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**wintersolstice****Real Member**- Registered: 2009-06-06
- Posts: 114

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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,493

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,493

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

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

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)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

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.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,493

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,493

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Yes, I will.

Catch you later (bed for me now).

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,493

Have a good night and see you back here later.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

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