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?

no, it's not possible

the hint is that it's a "chess board", with white & black alternating.
- the "rectangular bits" will have to fit in a one white, one black 2-square space on the board (because no color has 2 right by each other)
- however, the 2 squares cut off are the same color, so there's more of one color than the other.
That means one square by each of the cut off square can't be filled by a 2-square rectangle.

Posted by sach on 2002-12-10 13:10:36