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How do I devise an algorithm to solve a sliding puzzle?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,914

Hi;

Do you mean the 15 puzzle?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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The 15 puzzle is unsolvable.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,914

Some positions are not possible but others are.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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Ok, so how to do it?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,914

There is some math that tells you whether it is solveable or not but I have forgotten it.

Programming it, looks tough.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**mathaholic****Member**- From: idk
- Registered: 2012-11-29
- Posts: 2,909
- Website

Mathematica?

It's summer.

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But programming it is what I am thinking.

After all, programs are threre which solve them

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,914

I will try one and see what comes up.

**In mathematics, you don't understand things. You just get used to them.**

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Did you?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,914

I have not even scratched the surface because I am still wrestling with a representation of the puzzle itself. It is unlikely that I will get far even when I solve that small problem because I do not understand how the program should pick from its many choices.

**In mathematics, you don't understand things. You just get used to them.**

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Are you on Win 7?

The algorithm isn't simple, it involves a lot of graph theory...

*Last edited by Agnishom (2013-04-26 23:58:55)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,914

Heck no!

That is the problem right there. I am not very good with graph theory. As a matter of fact, I stink.

**In mathematics, you don't understand things. You just get used to them.**

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http://www.brian-borowski.com/Software/Puzzle/

Are they calling each state a node?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,914

Probably, that would make sense.

Here is the math behind every solution.

http://mathworld.wolfram.com/15Puzzle.html

Also, there are tons of these programs to download. I need some sleep, see you.

**In mathematics, you don't understand things. You just get used to them.**

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Okay Sweet Dreams!

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 93,914

Thanks and same to you.

**In mathematics, you don't understand things. You just get used to them.**

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