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April 22nd, 2010, 01:28 PM   #1
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A Chessboard Problem

A delightfully simple-seeming problem. A king is to make a tour of a chess board, visiting each square exactly once and returning to the same square where it begins. The trick is - the king prefers diagonal moves to regular moves. What is the maximal number of diagonal moves?
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May 14th, 2010, 06:04 AM   #2
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Re: A Chessboard Problem

Graph problem, maybe?
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May 16th, 2010, 11:42 AM   #3
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Re: A Chessboard Problem

Oh, I should have answered this when I was done. It turns out that the king only has to make 8 non-diagonal moves, 2 associated with each corner, which can be verified as soon as you consider a few possibilities.
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May 17th, 2010, 10:43 AM   #4
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Re: A Chessboard Problem

Thanks jason.spade. Difficult problem, I think.
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May 17th, 2010, 10:47 AM   #5
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Re: A Chessboard Problem

It seemed to be difficult. I guess maybe I needed less depth and more thought than I gave it.

I trust this generalizes to n X n boards with n > 1? Or at least even n > 1?
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