[问题求助] 棋盘求解——兴趣

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发表于 2010-10-1 20:19 |只看该作者 |倒序浏览

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QUESTION:

   You are going to place all numbers from 1 to 16 on a 4x4 chessboard such that all consecutive number pairs (1-2, 2-3, ..., 15-16) will be on the neighboring cells (left-right-top-down).
   In how many different ways can this be done?
   If the question was asked for a 2x2 chessboard, the answer would be 8

ANSWER:

Now doing it for 4 is way too complicated cause for a 4x4 square there are lots more versions and very hard to see which is unique, but this work didn't go to waste, I now know there are 8 versions for a 2x2 square and 40 for a 3x3 square, time to bust out ActionScript

we go for 3x3 aaaaand

So answer is 40...

Now that I know they both worked, we go for 4x4 aaaaand So answer is 552... But why ? Can students help me ? Thank you!

zan