We can label the squares of an 8 x 8 chess board from from 1 to 64 in 64! different ways.

For each arrangement we find D, the largest difference between the labels of two squares which are adjacent (orthogonally or diagonally).

What is the smallest possible D (and how would you prove it)?

(In reply to re: possible solution: proof by Brian Wainscott)

Nice, very concise.

Posted by SilverKnight on 2004-02-05 14:20:01