys are too good on here!!



The 1st answer was the 1st thing that came into my mind when I read the problem.... 

The 2nd answer was after i re-read it a couple of times..... 

I wish at times for second chances at long gone college exams


----------



## Scott Huish

> Last one from me,
> 
> what comes next
> 
> F, E, V, I, F, T, D, W
> 
> 
> ha ha you should all get this!!!



F


----------



## Scott Huish

I know the rest but I can't give you the rest. Those kinds of words would probably be frowned upon on this board.


----------



## Oaktree

Usually H, but sometimes any other letter


----------



## Scott Huish

> Usually H, but sometimes any other letter



Huh?


----------



## Scott Huish

Excel WorkbookAB1F2E3V4I5F6T157D-188W149F10USheet1

If you must, copy the formula in A10, down two more cells. But don't say I didn't warn you.


----------



## Oaktree

LOL... well, that's one way... or you could consider File/Edit/View/etc. in Excel


----------



## Scott Huish

You think that's why it's in the order it's in? LOL


----------



## Oorang

That _is_ why it's in the order it is.


----------



## GorD

I think everbody knows this one

4 hostages being held by an armed guard. 3 are one side of a wall and the other is on the other. Each has had a hat put on their head, there are two blue hats and two red hats. Everyone is facing the wall and can't turn round. The guard says that if anyone can correcly guess the colour of their hat the will all be saved, but if anyone guesses wrongly they will all be killed.
Who shoulld call out their colour to guarantee their safety.


x.................x......................x......................¦......................x


----------



## Scott Huish

Can the person by himself see over the wall?

If so, then he can see what the other three hats are and he should call his own color based on this information.


----------



## GorD

No He can't

As a bit of a clue, the person to call out can be one of two people depending on the circumstance

Also just to clarify in case it wasn't clear, the person furthest from the wall can see the two in front, and the middle person can see the one in front of him


----------



## Oaktree

If the guy farthest from the wall sees two hats of the same color (say, red), he knows his is of the opposite color (blue).

If the guy farthest from the wall hesitates/doesn't say anything, the middle guy would know that he has a different colored hat than the one guy he can see and could speak up accordingly.

Here's one for you (from Seth Godin's blog):

Let's say your goal is to reduce gasoline consumption.

And let's say there are only two kinds of cars in the world. Half of them are Suburbans that get 10 miles to the gallon and half are Priuses that get 50.

If we assume that all the cars drive the same number of miles, which would be a better investment:

(1) Get new tires for all the Suburbans and increase their mileage a bit to 13 miles per gallon.
(2) Replace all the Priuses and rewire them to get 100 miles per gallon (doubling their average!)


----------



## Cindy Ellis

Oaktree said:


> Let's say your goal is to reduce gasoline consumption.
> 
> And let's say there are only two kinds of cars in the world. Half of them are Suburbans that get 10 miles to the gallon and half are Priuses that get 50.
> 
> If we assume that all the cars drive the same number of miles, which would be a better investment:
> 
> (1) Get new tires for all the Suburbans and increase their mileage a bit to 13 miles per gallon.
> (2) Replace all the Priuses and rewire them to get 100 miles per gallon (doubling their average!)


Tires win
For every thousand milles driven by each group, increasing the Suburban mpg by 30% ( 10 mpg to 13 mpg) reduces gas consumption by ~23 gallons, while doubling the mpg of the prius group (50 mpg to 100 mpg) only saves 10 gallons.


----------



## Scott Huish

This question has 2 possible answers.

1. Reducing gasoline consumption

or

2. Reduction Percentage to the vehicles standard MPG

If you go with option 2 then Cindy is correct, but if you go with option 1, then the Prius is still the best investment, because you will reduce gasoline consumption overall.

In other words, while the GMC reduced its gasoline usage by more gallons, it still used way more gasoline than the Prius.

At it's best it uses approximately 76 gallons of gasoline, while the Prius only uses 10. I would go with the Prius.

Excel WorkbookABCD1Miles Driven: 1000234SuburbanGallons UsedPriusGallons Used510 mpg10050 mpg20613 mpg76.92307692100 mpg107Gallons Saved23.08108(Rounded to 2 decimal places)Sheet1


----------



## Scott Huish

Correction, the Suburban used more gasoline overall.


----------



## Cindy Ellis

??
The way I read it, we don't get to change the proportion of cars or the proportion of miles driven (50/50 proportion, and equal miles driven by each), so the best investment for "society" or for a company trying to reduce gasoline consumption would be to do the tire change.
Before any change, 2000 miles driven overall (half by prius and half by suburban) would require 120 gallons of gas.  If we invest in doubling the mpg of prius, with no other change, the same 2000 miles would now require 110 gallons of gas.  On the other hand, if we change the tires on the suburban to magic tires that get 13 mpg instead of 10 mpg, the same 2000 miles requires only ~87 gallons of gas.


----------



## Scott Huish

My example uses the same number of miles for both vehicles: 1000

For the Suburban to travel 1000 miles at 13 mpg, it takes a little less than 77 gallons to do it.

A Prius to travel 1000 miles at 100 mpg, takes 10 gallons.

The car that takes 10 gallons to drive a 1000 miles uses significantly less gasoline than the vehicle that travels at 13 mpg.

Since the goal is to reduce gasoline consumption, the Prius does a better job of this than the Suburban does.

Before any change both vehicles combined used 120 gallons of gas.
After both vehicles were changed, the combined usage of gasoline was approximately 86.92 gallons, the majority of this was used by the Suburban. The Prius only using 10 gallons of it.

You can pick any mileage amount you want as long as they are equal for both vehicles, but proportionately the results will be the same.


----------



## Cindy Ellis

I guess we just read the problem differently.  The way I read it, we were to choose between the two options...either change all of the suburbans' tires to the 13 mpg type, OR modify all of the priuses to use half the gas that they already did, based on which would have the greatest impact on gasoline usage.  
Maybe I misunderstood the original intent.
Cindy


----------



## GorD

I'm with you on this one Cindy - you still have to use both types of car to fulfil the same milage rquirements.

According to the blog the answer is the 10 to 13 mpg change

(I still can't get my head around all this talk of suburbans, prius's gasoline and tires (with an I)


----------



## Gerald Higgins

Surely Cindy is right on this.
Assuming the number of cars, and their mileage, remains constant, then the option that reduces fuel consumption the most, is replacing the tyres.
True, altering the Prius does deliver a larger percentage reduction in consumption for the Prius, but that wasn't an objective in the puzzle as originally stated.

Of course these options ignore the cost of doing these things. How much do new tyres cost, as compared to re-wiring the Prius ?


----------



## Scott Huish

Yes, the Suburban has a greater reduction in gasoline that it uses but that's only because it used so much dang gasoline in the first place.

To round it off:

25% of 100 is more than 50% of 20.

The goal according to the question was to reduce gasoline usage. Since the Prius already did this better to begin with, improving it's gas mileage will reduce gasoline usage more than the gas hogging Suburban.

The Prius saved 80 gallons in the first place, and approxmately 67 gallons after the modification.

67 gallons is a lot of gas to use compared to 20. The Prius is still the best choice rewired or not to reduce gas consumption.


----------



## GorD

I don't think anybodys arguing which is the better car - but if you have 10 employees who all need a car and these are the 10 cars you have (5 of each and all the employees are going to do the same mileage) then changing the 10 mph to 13 will save you more Petrol.

Can't see it any other way


----------



## RobMatthews

GorD said:


> I don't think anybodys arguing which is the better car - but if you have 10 employees who all need a car and these are the 10 cars you have (5 of each and all the employees are going to do the same mileage) then changing the 10 mph to 13 will save you more Petrol.
> 
> Can't see it any other way


Agree.

If you look at your first table, HotPepper, 
Option A (per the question) will use 96.92 gallons. (76.92+20) (Improved 'burban)
Option B uses 110 gallons. (100+10)

(original uses 120 gallons).

Can't get much clearer than that?


----------



## Scott Huish

OK, I see where I went wrong now. Thanks. It's one or the other but you will still have both vehicles. You can't go with all Priuses, which of course would be the better solution.


----------



## pgc01

Gettingbetter said:


> Since we all love Excel on here I thought I would put a brain teaser on that involves grids (you will probably end up drawing it in Excel anyway ha ha)
> 
> You have a 5 by 5 grid
> 
> You have to fit 5 Dogs and 3 cats into this grid
> 
> Imagine that the Dogs can move like a queen on a chess board,
> 
> Heres the puzzle, you have to position all 8 (5 Dogs and 3 Cats) onto the 5 by 5 grid so that all of the Cats are safe.
> 
> No tricks or anything like that, just pure logic! and *it can be done many diff ways* but is remarkably difficult.


 
Hi

Nice puzzle.

I checked the possible solutions and there is fact just one solution, in the sense that all the other ones can be obtained with operations like rotation or simmetry.

I then checked 4 cats and 4 dogs and there is more that one solution. I found one of the solutions very interesting, military like.


----------



## Andrew Fergus

pgc01 said:


> I then checked 4 cats and 4 dogs and there is more that one solution. I found one of the solutions very interesting, military like.


Would that involve each dog occupying a corner square?


----------



## pgc01

Andrew Fergus said:


> Would that involve each dog occupying a corner square?


 
Hi Andrew

Yes, it's like the cat's are back to back, protecting each other and covering all directions. The dogs are atacking from 4 directions at 90 degrees.

On the other hand it could be the dogs playing poker at the center and the cats watching from a respectful distance.

This may be a good idea for one of my next problems. With some flexibility like variable number of cats, dogs and board dimensions.


----------



## Oorang

What the dogs need is a mouse.


----------



## RobMatthews

Oorang said:


> What the dogs need is a mouse.


Either that or the cats need a lion.


----------



## Oorang

My dog's mouse removes a thorn from the paw of your lion. Your lion now has the "loyalty" effect and must make a saving roll to attack.


----------



## BubbaBBQ

Three weary business men arrive at the motel counter at the same time late one night.  Each ask for a room.  The night clerk explains that he only has one room left.  Fortunately, it's a 3 bedroom suite.  He offers them a discount on the room, so tax and all, the room is $ 30.00 for the night. (What a deal!)  Each of the business men put a $ 10 bill on the counter, keys were issued and the bell hop called to assist.

A short while later, the night clerk notices that he didn't calculate the tax correctly and the room should have been $25.00 for the night.  He calls the bell hop over, hands him 5 one dollar bills and sends him to the room to return the money.

On the way to the room, the bell hop is troubled by how the business men were bad tippers and how will he split $5 evenly to 3 men .  To resolve both issues, he puts $2 in his pocket to add to his original tip and gives each man $1 back.

Each man originally paid $10 and less the dollar back means each paid $9.

3 men times $9 = $27 plus the $2 dollar extra tip = $29.00. 

What happen to the other dollar?

Bubba


----------



## Ron Coderre

Nice bit of mis-direction there.
I won't spoil the fun by revealing it.


----------



## Domski

The men paid $9 each = $27. $25 for the room and $2 the bell hop = $27, the $29 is irrelevant.

Or is that too simple?

Dom


----------



## Colin Legg

The men did not pay $9 each, which is the misdirection Ron was referring to.
They paid $25 for the room in total, which is $8.33 each. Then they were each given a dollar back ($9.33 x 3 = $28) and the remaining $2 kept as a tip.


----------



## Colin Legg

5 men of equal weight need to cross a bridge in the fastest time possible.

The bridge is not very sturdy so only 2 men can cross the bridge at the same time.

The men only have 1 torch. It is very dark so the bridge can only be traversed if someone is carrying the torch. The men crossing the bridge must carry the torch (the way cannot be shone by someone holding the torch from either end) and they must stay together during the crossing.

This means that once 2 men have crossed the bridge, the torch has to be taken carried back to the other side to the remaining men otherwise they would not be able to cross. The torch cannot be thrown back (or some other workaround): it must be carried back.

The men have different fitness levels which means that it takes them different amounts of time to cross the bridge:


		Code:
__


Man A       1 minute
Man B       2 minutes
Man C       3 minutes
Man D       5 minutes
Man E       10 minutes

 
So, for example, if Man A and Man E cross the bridge together it would take them 10 minutes because they must stay together.


There are no tricks in this question. They all must cross the bridge (no swimming etc...); it is a straightforward maths problem: what is the quickest way for them to cross the bridge?


----------



## Domski

Colin Legg said:


> The men did not pay $9 each, which is the misdirection Ron was referring to.
> They paid $25 for the room in total, which is $8.33 each. Then they were each given a dollar back ($9.33 x 3 = $28) and the remaining $2 kept as a tip.



That'll teach me for logging on here not having slept for quite some time and slightly worse for it


----------



## crimson_b1ade

I actually agree with Domski. The $30 is actually irrelevant! Why? Because the 3 business men each received back $1. So collectively, their cash outflow is -$27 (-30 original payout + 3 received back = -27 outflow). ($25 to the hotel or $8.33 each, and $2 to the bellhop or $0.67 each for a total of $9 each)


----------



## crimson_b1ade

AE> 10 (10)

<A p 1 (11)<>AD> 5 (16)

<A p 1 (17)<>AC> 3 (20)

AB> 2 (23)

"A" goes back to get everyone else since he's the fastest.

23 minutes. does this work?



Colin Legg said:


> 5 men of equal weight need to cross a bridge in the fastest time possible.
> 
> The bridge is not very sturdy so only 2 men can cross the bridge at the same time.
> 
> The men only have 1 torch. It is very dark so the bridge can only be traversed if someone is carrying the torch. The men crossing the bridge must carry the torch (the way cannot be shone by someone holding the torch from either end) and they must stay together during the crossing.
> 
> This means that once 2 men have crossed the bridge, the torch has to be taken carried back to the other side to the remaining men otherwise they would not be able to cross. The torch cannot be thrown back (or some other workaround): it must be carried back.
> 
> The men have different fitness levels which means that it takes them different amounts of time to cross the bridge:
> 
> 
> Code:
> __
> 
> 
> Man A       1 minute
> Man B       2 minutes
> Man C       3 minutes
> Man D       5 minutes
> Man E       10 minutes
> 
> 
> So, for example, if Man A and Man E cross the bridge together it would take them 10 minutes because they must stay together.
> 
> 
> There are no tricks in this question. They all must cross the bridge (no swimming etc...); it is a straightforward maths problem: what is the quickest way for them to cross the bridge?


----------



## Colin Legg

crimson_b1ade said:


> AE> 10 (10)
> 
> <A (11)< 1 p>AD> 5 (16)
> 
> AC> 3 (20)
> 
> AB> 2 (23)
> 
> "A" goes back to get everyone else since he's the fastest.
> 
> 23 minutes. does this work?


 
That's the right sort of idea and it's a good, logical approach.
However, it is possible to do it in less than 23 minutes.


----------



## Sandeep Warrier

A & B go first => 2 min
B comes back => 2 min
D & E go => 10 min
A comes back => 1 min
A & C go => 3 min
A comes bacl => 1 min
A & B go => 2 min

Total time taken - 2+2+10+1+3+1+2 => 21 min
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Colin Legg

sandeep.warrier said:


> A & B go first => 2 min
> B comes back => 2 min
> D & E go => 10 min
> A comes back => 1 min
> A & C go => 3 min
> A comes bacl => 1 min
> A & B go => 2 min
> 
> Total time taken - 2+2+10+1+3+1+2 => 21 min


That's correct!


----------



## Sandeep Warrier

Colin Legg said:


> That's correct!





I solved a similar puzzle consisting of 4 members a couple of years back... it came in as a flash file complete with 2 kids, a dad and a grumpy old grandpa and a wobbling bridge ...

Good to know I still remembered the logic....
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## litrelord

crimson_b1ade said:


> AE> 10 (10)
> 
> <A p 1 (11)<>AD> 5 (16)
> 
> <A p 1 (17)<>AC> 3 (20)
> 
> AB> 2 (23)
> 
> "A" goes back to get everyone else since he's the fastest.
> 
> 23 minutes. does this work?



This was what I got only you dont' need to add on 1 minute each time for A to get across as he's goign at the same time. This gives 20 mins...

AB   2 Mins
AC   +3 Mins (5 Mins)
AD   +5 Mins (10 Mins)
AE   +10 Mins (20 Mins)

Unless I'm doing something wrong. 

Now is anyone going to post the answer to the 5x5 grid with 5 dogs and 3 cats because I just can't work it out and it's making me feel stupid 

Nick


----------



## Colin Legg

litrelord said:


> This was what I got only you dont' need to add on 1 minute each time for A to get across as he's goign at the same time.


In that solution, each time man A walks over with someone, he has to walk back across the bridge again with the torch to take the next man across. That's where the extra 1 minute on each "crossing" is coming from. 

21 minutes is the fastest.


----------



## litrelord

See, it's no wonder I can't work out the dogs and cats one if I overlook such a simple thing as the return journey.

Must be time for more (or maybe less) coffee!

Nick


----------



## pgc01

Hi all

Another brain teaser.

In a chess board you remove 2 squares at opposite corners (ex. A1 and H8). Is it possible to enter by one of these corners with a rook and leave by the other corner after passing by all the squares in the board?

Remember that a rook only moves either horizontally or vertically.


----------



## Sandeep Warrier

Hi Pedro,

Good question!!!

Tried out some basic combos.... always one square left out....

Excel WorkbookABCDEFGH1Start345678921215141312111031817162324252627419202122313029285363534333243444563738394041424746754535251504948Left Out855565758596061EndSheet1*Excel 2003*



Need to get in more thinking done i guess


----------



## Oaktree

I think the "G" in pgc stands for Gomory.


----------



## pgc01

Oaktree said:


> I think the "G" in pgc stands for Gomory.


 

I had never heard the name so I looked up the google definition:



> Gomory - is a strong and a mighty duchess, she appears as a fair woman, with a duchesses coronet about her middle. Her mount is a camel. ...


 
and I got worried. 

After a quick search I found, however, a match that made much more sense.


----------



## pgc01

sandeep.warrier said:


> Need to get in more thinking done i guess


 
Yes, that's the right direction. 

I didn't know you could find a solution in the web


----------



## DonkeyOte

Can the rook re-trace steps... ?


----------



## pgc01

DonkeyOte said:


> Can the rook re-trace steps... ?


 
Yes.


----------



## Sandeep Warrier

pgc01 said:


> I didn't know you could find a solution in the web



Neither did I.....


If the rook can retrace its steps... then...Excel WorkbookABCDEFGH1Start345678921215141312111031817162324252627419202122313029285363534333243444563738394041424746754535251504948/6263855565758596061EndSheet1*Excel 2003*

ORExcel WorkbookABCDEFGH10Start54/678910111112316151413121220191817262728291321222324253221301438373635343346471539404142434445481656555453525150491757585960616263EndSheet1*Excel 2003*<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## pgc01

I am very sorry Sandeep. I interpreted re-trace as go back the same way, not going back to any square you've been.

I must have been half asleep already when I answered that because it has no sense going back the same way (really dumb ).


So, no, *you are not allowed to re-trace *or else any path would do.


----------



## crimson_b1ade

here's what I have (using sandeep's table format ). I'm assuming that the rook keeps it's jumping abilities since a rook doesn't have to move one square at a time but can actually move several squares at a time. So in the below example, once the rook gets to position 59 it jumps to position 60, then moves back one square then finally down one square:<TABLE style="WIDTH: 164pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=220 border=0 x:str><COLGROUP><COL style="WIDTH: 34pt; mso-width-source: userset; mso-width-alt: 1645" width=45><COL style="WIDTH: 17pt; mso-width-source: userset; mso-width-alt: 841" span=6 width=23><COL style="WIDTH: 28pt; mso-width-source: userset; mso-width-alt: 1353" width=37><TBODY><TR style="HEIGHT: 13.5pt" height=18><TD class=xl22 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black 0.5pt solid; BORDER-LEFT: black 0.5pt solid; WIDTH: 34pt; BORDER-BOTTOM: black 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: white" width=45 height=18>*Start*</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black 1pt solid; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>1</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black 1pt solid; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>2</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black 1pt solid; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>3</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black 1pt solid; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>4</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black 1pt solid; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>5</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black 1pt solid; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>6</TD><TD class=xl25 style="BORDER-RIGHT: #666699 1pt solid; BORDER-TOP: black 1pt solid; BORDER-LEFT: black; WIDTH: 28pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=37 x:num>7</TD></TR><TR style="HEIGHT: 13.5pt" height=18><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black 1pt solid; WIDTH: 34pt; BORDER-BOTTOM: black 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: white" width=45 height=18 x:num>27</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>28</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>29</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>30</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>31</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>32</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>33</TD><TD class=xl25 style="BORDER-RIGHT: #666699 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 28pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=37 x:num>8</TD></TR><TR style="HEIGHT: 13.5pt" height=18><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black 1pt solid; WIDTH: 34pt; BORDER-BOTTOM: black 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: white" width=45 height=18 x:num>26</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>47</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>48</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>49</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>50</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>51</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>34</TD><TD class=xl25 style="BORDER-RIGHT: #666699 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 28pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=37 x:num>9</TD></TR><TR style="HEIGHT: 13.5pt" height=18><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black 1pt solid; WIDTH: 34pt; BORDER-BOTTOM: black 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: white" width=45 height=18 x:num>25</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>46</TD><TD class=xl27 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: yellow" width=23 x:num>59</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>61</TD><TD class=xl27 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: yellow" width=23 x:num>60</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>52</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>35</TD><TD class=xl25 style="BORDER-RIGHT: #666699 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 28pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=37 x:num>10</TD></TR><TR style="HEIGHT: 13.5pt" height=18><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black 1pt solid; WIDTH: 34pt; BORDER-BOTTOM: black 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: white" width=45 height=18 x:num>24</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>45</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>58</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>62</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>54</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>53</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>36</TD><TD class=xl25 style="BORDER-RIGHT: #666699 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 28pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=37 x:num>11</TD></TR><TR style="HEIGHT: 13.5pt" height=18><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black 1pt solid; WIDTH: 34pt; BORDER-BOTTOM: black 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: white" width=45 height=18 x:num>23</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>44</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>57</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>56</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>55</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>38</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>37</TD><TD class=xl25 style="BORDER-RIGHT: #666699 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 28pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=37 x:num>12</TD></TR><TR style="HEIGHT: 13.5pt" height=18><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black 1pt solid; WIDTH: 34pt; BORDER-BOTTOM: black 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: white" width=45 height=18 x:num>22</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>43</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>42</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>41</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>40</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>39</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>14</TD><TD class=xl23 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 28pt; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: white" width=37 x:num>13</TD></TR><TR style="HEIGHT: 13.5pt" height=18><TD class=xl24 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black 1pt solid; WIDTH: 34pt; BORDER-BOTTOM: #666699 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: white" width=45 height=18 x:num>21</TD><TD class=xl24 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: #666699 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>20</TD><TD class=xl24 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: #666699 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>19</TD><TD class=xl24 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: #666699 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>18</TD><TD class=xl24 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: #666699 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>17</TD><TD class=xl24 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: #666699 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>16</TD><TD class=xl24 style="BORDER-RIGHT: black 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 17pt; BORDER-BOTTOM: #666699 1pt solid; BACKGROUND-COLOR: white" width=23 x:num>15</TD><TD class=xl26 style="BORDER-RIGHT: #666699 1pt solid; BORDER-TOP: black; BORDER-LEFT: black; WIDTH: 28pt; BORDER-BOTTOM: #666699 1pt solid; BACKGROUND-COLOR: white" width=37>*End*





sandeep.warrier said:


> Hi Pedro,
> 
> Good question!!!
> 
> Tried out some basic combos.... always one square left out....
> 
> Excel WorkbookABCDEFGH1Start345678921215141312111031817162324252627419202122313029285363534333243444563738394041424746754535251504948Left Out855565758596061EndSheet1*Excel 2003*
> 
> 
> 
> Need to get in more thinking done i guess


----------



## Sandeep Warrier

Hi crimson_b1ade....

I think the 62 needs to be near End.... either at your current 13 or 15 (or 14??)

If your strategy is allowed then...Excel WorkbookABCDEFGH1Start34567892121514131211103181716232425262741920212231302928536353433324344456373839404142484775554535251504946856575859606162EndSheet1*Excel 2003*

At 45 the rook jumps to 46 and comes back to 47.....<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## pgc01

crimson_b1ade said:


> I'm assuming that the rook keeps it's jumping abilities since a rook doesn't have to move one square at a time but can actually move several squares at a time.


 
Hi crimson_b1ade

If the rook moves several squares at a time all the squares between the start and end position will be marked as used.

Remark:



> rook keeps it's jumping abilities


 
I think the rook has no jumping abilities, it must pass by all the squares in between. That's why you cannot move to from a square to another one in the same row or in the same column if there's another piece in between. Only the knight can jump.

P. S. Let's not discuss whether in _castling_ the rook jumps over or dances with the king.


----------



## schielrn

I alwyas leave one left out spot as well.  I have tried about 50 different variations and cannot see a pattern that would allow this to work correctly?  I tried to search in online because it was bugging me, but could not find the solution.    I will keep working on it in my free time though.


----------



## DonkeyOte

PGC01 said:
			
		

> So, no, you are not allowed to re-trace or else any path would do.



hence the question 

Perhaps ?

Excel WorkbookABCDEFGHI1Start345678910212171615141312113201918252627282930421222324353433323154039383736474849506414243444546535251760595857565554697086162636465666768EndSheet5


----------



## schielrn

Isn't the board suppose to be A1:H8?


----------



## pgc01

Good one, Luke! 

But no, it must be a regular chessboard, 8x8!


----------



## DonkeyOte

pgc01 said:


> Good one, Luke!
> 
> But no, it must be a regular chessboard, 8x8!



ROFL !  I didn't even bother to check* though I confess I did think it rather odd that I'd come up with a "solution" - I don't normally 

(*no pun intended)


----------



## rs2k

Good puzzle,


pgc01 said:


> Hi all
> 
> Another brain teaser.
> 
> In a chess board you remove 2 squares at opposite corners (ex. A1 and H8). Is it possible to enter by one of these corners with a rook and leave by the other corner after passing by all the squares in the board?
> 
> Remember that a rook only moves either horizontally or vertically.



Just throwing things out here, but, can this be done? it looks like a variant of 'The lion and the Man' puzzle were each enters by opposite corners and cant' meet. 

The crux of this is;


> "to enter by one of these corners" & "*passing *by all the squares"



I've been in work now for just over 3hrs and have jangled my head with this, there's always one bl%$dy square left!!!!

Colin


----------



## schielrn

rs2k said:


> I've been in work now for just over 3hrs and have jangled my head with this, there's always one bl%$dy square left!!!!
> 
> Colin


 I have been the same.  I was beginning to think the same as you, that this can't be done.

Pedro,

Will you post the link or PM me the link where the answer is, if there is one?  I have tried long enough.


----------



## Oaktree

Seems my Gomory (as in Gomory's theorem) hint went nowhere.

Think of it this way: suppose you're removing the white squares in opposite corners.  

Then, you're trying to cover the remaining 62 squares by starting on a black square and alternating between black and white squares as your rook moves throughout the board.

The problem is, you're starting with 30 white squares and 32 black squares... so, alternating isn't going to be possible to cover the board.  Pedro doomed you from the start


----------



## rs2k

> Seems my Gomory (as in Gomory's theorem) hint went nowhere.



That's not true, it went right over my head....!!!!


----------



## Scott Huish

You take a hammer and smash the rook and the pieces cover all of the board.


----------



## pgc01

We have a solution. Oaktree is the winner! 

I was careful when I asked the question, I did not ask "How can this be done", I asked "Is it possible?".

I gave a hint when Sundeep posted:



> Need to get in more thinking done i guess


 
I answered:



> Yes, that's the right direction.


 
*In fact, you did not have to do any move, just think.*

- When a rook passes by 2 squares in sequence they are always 1 white and 1 black.

- You remove 2 oposite corners and so you are left with 30 squares of one colour and 32 squares of the other colour.

- after the rook passes by 60 squares, it passed by 30 white an 30 black squares, there are 2 squares left but they are the same colour and so a rook could never pass by them one after the other.

Cheers
Thank you all


----------



## schielrn

And I kept reading is this possible, but then people started posted attemots, so I thought to myself that it must be possible.  That was the best brain teaser yet.


----------



## Sandeep Warrier

litrelord said:


> .....
> Now is anyone going to post the answer to the 5x5 grid with 5 dogs and 3 cats because I just can't work it out and it's making me feel stupid
> ....



Solution has already been posted... by Oaktree (i think)....

a recap:
5 dogs and 3 cats....

Excel WorkbookABCDE1dogdog2cat3dog4dogdog5catcatSheet1*Excel 2003*

The 5 dogs can move in the area marked in yellow.... cats are safe....<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Sandeep Warrier

This is not a brain teaser.... but tests speed of thought 

http://www.cut-the-knot.org/Games/WolfRabbit.shtml
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Hero-0952

LoL! Nice :D I Like this!


----------



## pgc01

Hi

Here's another one. Much easier than the last and you may already know it. If you do, please don't post the answer immediately, not to spoil the fun for the others.

I's something like this:

Jack is leaving his building and Mary, an old friend he has not seen for years, is passing by.
Jack: Mary, hi, I haven't seen for so long!
Mary: Jack, hi. How nice to see you. How is Ann?
Jack: Ann is great, and so are the kids.
Mary: You have kids? What are their ages?
Jack: Yes, I have 3. Since you always like puzzles I'll tell you like this: do you see this number on the door of the building (both look at the number), well the sum of their ages is equal to this number and the product of the ages is 36.
Mary: Can you give me something more?
Jack: Come to think of it, yes, and you should remember it. Last time I saw you I was with Ann and our eldest daughter. Don't you remember?
Mary: Yes, how could I forget. I can even tell you when, it was just after I moved to my current apartment. Well, now I know the age of your kids.

Question: What's the ages of the 3 kids?


----------



## Oaktree

Even in the case of twins, one child is born (albeit minutes) before the other and is therefore technically older.  With that in mind, I believe you've given us another "can't solve it" puzzle


----------



## pgc01

Oaktree said:


> Even in the case of twins, one child is born (albeit minutes) before the other and is therefore technically older. With that in mind, I believe you've given us another "can't solve it" puzzle


 
No, I hadn't thought about it. But you are right. Let's say that when they last met Mary remebers that Jack only had 1 kid, 2 or 3 yours old. And I see that you already solved it!


----------



## Sandeep Warrier

Hmmmm....

Going by regular simultaneous equation rules... we have here 3 unknowns and 1 equation (product of ages = 36).... unless I'm missing something obvious....


----------



## pgc01

So that there are no confusions, Jack and Mary were having a perfectly normal conversation in English.

So when I ask someone how old is her child the aswer will be 4 years old and not something like 4 years 2 months and 1 day.


----------



## schielrn

I'm not sure I am understanding this as there could be more than one possible answer in my mind? Cause as Sandeep said the only evidence we have is that the product of the 3 children is 36. Which could be split in a few different ways? But 2 of the 3 ways I was thinking would involve twins.


----------



## Scott Huish

If we assume whole number ages, my guess is 1,4,9 and the door number is 14.


----------



## pgc01

schielrn said:


> the only evidence we have is that the product of the 3 children is 36.


 
Hi schielrn

No, we also know that the sum of the ages must be equal to the number on the door. So, not any anwer will do.


----------



## pgc01

HOTPEPPER said:


> If we assume whole number ages, my guess is 1,4,9 and the door number is 14.


 
As you state it it's only a guess. You must prove that that's the answer.


----------



## yytsunamiyy

I admit to the asking aunty G after racking my brain. Interesting solution. Thanks for the knot in my brain pgc


----------



## schielrn

HOTPEPPER said:


> If we assume whole number ages, my guess is 1,4,9 and the door number is 14.


What about 2, 3 and 6?  And the door number being 11?


----------



## Scott Huish

Yeah, I thought of that too.

Also 3,3,4, Door #10


----------



## schielrn

I believe it to be actually 2,2,9. Based on the clues given and that each clue must eliminate something. But to Oaktree's point one is one twin would actually be older than the other.  So it could have been 1,6,6 but it is 2,2,9.

There are 8 possiblities:Excel WorkbookABCDE1Kid 1Kid 2Kid 3sumproduct2113638363121821364131216365149143661661336722913368236113693341036Sheet1
But of those 8 only 2 result in the same door number, so that must be the door number, otherwise what is the point of that clue. Then if there is an eldest child, the twins could not be the oldest, so it must be 2, 2 and 9. Is that correct?


----------



## pgc01

schielrn said:


> I believe it to be actually 2,2,9. Based on the clues given and that each clue must eliminate something. But to Oaktree's point one is one twin would actually be older than the other.  So it could have been 1,6,6 but it is 2,2,9.
> 
> There are 8 possiblities:
> 
> Excel WorkbookABCDE1Kid 1Kid 2Kid 3sumproduct2113638363121821364131216365149143661661336722913368236113693341036Sheet1
> 
> 
> But of those 8 only 2 result in the same door number, so that must be the door number, otherwise what is the point of that clue. Then if there is an eldest child, the twins could not be the oldest, so it must be 2, 2 and 9. Is that correct?


 
Yes. We've got a solution. And Schielrn is the winner! 

If fact, we don't know the numer on the building door, but Mary does!

This means that if the number on the door of the building was different from 13 she would immediately know the ages of the 3 kids. Since she still couldn't tell the ages, this means that the sum of the ages was 13, with the 2 possible solutions (1,6,6) or (2,2,9).

Now the second clue tells us that there was 1 eldest child. We know that last time Mary was with the couple the eldest daughter was there, we infer that there is one child older that the others, or else Jack would say "one of the twins" instead of "my eldest", and also Mary would answer "I remember now, you had twins", you don't ususally forget that your friend has twins.
Anyway, so that there would be no doubts I posted in the answer to Oaktree that at the time of their last meeting Jack "only had 1 kid, 2 or 3 yours old."

So, in concusion, as Schielrn said, the answer is (2,2,9).

Cheers
Thanks for trying


----------



## Scott Huish

I don't quite follow this:



> This means that if the number on the door of the building was different from 13 she would immediately know the ages of the 3 kids.



If the number wasn't 13 there are more possibilities, how could she possibly know?


----------



## pgc01

Hi Hotpepper

If the number was any other than 13 Mary would know immediately the ages of the 3 children.



pgc01 said:


> Jack: Yes, I have 3. Since you always like puzzles I'll tell you like this: *do you see this number on the door of the building (both look at the number)*, well the sum of their ages is equal to this number and the product of the ages is 36.
> Mary: *Can you give me something more*?


 
So Mary knows the sum of the ages.

If the number of the building was, for ex. 14, you can check in schielrn's table that there is 1 only solution for the ages: (1,4,9).

The same for all the other possible sums: 38,21,16,11, 10.

The only case where the sum and the product are not enough to determine the 3 ages is the case of Sum=13. In that case there are 2 possibilities. Since Mary needed more information, we know that that was the case, the number on the door was 13, and Mary need more information to determine which of the 2 solutions was the one.


----------



## Sandeep Warrier

Another one...

A 3X3 chess board, with one knight on each corner. What is the minimum number of moves required to interchange the position of the knights.... (No 2 knights can occupy the same square at the same time)

Start:Excel WorkbookABC123Sheet1*Excel 2003*

End:Excel WorkbookABC123Sheet1*Excel 2003*


----------



## Oorang

Hmmm, there may be a more optimum solution but simple rotation yields the swap in 16 moves.


----------



## Cindy Ellis

Oops....no longer relevant!


----------



## yytsunamiyy

sandeep.warrier said:


> Another one...
> 
> A 3X3 chess board, with one knight on each corner. What is the minimum number of moves required to interchange the position of the knights.... (No 2 knights can occupy the same square at the same time)
> 
> Start:
> Excel WorkbookABC123Sheet1#VALUE!*Excel 2003*


 
The absolute minimum number of moves would be one. Either you move around the board or you move the board through 180°.


----------



## Gettingbetter

I can do it in 8, surely theres no quicker way than that, I hope there is that would be interesting.


----------



## Sandeep Warrier

Gettingbetter said:


> I can do it in 8, surely theres no quicker way than that, I hope there is that would be interesting.



Could you post the 8 moves???
<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## Oaktree

I'm with Oorang on that one, it looks like 16 to me.


----------



## pgc01

Nice one Sundeep.

Until now I also can only do it in 16 moves.


----------



## arkusM

I can do it in 16 as well.


----------



## Oorang

8 is impossible and I'll prove it. 
To make the conversation easier, let's number the tiles:
<table border="1"><tbody><tr><td bgcolor="cyan">1</td><td bgcolor="#33ff33">2</td><td bgcolor="cyan">3</td></tr><tr><td bgcolor="#33ff33">4</td><td bgcolor="red">5</td><td bgcolor="#33ff33">6</td></tr><tr><td bgcolor="#3333ff">7</td><td bgcolor="#33ff33">8</td><td bgcolor="#3333ff">9</td></tr></tbody></table>

To solve this in 8 moves each piece would have to only move twice. All possible combinations of 0 or 1 moves from the starting position would leave any piece in an illegal finishing position. 
As there are 4 pieces any _more_ than 2 more than two moves would cause you to run out moves before all pieces are in the proper finishing position, thus each piece _must_ move twice.
From each start position there are only two legal moves: 1 vertical, 2 horizontal; or 2 vertical and 1 horizontal  (the green tiles).
Of those 2 legal moves, for all starting positions, only 1 move puts you in a position to move to a "Finishing Tile" in the next move. That move is 1 vertical, 2 horizontal.
So for a successful 8 move solution the first moves _must _be either: 1 to 6; 3 to 4; 7 to 6; or 9 to 4. There are no other options.
From any green square each piece will now have only 1 move left, and only one square that will take them to a legal finishing position. This means each piece only has one possible finishing position for an 8 square victory.
Now notice that 3 and 9 both both share the same one and only legal move (as do 1 and 7). Therefore if 3 takes it's one and only legal move. Then 9 has _no possible legal first move _and vice versa (the same for 1 & 7).
In an 8 move scenario, every piece has only 1 legal move, and that legal move makes illegal another piece's only legal move. QED an 8 move solution is impossible.

Of course what this _doesn't_ prove is that 16 is optimum I'll give you hint though... 5 is red for a reason


----------



## Sandeep Warrier

Oorang said:


> 8 is impossible and I'll prove it.





Oaktree said:


> I'm with Oorang on that one, it looks like 16 to me.





pgc01 said:


> Until now I also can only do it in 16 moves.



Which is why I want Gettingbetter to post his solution


----------



## Sandeep Warrier

Oorang said:


> I'll give you hint though... 5 is red for a reason



Would that be that in a 3X3 grid there is no legal way a knight can land up on 5 

And while we ponder on the most optimum solution....

In a 10X10 grid arrange 10 Queens so that all Queens are safe.


----------



## crimson_b1ade

New Brain Teaser:

Three New York supermodels are shown a selection of five scarfs at an Fifth Avenue department store. Three of the scarfs are deep blue and two, yellow. The three supermodels are placed in single file, facing forward, and then blindfolded. One scarf is draped on each, with two returned to the shelf. The blindfold is first removed from the supermodel in the back. She is asked if she can guess the color of her scarf by looking only at the two models in front of her. “No,” she says. The blindfold is removed from the supermodel in the middle, and she is asked the same question. (She can only look at the supermodel in front, not in back.) “I can’t,” she says. Immediately the supermodel in front, still blindfolded, blurts out, “I’m wearing a [blank] scarf. Can I keep it?”
What color scarf is she wearing? (Explain your answer)


----------



## Cindy Ellis

Blue...
The first model would know what scarf she was wearing if both models in front of her were wearing yellow.  This leaves yellow-blue, blue-yellow, or blue-blue as options.
The second model could deduce that her scarf color was blue if the front model were wearing yellow, since yellow-blue is the only option that includes yellow for the first model.
So...the front model knows she can't be wearing yellow.


----------



## crimson_b1ade

We've got a winner!! YAY



Cindy Ellis said:


> Blue...
> The first model would know what scarf she was wearing if both models in front of her were wearing yellow. This leaves yellow-blue, blue-yellow, or blue-blue as options.
> The second model could deduce that her scarf color was blue if the front model were wearing yellow, since yellow-blue is the only option that includes yellow for the first model.
> So...the front model knows she can't be wearing yellow.


----------



## mikerickson

Cindy Ellis said:


> ..The second model could deduce that her scarf color was blue if the front model were wearing yellow, since yellow-blue is the only option that includes yellow for the first model...


How smart are the super-models?

I first heard this with condemned prisoners (lots of motivation), but scarves for models...I guess they'd be motivated.

OK, here's mine. 

There are ten piles of bombs (15 bombs to a pile).
Nine of the piles contain conventional bombs, one has atomic bombs.
Some knuckle-head removed the signs so you don't know which pile has the atomic bombs.
However, you do know that a conventional bomb weighs 300 lb. and an atomic bomb weighs 400 lb.
You have a scale. (30,000 lb. load limit)
(The bombs are identical in size and appearance and the atom bombs don't leak radiation even if you had a Geiger counter.)

Using the scale only once, how do you determine which pile has the atomic bombs?


----------



## crimson_b1ade

you take a bomb from each of the piles until the total load on scale increases by 400lb.




mikerickson said:


> ....
> There are ten piles of bombs (15 bombs to a pile).
> Nine of the piles contain conventional bombs, one has atomic bombs.
> Some knuckle-head removed the signs so you don't know which pile has the atomic bombs.
> However, you do know that a conventional bomb weighs 300 lb. and an atomic bomb weighs 400 lb.
> You have a scale. (30,000 lb. load limit)
> (The bombs are identical in size and appearance and the atom bombs don't leak radiation even if you had a Geiger counter.)
> 
> Using the scale only once, how do you determine which pile has the atomic bombs?


----------



## mikerickson

One weighing only.
Load the scale, press a button, read the result.

No intermediate values.


----------



## crimson_b1ade

take one bomb from pile 1, two from pile 2, three bombs from pile 3 and so on. Take the difference in the total weight less 16,500 (300*1+300*2+300*3+300*4...so on until...300*10) divided by 100lbs (the difference between 300lbs and 400lbs) and the result is your pile with the atomic bombs.





mikerickson said:


> ...
> OK, here's mine.
> 
> There are ten piles of bombs (15 bombs to a pile).
> Nine of the piles contain conventional bombs, one has atomic bombs.
> Some knuckle-head removed the signs so you don't know which pile has the atomic bombs.
> However, you do know that a conventional bomb weighs 300 lb. and an atomic bomb weighs 400 lb.
> You have a scale. (30,000 lb. load limit)
> (The bombs are identical in size and appearance and the atom bombs don't leak radiation even if you had a Geiger counter.)
> 
> Using the scale only once, how do you determine which pile has the atomic bombs?


----------



## mikerickson

crimson_b1ade said:


> take one bomb from pile 1, two from pile 2, three bombs from pile 3 and so on. Take the difference in the total weight less 16,500 (300*1+300*2+300*3+300*4...so on until...300*10) divided by 100lbs (the difference between 300lbs and 400lbs) and the result is your pile with the atomic bombs.


A winner!


----------



## crimson_b1ade

New brain teaser:

<TABLE style="WIDTH: 32pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=42 border=0 x:str><COLGROUP><COL style="WIDTH: 32pt; mso-width-source: userset; mso-width-alt: 1536" width=42><TBODY><TR style="HEIGHT: 12.75pt" height=17><TD id=td_post_2206419 style="BORDER-RIGHT: #f0f0f0; BORDER-TOP: #f0f0f0; BORDER-LEFT: #f0f0f0; WIDTH: 32pt; BORDER-BOTTOM: #f0f0f0; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" width=42 height=17>What</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #f0f0f0; BORDER-TOP: #f0f0f0; BORDER-LEFT: #f0f0f0; BORDER-BOTTOM: #f0f0f0; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>movie</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #f0f0f0; BORDER-TOP: #f0f0f0; BORDER-LEFT: #f0f0f0; BORDER-BOTTOM: #f0f0f0; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>is this</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #f0f0f0; BORDER-TOP: #f0f0f0; BORDER-LEFT: #f0f0f0; BORDER-BOTTOM: #f0f0f0; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>from?</TD></TR></TBODY></TABLE>


----------



## Ron Coderre

crimson_b1ade said:


> New brain teaser:
> 
> <TABLE style="WIDTH: 32pt; BORDER-COLLAPSE: collapse" border=0 cellSpacing=0 cellPadding=0 width=42 x:str><COLGROUP><COL style="WIDTH: 32pt; mso-width-source: userset; mso-width-alt: 1536" width=42><TBODY><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #f0f0f0; BORDER-LEFT: #f0f0f0; BACKGROUND-COLOR: transparent; WIDTH: 32pt; HEIGHT: 12.75pt; BORDER-TOP: #f0f0f0; BORDER-RIGHT: #f0f0f0" id=td_post_2206419 height=17 width=42>What</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #f0f0f0; BORDER-LEFT: #f0f0f0; BACKGROUND-COLOR: transparent; HEIGHT: 12.75pt; BORDER-TOP: #f0f0f0; BORDER-RIGHT: #f0f0f0" height=17>movie</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #f0f0f0; BORDER-LEFT: #f0f0f0; BACKGROUND-COLOR: transparent; HEIGHT: 12.75pt; BORDER-TOP: #f0f0f0; BORDER-RIGHT: #f0f0f0" height=17>is this</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-BOTTOM: #f0f0f0; BORDER-LEFT: #f0f0f0; BACKGROUND-COLOR: transparent; HEIGHT: 12.75pt; BORDER-TOP: #f0f0f0; BORDER-RIGHT: #f0f0f0" height=17>from?</TD></TR></TBODY></TABLE>


 
I PM'd my response to you.
Enjoyed that one.


----------



## lenze

Ok It's been 8 years since I posted the question of "Maynard the Census Taker" on the board (in the old, defunct lounge). We had fun with it then so I'll repost it here!

Maynard the census taker went to a certain house and was told 3 people lived there and that the product of their ages was 1296 and that the sum of their ages was equal to the house number. It was near lunch time, so Maynard left to think about this. After lunch, Maynard returned for more information. He was told, "I forgot to mention, I live here with my son and grandson". Now, what are the ages of the residents and what is the house number?

lenze
Appeal: If you remember the original, please don't spoil the answer for others


----------



## crimson_b1ade

I get multiple answers. Is that possible?




lenze said:


> Ok It's been 8 years since I posted the question of "Maynard the Census Taker" on the board (in the old, defunct lounge). We had fun with it then so I'll repost it here!
> 
> Maynard the census taker went to a certain house and was told 3 people lived there and that the product of their ages was 1296 and that the sum of their ages was equal to the house number. It was near lunch time, so Maynard left to think about this. After lunch, Maynard returned for more information. He was told, "I forgot to mention, I live here with my son and grandson". Now, what are the ages of the residents and what is the house number?
> 
> lenze
> Appeal: If you remember the original, please don't spoil the answer for others


----------



## lenze

There is only ONE correct answer. This is a logic problem!!

lenze


----------



## crimson_b1ade

I used a 125 x 125 multiplication table (figured the eldest isn't older than 125 yrs) to find the results of 1296/4, 1296/3, 1296/2, 1296/1 (didn't go beyond four as the denominator since the numbers look improbable after that) and came up with the following answers (some of which are improbable for a grandpa, son, and grandson). The house number is not given so I think it's impossible for anyone to say exactly:



<CENTER><TABLE cellSpacing=0 cellPadding=0 align=center><TBODY><TR><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-TOP: #000000 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid" bgColor=#0c266b colSpan=6><TABLE width="100%" align=center border=0><TBODY><TR><TD align=left>Microsoft Excel - Book2.xls</TD><TD style="FONT-SIZE: 9pt; COLOR: #ffffff; FONT-FAMILY: caption" align=right>___Running: xl2002 XP : OS = </TD></TR></TBODY></TABLE></TD></TR><TR><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; HEIGHT: 25px" bgColor=#d4d0c8 colSpan=6><TABLE width="100%" align=center border=0 VALIGN="MIDDLE"><TBODY><TR><TD style="FONT-SIZE: 10pt; COLOR: #000000; FONT-FAMILY: caption">File Edit View Insert Options Tools Data Window Help About</TD><TD vAlign=center align=right><FORM name=formCb108108><INPUT type=button value="Copy Formula" name=btCb946959 *******='window.clipboardData.setData("Text",document.formFb139974.sltNb672998.value);'></FORM></TD></TR></TBODY></TABLE></TD></TR><TR><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid" bgColor=white colSpan=6><TABLE border=0><TBODY><TR><FORM name=formFb139974><TD style="WIDTH: 60px" align=middle bgColor=white><SELECT onchange="document.formFb139974.txbFb115945.value = document.formFb139974.sltNb672998.value" name=sltNb672998><OPTION value==A2*B2*C2 selected>D2<OPTION value==A2+B2+C2>E2<OPTION value==A3*B3*C3>D3<OPTION value==A3+B3+C3>E3<OPTION value==A4*B4*C4>D4<OPTION value==A4+B4+C4>E4<OPTION value==A5*B5*C5>D5<OPTION value==A5+B5+C5>E5<OPTION value==A6*B6*C6>D6<OPTION value==A6+B6+C6>E6<OPTION value==A7*B7*C7>D7<OPTION value==A7+B7+C7>E7<OPTION value==A8*B8*C8>D8<OPTION value==A8+B8+C8>E8<OPTION value==A9*B9*C9>D9<OPTION value==A9+B9+C9>E9<OPTION value==A10*B10*C10>D10<OPTION value==A10+B10+C10>E10<OPTION value==A11*B11*C11>D11<OPTION value==A11+B11+C11>E11<OPTION value==A12*B12*C12>D12<OPTION value==A12+B12+C12>E12<OPTION value==A13*B13*C13>D13<OPTION value==A13+B13+C13>E13<OPTION value==A14*B14*C14>D14<OPTION value==A14+B14+C14>E14<OPTION value==A15*B15*C15>D15<OPTION value==A15+B15+C15>E15<OPTION value==A16*B16*C16>D16<OPTION value==A16+B16+C16>E16<OPTION value==A17*B17*C17>D17<OPTION value==A17+B17+C17>E17<OPTION value==A18*B18*C18>D18<OPTION value==A18+B18+C18>E18<OPTION value==A19*B19*C19>D19<OPTION value==A19+B19+C19>E19<OPTION value==A20*B20*C20>D20<OPTION value==A20+B20+C20>E20<OPTION value==A21*B21*C21>D21<OPTION value==A21+B21+C21>E21<OPTION value==A22*B22*C22>D22<OPTION value==A22+B22+C22>E22<OPTION value==A23*B23*C23>D23<OPTION value==A23+B23+C23>E23<OPTION value==A24*B24*C24>D24<OPTION value==A24+B24+C24>E24<OPTION value==A25*B25*C25>D25<OPTION value==A25+B25+C25>E25<OPTION value==A26*B26*C26>D26<OPTION value==A26+B26+C26>E26</OPTION></SELECT></TD><TD align=right width="3%" bgColor=#d4d0c8>*=*</TD><TD align=left bgColor=white><INPUT size=80 value==A2*B2*C2 name=txbFb115945></TD></FORM></TR></TBODY></TABLE></TD></TR><TR><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-TOP: #000000 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%">


</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle><CENTER>A</CENTER></TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle><CENTER>B</CENTER></TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle><CENTER>C</CENTER></TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle><CENTER>D</CENTER></TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; COLOR: black; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle><CENTER>E</CENTER></TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>1</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-TOP: #000000 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">Grandpa</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-TOP: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">Son</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-TOP: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">Grandson</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-TOP: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">Multp</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-TOP: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">House#</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>2</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">108</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">12</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">121</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>3</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">108</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">6</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">2</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">116</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>4</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">108</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">4</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">3</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">115</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>5</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">108</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">3</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">4</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">115</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>6</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">81</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">16</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">98</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>7</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">81</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">8</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">2</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">91</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>8</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">81</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">4</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">4</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">89</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>9</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">72</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">18</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">91</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>10</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">72</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">9</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">2</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">83</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>11</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">72</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">6</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">3</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">81</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>12</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">54</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">24</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">79</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>13</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">54</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">12</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">2</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">68</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>14</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">54</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">8</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">3</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">65</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>15</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">54</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">6</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">4</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">64</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>16</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">48</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">27</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">76</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>17</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">48</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">9</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">3</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">60</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>18</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">36</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">36</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">73</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>19</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">36</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">18</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">2</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">56</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>20</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">36</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">12</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">3</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">51</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>21</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">36</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">9</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">4</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">49</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>22</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">27</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">24</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">2</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">53</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>23</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">27</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">16</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">3</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">46</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>24</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">27</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">12</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">4</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">43</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>25</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">24</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">18</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">3</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">45</TD></TR><TR><TD style="BORDER-TOP: #000000 0.5pt solid; FONT-SIZE: 10pt; BORDER-LEFT: #000000 0.5pt solid; COLOR: #000000; FONT-FAMILY: menu; BACKGROUND-COLOR: #d4d0c8" align=middle width="2%"><CENTER>26</CENTER></TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">18</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">18</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">4</TD><TD style="BORDER-RIGHT: #d4d0c8 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">1296</TD><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-BOTTOM: #d4d0c8 0.5pt solid">40</TD></TR><TR><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-TOP: #808080 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; BORDER-BOTTOM: #000000 0.5pt solid; BACKGROUND-COLOR: #d4d0c8" colSpan=6><TABLE width="100%" align=left VALIGN="TOP"><TBODY><TR><TD style="BORDER-RIGHT: #000000 0.5pt solid; BORDER-TOP: #808080 0.5pt solid; BORDER-LEFT: #000000 0.5pt solid; WIDTH: 120pt; BORDER-BOTTOM: #000000 0.5pt solid; BACKGROUND-COLOR: #ffffff" align=left>Sheet1</TD><TD></TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE>
</CENTER>



lenze said:


> There is only ONE correct answer. This is a logic problem!!
> 
> lenze


----------



## lenze

Crimson: You are so close!! Remember, this is a LOGIC problem. Your grid holds the answer
If it hits you, refrain from posting so others can try their hand at it! 
lenze


----------



## Oorang

Is the grandson the son of the son?


----------



## Oorang

CB, Did the Knight Puzzle put you in mind of that?


----------



## Expiry

mikerickson said:


> Some knuckle-head removed the signs so you don't know which pile has the atomic bombs.



What an idiot! He should be sacked for that. Some people just don't care about safety.


----------



## lenze

> Is the grandson the son of the son?


That's irrelevant
lenze
Edit: On second thought, maybe not
<!-- / message --><!-- sig -->


----------



## schielrn

I would say the answer based on Crimson_Blade's table is row 9. As this seems to be in conjuction with the 3 kids question earlier.   Unless of course there are adopted children or son's from other marriages?  I just assumed they had to be related by blood.


----------



## lenze

schielm:http://www.mrexcel.com/forum/member.php?u=76414
I won't comment on the correctiveness(is that a word?)of your answer, but PM me how you arrived at that conclusion
lenze


----------



## Sandeep Warrier

Looks like my last question was missed out.... So here it is once more.... (Along with a new one.....)


*Question 1:*

In a 10X10 grid, arrange 10 Queens such that all Queens are safe.Excel WorkbookABCDEFGHIJ1Q1Q2Q3Q4Q5Q6Q7Q8Q9Q102345678910Sheet1*Excel 2003*

*Question 2:*

A 4X4 grid is filled with 16 items. Remove 6 items so that no row or column has an odd number of items in them.Excel WorkbookABCD13jjjj14jjjj15jjjj16jjjjSheet1*Excel 2003*


----------



## Gerald Higgins

Sandeep - for Question 1, can you define "safe" ?
Do you mean so that no Queen is under attack from any other ?

For question 2, are we allowed to move them as well, or only to REmove them ?


----------



## crimson_b1ade

I would say Q2 is impossible.



sandeep.warrier said:


> Looks like my last question was missed out.... So here it is once more.... (Along with a new one.....)
> 
> 
> #VALUE!#VALUE!*Excel 2003*


----------



## Oaktree

It's possible, and there are multiple solutions.  It's possible to also have the main diagonals and the four corners to have even numbers of items at the same time.


----------



## Scott Huish

Here's my solution to Q2:

Excel WorkbookABCD13jj14jjjj15jjjj16jjjSheet1



The question says to remove 6 items. A j is composed of 2 items.


----------



## schielrn

Spoiler Alert!  You have to highlight the table to see the answer if you want.

Here is my solution to Q2:

<TABLE style="WIDTH: 192pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=256 border=0><COLGROUP><COL style="WIDTH: 48pt" span=4 width=64><TBODY><TR style="HEIGHT: 15pt" height=20><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; WIDTH: 48pt; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" align=right width=64 height=20>1</TD><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 48pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right width=64>1</TD><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 48pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" width=64></TD><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 48pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" width=64></TD></TR><TR style="HEIGHT: 15pt" height=20><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" height=20></TD><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD></TR><TR style="HEIGHT: 15pt" height=20><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" height=20></TD><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" align=right height=20>1</TD><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD><TD class=xl63 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD></TR></TBODY></TABLE>



Here is a way with the corners and diagonals as Oaktree stated:

<TABLE style="WIDTH: 192pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=256 border=0><COLGROUP><COL style="WIDTH: 48pt" span=4 width=64><TBODY><TR style="HEIGHT: 15pt" height=20><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; WIDTH: 48pt; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" align=right width=64 height=20>1</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 48pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right width=64>1</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 48pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" width=64></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 48pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" width=64></TD></TR><TR style="HEIGHT: 15pt" height=20><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" height=20></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD></TR><TR style="HEIGHT: 15pt" height=20><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" align=right height=20>1</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD></TR><TR style="HEIGHT: 15pt" height=20><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" height=20></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent"></TD><TD class=xl65 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right>1</TD></TR></TBODY></TABLE>


----------



## Gerald Higgins

Hotpepper - if a j is considered to be 2 items, then the statement that the grid is filled with 16 items is inconsistent with the picture showing 16 j's, which is 32 items.


----------



## Scott Huish

Not necessarily, a j can be considered an item by itself, but is composed of two items.

Much like a car is one item, but is made from many items.


----------



## barry houdini

On the census question - I agreed with schielrn. The fact that Maynard goes back for "more information" implies that he couldn't work out the answer despite, presumably, knowing the house number - this implies that there were at least 2 possible solutions for the same house number - going by cb's table that makes it 91, although whether the answer is 81, 8 and 2 or 72, 18 and 1 I'm not sure......is 81 too old to have an 8 year old son..........or am I on completely the wrong track?


----------



## schielrn

barry houdini said:


> is 81 too old to have an 8 year old son..........or am I on completely the wrong track?


Or is 8 too young to have a 2 year old son?


----------



## barry houdini

schielrn said:


> Or is 8 too young to have a 2 year old son?


 
But if the ages are 81, 8 and 2 we know that one of the children is the son of the 81 year old (man or woman, we aren't told) and the other is his or her grandson, that doesn't follow that the 8 year old is the father of the 2 year old! the grandson could be the son of one of the 81-year old's other children.......


----------



## pgc01

barry houdini said:


> But if the ages are 81, 8 and 2 we know that one of the children is the son of the 81 year old (man or woman, we aren't told) and the other is his or her grandson, that doesn't follow that the 8 year old is the father of the 2 year old! the grandson could be the son of one of the 81-year old's other children.......


 
It could even happen that the 2 year old was his son and the 8 year old one of his grandson. The same for the other solution.


----------



## barry houdini

Yes, that's right, so is it one of those 2 or am I on the wrong track?

Of course the census taker was given the initial information by one of the residents. Presumably not a 1 or 2 year old. If he spoke to an 8 year old boy he would know that he wasn't 18 and vice versa and could therefore work out which combination applied, even without more information, so he must have spoken to the grandparent and not known whether (s)he was 72 or 81......but then that still doesn't give you the information does it?


----------



## Sandeep Warrier

Gerald Higgins said:


> Sandeep - for Question 1, can you define "safe" ?
> Do you mean so that no Queen is under attack from any other ?




Yes. Safe means that no Queen is under attack from any other.




Gerald Higgins said:


> For question 2, are we allowed to move them as well, or only to REmove them ?



It does not matter if you move them. The question can be re-interpreted to mean - Insert 10 items in a 4X4 grid so that all rows and columns have an even number of items.


----------



## Sandeep Warrier

HOTPEPPER said:


> The question says to remove 6 items. A j is composed of 2 items.



LOL.... "j" as an item was actually a misrepresentation (font problem). In my initial table it was a webding or wingding...


----------



## pgc01

Another solution.

Using the same (great) idea from schielrn: If you want to see the solution select the cells.

<table border="1" cellpadding="1" style="background:#FFF; border-collapse:collapse;border-width:2px;border-color:#CCCCCC;font-family:Arial,Arial; font-size:10pt" ><tr><th style="border-width:1px;border-color:#888888;background:#9CF " > </th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  width=30  >A</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  width=30  >B</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  width=30  >C</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  width=30  >D</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  width=30  >E</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  width=30  >F</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  width=30  >G</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  width=30  >H</th></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>1</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>2</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>3</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-top-width: 2px;border-color:#000000;border-left-width: 2px;border-color:#000000; ">  <font color="#FFFFFF" > x</font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-top-width: 2px;border-color:#000000; ">  <font color="#FFFFFF" > x</font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-top-width: 2px;border-color:#000000; ">  <font color="#FFFFFF" > x</font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-top-width: 2px;border-color:#000000;border-Right-width: 2px;border-color:#000000; ">  <font color="#FFFFFF" > x</font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>4</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-left-width: 2px;border-color:#000000; ">  <font color="#FFFFFF" > x</font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-width: 1px;border-color:#888888; ">  <font color="#FFFFFF" > x</font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-width: 1px;border-color:#888888; ">  <font color="#FFFFFF" >  </font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-Right-width: 2px;border-color:#000000; ">  <font color="#FFFFFF" >  </font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>5</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-left-width: 2px;border-color:#000000; ">  <font color="#FFFFFF" > x</font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-width: 1px;border-color:#888888; ">  <font color="#FFFFFF" >  </font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-width: 1px;border-color:#888888; ">  <font color="#FFFFFF" > x</font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-Right-width: 2px;border-color:#000000; ">  <font color="#FFFFFF" >  </font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>6</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-bottom-width: 2px;border-color:#000000;border-left-width: 2px;border-color:#000000; ">  <font color="#FFFFFF" > x</font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-bottom-width: 2px;border-color:#000000; ">  <font color="#FFFFFF" >  </font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-bottom-width: 2px;border-color:#000000; ">  <font color="#FFFFFF" >  </font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-bottom-width: 2px;border-color:#000000;border-Right-width: 2px;border-color:#000000; ">  <font color="#FFFFFF" > x</font></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>7</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>8</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td colspan=9 style="background:#9CF; padding-left:1em" > [Book1]Sheet2</td></tr></table>


----------



## Gerald Higgins

HOTPEPPER said:


> Not necessarily, a j can be considered an item by itself, but is composed of two items.
> 
> Much like a car is one item, but is made from many items.


 
Well this could debate could go on and on.
Yes of course, in the loosest sense, a car is one item, and each of it's components are also items.
As are the individual atoms of which the tyres, wiper blades and so on, are made.
Applying your logic to this puzzle, you could choose to describe a group of any 2 or more j's in this puzzle as "an item", in which case solving the problem becomes trivial.

Reading Sandeep's later posts, I think it's clear he didn't intend that kind of interpretation.


----------



## Oaktree

IMO, 10 queens on a 10x10 board is a lot easier than 8 queens on an 8x8 board.

Here's a solution for the 10 queens:

Book2ABCDEFGHIJ1621374258637984910105Sheet1


----------



## mikerickson

Here is a conundrum.

You walk one mile south, one mile east and one mile north.
After this three mile walk, you end up back where you started.

Your journey might have begun at the North Pole. 

What other place on the earth might you have started from?


----------



## Gerald Higgins

Mike - I believe there are theoretically an infinite number of locations that fit that bill, and for practical purposes there are many, although they're all pretty close to each other (without wishing to give it away). Am I right ?


----------



## mikerickson

Gerald, I sounds like you've got it.


----------



## Scott Huish

Although theoretically you would end up where you started, i.e. the North Pole, given that description, you can't possibly end up where you started exactly. You would have to walk approximately 1.4 miles northwest back to do that. (a squared + b squared = c squared) So as long as you are in the same place and a mile away is still in the same place (i.e. the same country for example), you could do this almost anywhere except where a mile away from any point in the journey puts you in a different city or country for example.


----------



## lenze

I think Gerald is on the right track! There are an INFINITE number of places you could start!! 
lenze


----------



## Aaron.B

I'm going with the south pole.

The globe is not a plane.


----------



## pgc01

I also see a 2 * infinite number of locations where you could start your trip. By a 2 * infinite I mean an infinite number of longitude values (any value) * an infinite number of latitude values (an infinite series of values).

BTW, I tried (not manually) all the possible solutions for the 10 queen problem and found 724 different solutions.


----------



## mikerickson

HotPepper, starting from the North pole, one would get back to the North Pole, exactly. Pythagorean theorm only works on the plane. The sum of the angles of any triangle on a spherical surphace is greater than 180.

Aaron, If one is standing on the South Pole, how does one make the first leg of the journey, "walk 1 mile south"?

PGC, one could look at it that, given any positive integer N, there is an uncountably infinite set of solutions associated with N. 
(Count of solutions) = (Count of Integers)*(Count of Real numbers >0 and <1)


----------



## pgc01

mikerickson said:


> PGC, one could look at it that, given any positive integer N, there is an uncountably infinite set of solutions associated with N.
> (Count of solutions) = (Count of Integers)*(Count of Real numbers >0 and <1)


 
Mike, I agree, the number of solutions in infinite. I meant that the solutions are the cartesian product of 2 infinite sets of values.

BTW, they are 2 different types of infinites. Under the mathematics of infinite sets, the latitudes have a are a set of infinite values that is denumerable, and so it's an *ℵ*<sub>0</sub> (aleph-zero) while the longitude set is continuum and so has a higher cardinality (according to the continuum hypotesis it would be a *ℵ*<sub>1</sub>).


----------



## Sandeep Warrier

pgc01 said:


> ...
> BTW, I tried (not manually) all the possible solutions for the 10 queen problem and found 724 different solutions.



Also, it's interesting to note that for the problem of N Queens in an NXN board where N>=6, a mathematical formulation exists to give at least one solution.


----------



## mikerickson

Before we dive into set theory, HERES THE ANSWER to the question:

To walk one mile south, one mile east and then one mile north, ending at the starting location:

Consider a circle 1 mile in circumference, centered on the south pole.

Pick a point on that circle (call it A). 
Start walking from a point 1 mile north of A
1[walk one mile south]
You are now at A
2[walk one mile east]
You are now at A again, having crossed every line of longitude.
3[walk one mile north]
You are at the starting point.

Where the set theory comes in is that there are *c* possible starting points for the procedure in the solution. (*c* stands for "continuum", the cardnality of the set of all Real numbers).
One starting point for each point on the circle.

However, there are other circles one could use. A circle 1/2 mile in circumference would work. (Traverse the circle twice while walking east)

Every solution would involve a circle of circumference 1/n for some natural number n.

So the total count of all solutions would be the cardnality of *N* X *R*. In aleph notation that would be  ℵ0 * ℵ1, which equals ℵ1.


----------



## Oaktree

I thought you were going to be walking on a cruise ship that's moving in a different direction than your feet.  Maybe I just watched this video one too many times (from Saturday Night Live) 

http://www.youtube.com/watch?v=k8F3UE9qFsg


----------



## crimson_b1ade

*New Brain Teaser:* Discover the mathematical relationship between the below series of numbers to fill in the last two missing numbers:

<TABLE style="WIDTH: 144pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=192 border=0 x:str><COLGROUP><COL style="WIDTH: 48pt" span=3 width=64><TBODY><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; WIDTH: 48pt; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: yellow" width=64 height=17 x:num>3</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 48pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: yellow" width=64 x:num>1</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 48pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: yellow" width=64 x:num>4</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: yellow" height=17 x:num>1</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: yellow" x:num>5</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: yellow" x:num>9</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: yellow" height=17 x:num>2</TD><TD class=xl23 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: #ff99cc">?</TD><TD class=xl23 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: #ff99cc">?</TD></TR></TBODY></TABLE>


----------



## pgc01

Not everyone will like this one as it involves lots of calculations. I found it interesting when I heard it and so I will share it and hope someone else has fun with it.

A woman goes to a newsstand and gets 4 magazines/papers and goes to the counter to pay. The man in the counter picks up a calculator, does the calculations and says:
- It's 7 euros and 11 cents, madam.
The woman looked at him puzzled, and said:
- I saw how you did the calculations, you kept pressing the multiplication key instead of the summing key. How is that??
Man: I'm so sorry, madam. You must be right. Let me explain, I've been using the same calculator for over 10 years and it just broke 1 minute ago. I picked up this new one and I now see that the keys are not in the same position. Please believe me, it was not intentional.
He redoes the calculations, this time pressing the "+" key, as he should, and says:
- It's 7 euros and 11 cents, madam.


Question: what was the price of each of the 4 articles?

P. S. No vba.
If you already know the solution, please wait some time before posting it, to not spoil the fun for the others.


----------



## crimson_b1ade

are there "cents" in Euros? I thought "cents" were used in U.S. currency.



pgc01 said:


> Not everyone will like this one as it involves lots of calculations. I found it interesting when I heard it and so I will share it and hope someone else has fun with it.
> 
> A woman goes to a newsstand and gets 4 magazines/papers and goes to the counter to pay. The man in the counter picks up a calculator, does the calculations and says:
> - It's 7 euros and 11 cents, madam.
> The woman looked at him puzzled, and said:
> - I saw how you did the calculations, you kept pressing the multiplication key instead of the summing key. How is that??
> Man: I'm so sorry, madam. You must be right. Let me explain, I've been using the same calculator for over 10 years and it just broke 1 minute ago. I picked up this new one and I now see that the keys are not in the same position. Please believe me, it was not intentional.
> He redoes the calculations, this time pressing the "+" key, as he should, and says:
> - It's 7 euros and 11 cents, madam.
> 
> 
> Question: what was the price of each of the 4 articles?
> 
> P. S. No vba.
> If you already know the solution, please wait some time before posting it, to not spoil the fun for the others.


----------



## barry houdini

crimson_b1ade said:


> are there "cents" in Euros?


 
Short answer is "yes" 

longer answer: "cent", of course, just comes from the latin for one hundred and some European countries already had their own version of the cent before the Euro replaced them (e.g. 100 centimes in a French franc). 

I assume they just needed to use terminology which wouldn't appear to favour some countries over others - Euro and cent were probably seen to be fairly neutral and uncontroversial......


----------



## milesUK

crimson_blade. next two digits I beleive are 6 & 5.


----------



## pgc01

milesUK said:


> crimson_blade. next two digits I beleive are 6 & 5.


 
I agree. I wouldn't be sure, however, about the next one.


----------



## Oaktree

In mod 12, there are an infinite number of solutions to Crimson's puzzle: 3+1=4+1=5+9=2+?=?


----------



## pgc01

Oaktree said:


> In mod 12, there are an infinite number of solutions to Crimson's puzzle: 3+1=4+1=5+9=2+?=?


 
Nice! Also in mod 6.


----------



## crimson_b1ade

I'm very impressed!! The answer can also be found by typing in the numbers into yahoo search.



milesUK said:


> crimson_blade. next two digits I believe are 6 & 5.


----------



## Pugster

An ant walks at 1 inch/minute along a 12 inch rubber band. If you stretch the rubber band at a rate of 1inch/minute. How long will it take for the ant to cross the band?


----------



## Scott Huish

The ant will never make it because eventually the rubber band will snap and the ant will get flung across the room.

But if you assume that the rubber band can't snap, he will also never make it because for every inch he advances, there's always 12 more inches to go.


----------



## mikerickson

Hmmm...Let the ant walk half way and then stop. Streatch the rubber band.
The ant still half way between the new (streatched) start and stop points.

Let B(t) be the length of the band at time t.
Let A(t) be the percentage of that length that the ant has traveled at time t.
Let X(t) be the position of the ant at time t.
We seek T such that A(T) = 1 i.e. X(T) = B(T)

dB/dt = 1
B(0) = 12
B(t) = 12 + t

X(t) = B(t) * A(t)
dX/dt = A (dB/dt) + B (dA/dt) = 1

A + B(dA/dt) = 1

dA/dt = (1-A) / B = (1-A) / (12+t)
A(0) = 0

At which point, my dislike of differential equations returns to haunt me.


----------



## Pugster

HOTPEPPER said:


> The ant will never make it because eventually the rubber band will snap and the ant will get flung across the room.
> 
> But if you assume that the rubber band can't snap, he will also never make it because for every inch he advances, there's always 12 more inches to go.



Not true. The way to visualise this one is to think that every stretch of the band also increases the start-ant distance as well as the ant-finish distance. So some of the extra stretched inch has already been covered by the ant so it will always be getting closer to the finish.


----------



## pgc01

Hi

This is a one-dimension problem so we only need the X axis.

Let's say that the rubber band's initial position overlaps X=0 to X=12. We will stretch the rubber band from the right and so after on minute it will be on X=0 to 13, after 2 minutes on X=0 to 14, etc. After a time t the rubber band has a length of (12 + t) and overlaps X=0 to 12 + t.

The ant starts from X=0 at t=0 and travels to the other end of the rubber band with a velocity of 1 inch/minute

I think the important point here is that the total velocity of the ant, as seen from the external observer is the sum of 2 velocities
- its own velocity, 1 inch/minute
- the velocity of the point of the rubber band where the ant is at that moment. The velocity of a point is x/(12+t)

The total velocity of the ant is then:

dx/dt = 1 + x/(12+t)

Solving this equation (back to school ), I got

x(t)=(12+t) * ln(1+t/12)

We want to know when the ant gets to the end of the rubber which has a length of (12 + t) at time t

12+t=(12+t) * ln(1+t/12)
ln(1+t/12)=1

t=12*(e-1)

This about 20 minutes 37 seconds.

There may be, of course, an easier way to solve it but I couldn't find it yet.


----------



## Sandeep Warrier

Find the numbers n and m such that 

[FONT=&quot]
	

	
	
		
		

		
			





[/FONT]<link rel="File-List" href="file:///C:%5CDOCUME%7E1%5Csandeepw%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml"><link rel="Edit-Time-Data" href="file:///C:%5CDOCUME%7E1%5Csandeepw%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_editdata.mso"><link rel="OLE-Object-Data" href="file:///C:%5CDOCUME%7E1%5Csandeepw%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_oledata.mso"><!--[if !mso]> <style> v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} w\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} </style> <![endif]--><!--[if gte mso 9]><xml>  <w:WordDocument>   <w:View>Normal</w:View>   <w:Zoom>0</w:Zoom>   <w:PunctuationKerning/>   <w:ValidateAgainstSchemas/>   <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>   <w:IgnoreMixedContent>false</w:IgnoreMixedContent>   <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>   <w:Compatibility>    <w:BreakWrappedTables/>    <w:SnapToGridInCell/>    <w:WrapTextWithPunct/>    <w:UseAsianBreakRules/>    <w:DontGrowAutofit/>   </w:Compatibility>   <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>  </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml>  <w:LatentStyles DefLockedState="false" LatentStyleCount="156">  </w:LatentStyles> </xml><![endif]--><style> <!--  /* Style Definitions */  p.MsoNormal, li.MsoNormal, div.MsoNormal     {mso-style-parent:"";     margin:0in;     margin-bottom:.0001pt;     mso-pagination:widow-orphan;     font-size:12.0pt;     font-family:"Times New Roman";     mso-fareast-font-family:"Times New Roman";} @page Section1     {size:8.5in 11.0in;     margin:1.0in 1.25in 1.0in 1.25in;     mso-header-margin:.5in;     mso-footer-margin:.5in;     mso-paper-source:0;} div.Section1     {page:Section1;} --> </style><!--[if gte mso 10]> <style>  /* Style Definitions */  table.MsoNormalTable     {mso-style-name:"Table Normal";     mso-tstyle-rowband-size:0;     mso-tstyle-colband-size:0;     mso-style-noshow:yes;     mso-style-parent:"";     mso-padding-alt:0in 5.4pt 0in 5.4pt;     mso-para-margin:0in;     mso-para-margin-bottom:.0001pt;     mso-pagination:widow-orphan;     font-size:10.0pt;     font-family:"Times New Roman";     mso-ansi-language:#0400;     mso-fareast-language:#0400;     mso-bidi-language:#0400;} </style> <![endif]-->[FONT=&quot]<!--[if gte vml 1]><v:shapetype id="_x0000_t75"  coordsize="21600,21600" o:spt="75" oreferrelative="t" path="m@4@5l@4@11@9@11@9@5xe"  filled="f" stroked="f">  <v:stroke joinstyle="miter"/>  <v:formulas>   <v:f eqn="if lineDrawn pixelLineWidth 0"/>   <v:f eqn="sum @0 1 0"/>   <v:f eqn="sum 0 0 @1"/>   <v:f eqn="prod @2 1 2"/>   <v:f eqn="prod @3 21600 pixelWidth"/>   <v:f eqn="prod @3 21600 pixelHeight"/>   <v:f eqn="sum @0 0 1"/>   <v:f eqn="prod @6 1 2"/>   <v:f eqn="prod @7 21600 pixelWidth"/>   <v:f eqn="sum @8 21600 0"/>   <v:f eqn="prod @7 21600 pixelHeight"/>   <v:f eqn="sum @10 21600 0"/>  </v:formulas>  <vath o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>  <o:lock v:ext="edit" aspectratio="t"/> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:225pt;  height:138.75pt' ole="">  <v:imagedata src="file:///C:\DOCUME~1\sandeepw\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"   o:title=""/> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml>  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025"   DrawAspect="Content" ObjectID="_1339491478">  </o:OLEObject> </xml><![endif]-->[/FONT]<input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="jsCall();" id="jsProxy" type="hidden">


----------



## pgc01

Hi Sandeep

This is a math approach. Maybe there's a simpler one?

The problem is:

What are the pairs m, n that satisfy:

∑ (For i=1 to m-1) i = ∑ (For j=m+1 to n) j

(I wrote this in text form because your link may be dead in the future).

This has infinite solutions.

For t= 2,3,4,5,...

m = ((3 + 8<sup>0.5</sup>)<sup>t</sup> - (3 - 8<sup>0.5</sup>)<sup>t</sup>)/(2*8<sup>0.5</sup>)

n = ((3 + 8<sup>0.5</sup>)<sup>t</sup> + (3 - 8<sup>0.5</sup>)<sup>t</sup>)/(2*8<sup>0.5</sup>)


Example, these are the first pairs:

With t in A2, 

m in B2: =((3+8^0.5)^A2-(3-8^0.5)^A2)/2/8^0.5

n in C2: =(((3+8^0.5)^A2+(3-8^0.5)^A2)/2-1)/2

Copy down


<table border="1" cellpadding="1" style="background:#FFF; border-collapse:collapse;border-width:2px;border-color:#CCCCCC;font-family:Arial,Arial; font-size:10pt" ><tr><th style="border-width:1px;border-color:#888888;background:#9CF " > </th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  width=30  >A</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  >B</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  >C</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  width=30  >D</th></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>1</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-width: 1px;border-color:#888888; ">t</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-width: 1px;border-color:#888888; ">m</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-width: 1px;border-color:#888888; ">n</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>2</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">2</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                                  6 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                           8 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>3</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">3</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                               35 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                        49 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>4</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">4</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                             204 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                      288 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>5</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">5</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                         1,189 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                  1,681 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>6</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">6</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                         6,930 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                  9,800 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>7</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">7</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                       40,391 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                57,121 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>8</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">8</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                     235,416 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">              332,928 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>9</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">9</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                 1,372,105 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">          1,940,449 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>10</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">10</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">                 7,997,214 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">        11,309,768 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>11</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">11</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">               46,611,179 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">        65,918,161 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>12</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">12</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">            271,669,860 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">     384,199,200 </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>13</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td colspan=5 style="background:#9CF; padding-left:1em" > [Book1]Sheet4</td></tr></table>


----------



## pgc01

Sorry, the expression for n is wrong:

n = (((3 + 8<SUP>0.5</SUP>)<SUP>t</SUP> + (3 - 8<SUP>0.5</SUP>)<SUP>t</SUP>)/2-1)/2

The formula is, however, right and so are the (m,n) pairs in the table.


----------



## Sandeep Warrier

Hi Pedro,

How did you come up with the formula?

A friend of mine came up with a sort of a brute force method... (A1 denotes the upper limit of numbers it will check)

<font face=Courier New><SPAN style="color:#00007F">Sub</SPAN> Test()<br>    left1 = 0<br>    right1 = 0<br>    a = 0<br>    b = 0<br>    c = 0<br>    result = 0<br>    limit1 = Range("A1").Value<br>    <SPAN style="color:#00007F">For</SPAN> a = Start <SPAN style="color:#00007F">To</SPAN> limit1<br>    <SPAN style="color:#00007F">For</SPAN> b = 1 <SPAN style="color:#00007F">To</SPAN> a<br>       left1 = b * (b + 1) / 2<br>       right1 = (a * (a + 1) / 2) - left1 + b<br>       <SPAN style="color:#00007F">If</SPAN> left1 - right1 = 0 And a > 1 <SPAN style="color:#00007F">Then</SPAN><br>        MsgBox a & " " & b<br>       <SPAN style="color:#00007F">End</SPAN> <SPAN style="color:#00007F">If</SPAN><br>     <SPAN style="color:#00007F">Next</SPAN><br>    <SPAN style="color:#00007F">Next</SPAN> a<br><SPAN style="color:#00007F">End</SPAN> <SPAN style="color:#00007F">Sub</SPAN><br></FONT>
<input id="gwProxy" type="hidden"><!--Session data--><input *******="if(typeof(jsCall)=='function'){jsCall();}else{setTimeout('jsCall()',500);}" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="if(typeof(jsCall)=='function'){jsCall();}else{setTimeout('jsCall()',500);}" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="if(typeof(jsCall)=='function'){jsCall();}else{setTimeout('jsCall()',500);}" id="jsProxy" type="hidden"><input id="gwProxy" type="hidden"><!--Session data--><input *******="if(typeof(jsCall)=='function'){jsCall();}else{setTimeout('jsCall()',500);}" id="jsProxy" type="hidden">


----------



## pgc01

> How did you come up with the formula?


 
Well, I understood that you wanted the general solution. 

This means that now you have a brain teaser, how to get the expressions .


Other solutions:

1 - vba

The code you posted seems to work ok but is very inefficient. To get to the pair (9800,6930) it took about 18 seconds in my pc.

This code gets to the pair (9800,6930) in about 15 ms in my pc, 1000+ times faster.



		Code:
__


Sub Test()
Dim m As Long, n As Long, lRow As Long
 
For n = 2 To 40000
    m = Sqr(n * (n + 1) \ 2)
    If m * m = n * (n + 1) \ 2 Then
        lRow = lRow + 1
        Range("A" & lRow).Value = m
        Range("B" & lRow).Value = n
    End If
Next n
End Sub

 
For bigger values we'd have to deal with the maximum of the long data type.

2 - Formulas

If one did not know the expressions for the pair one could also use an array formula to implement an algorithm similar to the vba.

If you try it, expect excel to take its time to do the calculations.

In A2:

=MIN(IF(MOD((ROW($2:$1000000)*(ROW($2:$1000000)+1)/2)^0.5,1)=0,IF(ISNA(MATCH(ROW($2:$1000000),$A$1:A1,0)),ROW($2:$1000000))))

... entered with CSE

In B2:

=(A2*(A2+1)/2)^0.5

Copy down


<table border="1" cellpadding="1" style="background:#FFF; border-collapse:collapse;border-width:2px;border-color:#CCCCCC;font-family:Arial,Arial; font-size:10pt" ><tr><th style="border-width:1px;border-color:#888888;background:#9CF " > </th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  >A</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  >B</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center"  width=30  >C</th></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>1</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>2</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">8</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">6</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>3</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">49</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">35</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>4</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">288</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">204</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>5</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">1681</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">1189</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>6</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">9800</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">6930</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>7</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">57121</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">40391</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>8</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">332928</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">235416</td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>9</b></td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td  style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td colspan=4 style="background:#9CF; padding-left:1em" > [Book1]Sheet1</td></tr></table>


P. S. Your friend's code does not declare the variables, a bad practice.


----------



## Scott Huish

What number should come next in this series

479126   62974   4796   697  ?


----------



## barry houdini

79?


----------



## TinaP

79


----------



## ZAX

What is the next number in this sequence?
2,3,5,8,13,21,34,55,?

A ship of 300m height was sailing, it was 100m under the water and 200m above the water, then, a wave of 100m height came, how much of the ship will be under the water and how much will be above the water?

A farmer was asked once, How much sheep, goats and cows do you have?
he answered:
-I have all sheep except 18
-I have all goats except 15
-I have all cows except 13
How much sheep, goats and cows does he have?

Jack is a poor hungry kid who had a loaf of bread, he sat there watching while his neighbors were making kabab, but he had an idea that he climbed a tree and put his loaf in the steam that is coming up so that the bread taste like kabab, but that greedy neighbor saw him, he insisted that he pays for that ,Jack refused but the man was so hard-headed to stop, they went together to the court to settle this down, after the neighbor insisted that Jack pays, the judge told him to pay, but that little Jack had a smart move to do that saved him and impressed the judge.
What did Jack do?

Beautiful and round, I'm usually around, sometimes I'm dark, sometimes I'm lit and sometimes I'm both, everybody would step on me but only a few did.

Sorry if mine were silly, too easy or unclear, but I'm not used to telling Brain Teasers especially in English lol.
ZAX


----------



## schielrn

89

100m under the water and 200m above the water

10 cows 8 goats and 5 sheep

Not sure on the Jack one off the top of my head at the moment

I'm guessing the last one is the moon.


----------



## ZAX

They're all right, I wonder how many seconds you needed to solve them!
Jack clanked the money in his pocket, "Here," Jack said "I ate the smell of your Kabab and you heard the clank of my money!"
I'm sorry if they were silly 
ZAX


----------



## schielrn

I like the Jack one, but not sure if I would have ever thought of that.  The one that took the longest was the cow, sheep, goat as I put them into mathematical equations to calculate them.

And the ship one I was actually asked in an interview one time.


----------



## Doreen17

I've checked the very first teaser about the bath tub and that was easy, but then I switched to the last page and it's all numbers and calculations I don't feel smart anymore


----------

