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February 26th, 2013, 01:48 PM   #1
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Permutation

I am going through some permutation tutorials, one of them has an exercise asking in a 15-puzzle, if we assume the top right corner is 2, how many configurations satisfy this?

I think the answer is 14! Am I right?

My sincere thanks
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February 26th, 2013, 01:52 PM   #2
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Re: Permutation

What about the empty space. Doesn't that make it 15!?
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February 26th, 2013, 02:07 PM   #3
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Originally Posted by greg1313
What about the empty space. Doesn't that make it 15!?
I think you are correct
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February 27th, 2013, 07:15 AM   #4
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Re: Permutation

If you are allowed to move each square independently then there are 15! ways to place the other 15 squares. However, in a typical "15 puzzle", you cannot do that. You can only move into configurations that are even permutations of the original positions (which is, typically, ).
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February 27th, 2013, 12:11 PM   #5
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Re: Permutation

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Originally Posted by HallsofIvy
If you are allowed to move each square independently then there are 15! ways to place the other 15 squares. However, in a typical "15 puzzle", you cannot do that. You can only move into configurations that are even permutations of the original positions (which is, typically, ).
The question is how many permutations, not how many can you get from a given start. So your note is not relevant for this question.
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