**A CHESSBOARD FALLACY.— solution**

The explanation of this little fallacy is as follows. The error lies in
assuming that the little triangular piece, marked C, is exactly the same height
as one of the little squares of the board. As a matter of fact, its height (if
we make the sixty-four squares each a square inch) will be
1^{1}/_{7} in. Consequently the rectangle is really
9^{1}/_{7} in. by 7 in., so that the area is sixty-four square
inches in either case. Now, although the pieces do fit together exactly to form
the perfect rectangle, yet the directions of the horizontal lines in the pieces
will not coincide. The new diagram above will make everything quite clear to the
reader.

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