Brain Teasers

[pgc01]

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 ℵ₀ (aleph-zero) while the longitude set is continuum and so has a higher cardinality (according to the continuum hypotesis it would be a ℵ₁).

 

[Sandeep Warrier]

...
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.

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]

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]

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

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