Henry Ernest Dudeney/Puzzles and Curious Problems/185 - The Dissected Chessboard/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $185$

Here is an ancient and familiar fallacy.

If you cut a chessboard into four pieces in the manner indicated by the black lines in Figure $\text A$,

and then reassemble the pieces as in Figure $\text B$,

you appear to gain a square by the operation,

since this second figure would seem to contain $13 \times 5 = 65$ squares.

I have explained this fallacy over and over again, and the reader probably understands all about it.

The present puzzle is to place the same four pieces together in another way

so that it may appear to the novice that instead of gaining a square we have lost one,

the new figure apparently containing only $63$ cells.