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number of possible number arrangements https://www.calcudoku.org/forum/viewtopic.php?f=2&t=148 |
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Author: | pnm [ Thu Jan 26, 2012 8:49 pm ] |
Post subject: | 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 |
Author: | starling [ Thu Jan 26, 2012 9:07 pm ] |
Post subject: | 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. |
Author: | pnm [ Thu Jan 26, 2012 9:40 pm ] |
Post subject: | 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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