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?

Well, I have to admit that the answer 15 is something that I have thought of as well. Intuitively, I can see why it has to be 15.

But I'm yet to think of a good rigorous proof of that, and that's the only kind of a proof I want to post as a solution.

So, anyone who wants the bragging rights is welcome to submit away :)

Posted by levik on 2002-05-02 11:09:10