perplexus.info :: Geometry : Chessboard Puzzle

Chessboard Puzzle (Posted on 2002-11-17)

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?

Submitted by maverick

Rating: 2.6250 (8 votes)

Solution: (Hide)

Nick Reed's comment provides a perfect solution to the puzzle.
To reiterate: it cannot be done. Removing two diagonally opposite squares will result in a chessboard with 32 squares of one color, and 30 of another. Since one 2x1 piece of paper will always cover one square of each color, you would need an equal number of black and white squares to cover the whole board.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Hmmm...	Lawrence	2003-08-30 14:25:49
Good problem	cges	2002-12-11 08:36:08
chess	sach	2002-12-10 13:10:36
Squares	Nick Reed	2002-11-17 10:48:40

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