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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  
Senior Member Joined: Dec 2008 Posts: 206 Thanks: 0  Re: What is the total number of moves a knight can make ? Quote:
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  
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Re: What is the total number of moves a knight can make ? Quote:
When is odd, then the number of moves is and when even, . This is my theory. NOT A GUARANTEED FACT.  
July 19th, 2009, 05:57 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,644 Thanks: 2084 
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 reentrant tour for that board. There are five distinct reentrant knight's tours with quaternary symmetry on the 6×6 board.

July 19th, 2009, 09:34 PM  #5  
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Re: Quote:
 

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