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?

As others have correctly stated, if the scratch if just a thin line (not necessarily zero width) then 15 squares is the max damaged. But, depending on the thickness the scratch may be able to mark 22 squares (this is dependent on the board itself...any gaps in the seems? any border color? etc).

In the 15 case, the artisan can use 8 pieces of veneer, one to cover the entire thing and 7 more to get the colors right.
In the 22 case, it would take 9 pieces to do the same.

Basically, this just isn't a good problem. At least, it's not worded well.

Posted by FingLao on 2002-05-22 13:53:31