A standard 8 x 8 wooden chessboard has a straight line scratch in its surface, and is taken in for repair. The artisan who it is brought to decides to cover each affected square with a thin wooden veneer of the appropriate color.

Assuming that a different veneer is needed for each square of the board, what is the maximum number of such veneers that the artisan will require to do the job?

(In reply to Proof at last (I think) by TomM)

Congratulations, Tom! This is a great proof. I hope you don't mind that I used it verbatim as the solution to this problem (with due credit, of course)

Posted by levik on 2002-05-31 15:04:21