Calculating Chess Knight Moves on a n x n Board

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SUMMARY

The discussion centers on calculating the maximum number of moves a chess knight can make on an n x n board without revisiting any square. The established values for m(n) are as follows: m(0) = 0, m(1) = 0, m(2) = 0, m(3) = 2, m(4) = 5, m(5) = 10, m(6) = 17, m(7) = 24, and m(8) = 35. Participants suggest experimenting with a 9x9 board, anticipating that the knight can exceed 35 moves. The discussion also raises questions about the knight's movement on non-square m x n boards.

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arcnets
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Hi all,
I found this problem in a Martin Gardner book. You have a chess board of n x n squares. How many moves m(n) can a chess knight make on this board without crossing or touching its own path?

m(0) = 0
m(1) = 0
m(2) = 0
m(3) = 2
m(4) = 5
m(5) = 10
m(6) = 17
m(7) = 24
m(8) = 35

http://home.t-online.de/home/b_c.kuss/mgard.JPG

Anyone know how to continue this? Thanks!
 
Last edited:
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Make a 9x9 board, and try it. You should be able to make more than 35 moves.
 
How does it change also for a m x n board?
 

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