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 July 18th, 2009, 05:43 PM #1 Newbie   Joined: Jul 2009 Posts: 10 Thanks: 0 What is the total number of moves a knight can make ? 1.What is the total number of moves a knight can make on an 8 x 8 chessboard? 2. Determine the number of all possible moves of a knight on an n x n chessboard (n >= 3).
July 18th, 2009, 07:13 PM   #2
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Re: What is the total number of moves a knight can make ?

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 1.What is the total number of moves a knight can make on an 8 x 8 chessboard?
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I am not very sure what u mean by this . I can use a single knight to cover all the 64 squares in a chess board.
What does ur move mean?? Do u mean without repetition or something ???

July 18th, 2009, 07:28 PM   #3
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Re: What is the total number of moves a knight can make ?

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 Originally Posted by tvthinh 1.What is the total number of moves a knight can make on an 8 x 8 chessboard? 2. Determine the number of all possible moves of a knight on an n x n chessboard (n >= 3).
Close to a decade ago, one of my friend has demonstrated his ability on a chessboard that a knight can move to all square parts in a 8x8 square board. I have also imagined that 4x4 can also be possible, but 3x3 leaves out the center square, and same with 5x5.
When $n=>= 3$ is odd, then the number of moves is $n^2-1$ and when even, $n^2$.

This is my theory. NOT A GUARANTEED FACT.

 July 19th, 2009, 05:57 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,379 Thanks: 2011 There is no knight's tour for a 4x4 board. It's easy to find a tour for the entire 5x5 board, but there is no re-entrant tour for that board. There are five distinct re-entrant knight's tours with quaternary symmetry on the 6×6 board.
July 19th, 2009, 09:34 PM   #5
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 Originally Posted by skipjack There is no knight's tour for a 4x4 board. It's easy to find a tour for the entire 5x5 board, but there is no re-entrant tour for that board. There are five distinct re-entrant knight's tours with quaternary symmetry on the 6×6 board.
Nice! Thanks for letting me know.

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