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

by : $185$

 * The Dissected Chess-Board
 * 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.


 * Dudeney-Puzzles-and-Curious-Problems-185.png


 * 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.


 * It is best to use the diagram that is not chequered in black and white cells.

Also see

 * Sam Loyd's Missing Square, upon which this entry was based


 * Puzzles and Curious Problems: $189$ - Problem of the Extra Cell, where he raises the initial problem once more.