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?
"Consider the lily."
No, wait, consider the chessboard. It has 32 white squares and 32 black squares.
Can you see where we're going with this?
Removing any two diagonal corners means you'll end up with 32 of one colour and 30 of another (diagonal corners are the same colour, after all).
And a single piece of paper always covers one white square and one black square.
So - it is impossible to cover all the squares.
Squares
