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**wintersolstice****Real Member**- Registered: 2009-06-06
- Posts: 125

here's an interesting puzzle (no idea what difficulty level this would be.)

the idea is to create 10 different expressions each totaling 12, using 5 of the same digit (so 5 0's, 5 1's, 5 2's, 5 6's, 5 5's, 5 7's 5 8's and 5 9's)

rules:

1)you have to use EXACTLY 5 of that number no more no less

2)you can't use any other numbers (e.g.

would add a 2 you can't do that)3) you can use any arithmetic symbols, the √ symbol (since it has no number on it) and factorial (!)

4) you can also use decimal point and recurring sign (e.g. 8 = 8/10 and 8(recurring) = 8/9

5) you can't put two(or more) numbers together (e.g. you can put two 5's together to get 55 and you can't do 55 =55/10

6) you can also use brackets

there may be multiple solutions to some of them:D

heres the first one to start you off

EDIT the following solution is invalid since it works for all digits (except 0)

D/D + ((D+D)/D)

any other such solution is also invalid

*Last edited by wintersolstice (2013-09-13 02:34:33)*

Why did the chicken cross the Mobius Band?

To get to the other ...um...!!!

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,467

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,558

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,467

That is the one the program I wrote could not get!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,558

Far too complex for it, I suppose! Took me a while to see it, though, as I was going for trickier combinations, thinking that 7 is a bit awkward to change into something usable.

Here's another that works for all digits, making it invalid:

*Last edited by phrontister (2013-09-14 15:38:30)*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,558

Hi Bobby,

That is the one the program I wrote could not get!

Got any hints as to how to go about creating such a program? My mind went blank when I started trying to think up something.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,467

Hi;

I know of at least one other. It is more automatic than mine but since it was written by someone else I do not understand it well enough to modify.

I am looking for it and will post it as soon as I get it.

http://blog.wolfram.com/2012/02/02/happy-109876-54321/

At the bottom is the link to a notebook that can do them.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,558

Thanks for that, Bobby.

I've read through the nb but will have to repeat that a few times before I can understand it well enough to try anything out. Of course, I'm wondering too how to include operators other than just those used there, but I guess I'd just add them to the 'ops' list.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,467

Yep, that is what I would try first! Play with it a bit.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,558

Yes, I will.

Catch you later (bed for me now).

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,467

Have a good night and see you back here later.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Grimbal****Member**- Registered: 2013-11-24
- Posts: 7

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