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 re: Proof at last (I think) by levik)

I don't think 15 is correct. Even forgetting about the width objection, imagine a line from one corner of the board to a diagonally opposite one. It will affect all eight squares on the diagonal and also 7 intersections, where it will affect two more squares... so the total number of venners needed would be 8+2*7=22.

Posted by gregada on 2003-08-11 14:32:34