Henry Ernest Dudeney/Puzzles and Curious Problems/189 - Problem of the Extra Cell

by : $189$

 * Problem of the Extra Cell

Here is a fallacy that is widely known but imperfectly explained.
 * ''Doubtless many readers will recognize it, and some of them have probably been not a little perplexed.


 * In diagram $A$ the square representing a chessboard is cut into $4$ pieces along the dark lines,
 * and these four pieces are seen re-assembled in Diagram $B$.


 * Dudeney-Puzzles-and-Curious-Problems-189.png


 * But in $A$ we have $64$ of these little squares, whereas in $B$ we have $65$.
 * Where does the additional cell come from?


 * Examine it carefully and see if you can discover whether it is really possible that you can increase the size of a slice of bread and butter
 * merely by cutting it into pieces and putting them together again differently.

Also see

 * Sam Loyd's Missing Square
 * $185$ - The Dissected Chessboard in the same collection.