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?

The worst scratch will extend between squeares on opposite corners of the board, slightly missing the middle of the board. It passes through the 8 white squares one the diagonal, and the 7 black squares directly under them (or vice versa). You can't reach 8+8 because the 2 8 same-color-lines are not parallel/close.

Posted by Daniel on 2002-05-02 09:35:50