# Kids homework!!



## pompey007 (Sep 22, 2010)

If you had to design a dartboard so that when all 3 darts scored you could get every number from 3 to 100. What is the minimum number of numbers you would need and what would those numbers be?

How would you go about this?


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## schielrn (Sep 22, 2010)

Does this assume that you can get doubles and triples?  Also, does each pie (number section) need to be the same size?  Are there any other stipulations to this we may need to know?


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## pompey007 (Sep 22, 2010)

No doubles and triples. I believe that the size of each section is irrelevant as it is the value of its number that will be used.

Thanks


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## cornflakegirl (Sep 23, 2010)

Are you allowed a zero?


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## pompey007 (Sep 23, 2010)

cornflakegirl said:


> Are you allowed a zero?



I don't think so.

It was quite ambiguous; it was something like "design your own dartboard where every number from 3-100 can be scored with 3 darts"

I can see how you can do it by using loads of different numbers (eg every number from1-34 would do), but I was wondering how you could calculate the smallest number of numbers you need?


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## cornflakegirl (Sep 23, 2010)

How old is the child? Would they score extra points for ingenious solutions involving 0 and possibly negative numbers, or would this be frowned upon? 

It's an intriguing puzzle - I think it's harder than it seems initially - the restriction to three darts is quite, well, restricting. I shall have a play later.


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## pompey007 (Sep 23, 2010)

cornflakegirl said:


> How old is the child? Would they score extra points for ingenious solutions involving 0 and possibly negative numbers, or would this be frowned upon?
> 
> It's an intriguing puzzle - I think it's harder than it seems initially - the restriction to three darts is quite, well, restricting. I shall have a play later.



Assume as simple an answer as possible, I will reveal age later as it is quite surprising!!

Good luck


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## Gerald Higgins (Sep 23, 2010)

Do you have to actually use all three darts, and score with them ?
For example, if the target value is 4, and one of the segments is 4, can you achieve it by using one dart in 4, and not throwing the other 2 (or letting them miss) ?
Or, do you have to make 4, for example, by using a 2 and two 1s ?


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## pompey007 (Sep 23, 2010)

Gerald Higgins said:


> Do you have to actually use all three darts, and score with them ?
> For example, if the target value is 4, and one of the segments is 4, can you achieve it by using one dart in 4, and not throwing the other 2 (or letting them miss) ?
> Or, do you have to make 4, for example, by using a 2 and two 1s ?



Assume that you have to use all three darts, therefore

1,1,1=3
1,1,2=4
1,2,2=5
2,2,2=6


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## CMIIandExcel (Sep 23, 2010)

First Guess of the top of the head:
7 numbers;
1, 2, 4, 16, 32, 64.

Regards

Mike


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## Gerald Higgins (Sep 23, 2010)

Mike - I don't think you can score 99 in 3 darts with that combination.


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## CMIIandExcel (Sep 23, 2010)

Opps i missed the 8 from the list

7 numbers:

1, 2, 4, *8*, 16, 32, 64.

Your right 99 cannot be got in three.

back to the drawing board 

Mike


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## milesUK (Sep 23, 2010)

Mike, good but you'd surely need more than 3 darts for some numbers. 15 for example.


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## cornflakegirl (Sep 23, 2010)

Mike - I thought it would be that sort of solution too, but having to use exactly 3 darts each time really does make it trickier!


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## Peter_SSs (Sep 23, 2010)

My attempt is 18:
1, 2, 3, 4, 5, 6, 7, 	8, 9, 10, 11, 12, 13, 14, 15, 16, 32, 64


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## cornflakegirl (Sep 23, 2010)

My best so far is 13:
1,2,3,4,5,6,7,8,9,10,20,40,50


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## Peter_SSs (Sep 23, 2010)

Good improvement!


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## cornflakegirl (Sep 23, 2010)

Okay, now down to 11:

1,2,3,4,5,10,15,20,40,60,80

or

1,2,3,4,5,10,15,20,25,50,75


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## Expiry (Sep 23, 2010)

Gerald Higgins said:


> Do you have to actually use all three darts, and score with them ?
> For example, if the target value is 4, and one of the segments is 4, can you achieve it by using one dart in 4, and not throwing the other 2 (or letting them miss) ?
> Or, do you have to make 4, for example, by using a 2 and two 1s ?



Are you asking that because you're rubbish at darts?


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## cornflakegirl (Sep 23, 2010)

pompey007 said:


> Assume as simple an answer as possible, I will reveal age later as it is quite surprising!!
> 
> Good luck



I really hope it's not a primary school child. If it is, you probably need to shoot the teacher for trying to put kids off maths - enough of them hate it already!


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## Gerald Higgins (Sep 24, 2010)

> Are you asking that because you're rubbish at darts?


 
Keep out of the black, and into the red . . . .


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## RoryA (Sep 24, 2010)

there's nothing in this game for two in a bed.


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## Gerald Higgins (Sep 24, 2010)

Thank you Rorya.

"Look at what you could have won !"
"Never mind Jim, we've had a lovely day"


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## RoryA (Sep 24, 2010)

A speedboat, Jim? That's lovely but we live in Otley.


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## Gerald Higgins (Sep 24, 2010)

> Okay, now down to 11:
> 
> 1,2,3,4,5,10,15,20,40,60,80
> 
> ...


 
Now down to 10:

1,2,3,4,5,10,15,20,40,75


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## shg (Sep 24, 2010)

I think this can be done with Fibonacci numbers, but have not confirmed:

1 2 3 5 8 13 21 34 55


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## Gerald Higgins (Sep 24, 2010)

rorya said:


> A speedboat, Jim? That's lovely but we live in Otley.


 
Rory, looking at your picture, I'm guessing maybe YOU were a winner ?


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## Gerald Higgins (Sep 24, 2010)

shg4421 said:


> I think this can be done with Fibonacci numbers, but have not confirmed:
> 
> 1 2 3 5 8 13 21 34 55


 
I don't think you can score 100 with that combination.


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## Gerald Higgins (Sep 24, 2010)

Gerald Higgins said:


> Now down to 10:
> 
> 1,2,3,4,5,10,15,20,40,75


 
Sorry, this doesn't actually work, I hadn't tested it properly.

You can't actually get 76 this way.


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## shg (Sep 24, 2010)

Your 11-number solution still looks good.

The Fibonacci numbers through 89 have 16 holes.


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## pompey007 (Sep 27, 2010)

Hi,

Thanks for all the input, the puzzle certainly is harder than it initially looks!

To be fair, the original homework was "design a dartboard so that when all 3 darts scored you could get every number from 3 to 100", so you could have used lots of numbers (eg 1-34).

I added the part about the minimum number thinking that a simple formula and/or excel could be used to formulate a solution.


Finally, the homework was for 7 year-olds!!! It was a follow up to some very simple stuff, so I assumed it would be easy! (When it started to look hard, I just told him not to do it, so hopefully it has not put him off maths!!)


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## cornflakegirl (Sep 27, 2010)

pompey007 said:


> (When it started to look hard, I just told him not to do it, so hopefully it has not put him off maths!!)



Good call! What's the betting the teacher hasn't worked out the solution...

(I still feel there ought to be a nice general solution type thing. I just have no idea what it is  )


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## Oaktree (Sep 27, 2010)

Teacher never said they had to be integers


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## Michael M (Sep 27, 2010)

Here's my "GUESS"..using 3 darts or less....
But it did my head in when I got to 50 !!

```
1
1
2
3
6
9
15
24
39
63
```


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## shg (Sep 27, 2010)

Can't get to 37, 38, or 20 other numbers.


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## Michael M (Sep 27, 2010)

****.....well there goes my guess, AND strangely enough, my care factor as well....LOL !


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