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

Puzzles and Curious Problems by Henry Ernest Dudeney: $189$

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 $B$.

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.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Geometrical Problems: Dissection Puzzles: $189$. -- Problem of the Extra Cell
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Dissection Puzzles: $352$. Problem of the Extra Cell