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July 18th, 2009, 05:43 PM   #1
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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).
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July 18th, 2009, 07:13 PM   #2
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Re: What is the total number of moves a knight can make ?

Quote:
1.What is the total number of moves a knight can make on an 8 x 8 chessboard?
.
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 ???
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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 is odd, then the number of moves is and when even, .

This is my theory. NOT A GUARANTEED FACT.
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July 19th, 2009, 05:57 AM   #4
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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 66 board.
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July 19th, 2009, 09:34 PM   #5
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Re:

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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 66 board.
Nice! Thanks for letting me know.
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