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 April 22nd, 2010, 01:28 PM #1 Senior Member   Joined: Apr 2008 Posts: 435 Thanks: 0 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?
 May 14th, 2010, 06:04 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: A Chessboard Problem Graph problem, maybe?
 May 16th, 2010, 11:42 AM #3 Senior Member   Joined: Apr 2008 Posts: 435 Thanks: 0 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.
 May 17th, 2010, 10:43 AM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: A Chessboard Problem Thanks jason.spade. Difficult problem, I think.
 May 17th, 2010, 10:47 AM #5 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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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