Take a chessboard, it has 64 squares. Now cut off any two corner squares which are diagonally opposite.

You are given many rectangular bits of paper which have area equal to that of two such squares kept side by side. The PROBLEM is to cover the modified chess board with such pieces of paper.

No overlapping or folding is allowed. All the pieces should lie on the area of the modified chess board. Is this possible, and if not why?

It's not possible because there is a 6x6 square in the middle and along the outside two areas of 13 each with an effective width of 1. There will always be 2 blocks that are at best, diagonal. but never vertical or horizontal. As soon as you decide to stagger anything, you'll always be left with 1 empty block, and eventually, the 2 not together.

Posted by Lawrence on 2003-08-30 14:25:49