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

Posts: 2258
Joined: Thu May 12, 2011 11:58 pm
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?"

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

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

Posts: 175
Joined: Fri May 13, 2011 2:11 am
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.

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

Posts: 2258
Joined: Thu May 12, 2011 11:58 pm
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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