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 number of possible number arrangements 
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Posted on: Thu Jan 26, 2012 8:49 pm




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Joined: Thu May 12, 2011 11:58 pm
Post number of possible number arrangements
Following up on sneaklyfox's question in the Timed Puzzle Bonus thread:
"How many combinations are there for the solution arrangement for a 4x4 puzzle?"

You can refer to this page on Latin squares.

To get the number for 4x4, multiply the given number L(4, 4) = 4 by (n - 1)! x n!:

4! x 3! x 4 = 24 x 6 x 4 = 576.

The numbers get interesting for larger n...
Not going to run out of 9x9 puzzles anytime soon, for example :-)
(and this is not counting the cage and operator arrangements (!!))

Patrick


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Posted on: Thu Jan 26, 2012 9:07 pm




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Joined: Fri May 13, 2011 2:11 am
Post Re: number of possible number arrangements
I have no idea how they're getting to the L(n,n) numbers, but that makes sense as a formula. I had sort of guessed the n!*(n-1)! part, because by the fundamental counting theorem the top row's obviously going to follow n!, and the second (n-1)!, but after that you have to start excluding combinations and it gets messy.


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Posted on: Thu Jan 26, 2012 9:40 pm




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Joined: Thu May 12, 2011 11:58 pm
Post Re: number of possible number arrangements
starling wrote:
I have no idea how they're getting to the L(n,n) numbers, but that makes sense as a formula.

Same here, I have no good intuition yet about how to count these arrangements...


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