536 Puzzles and Curious Problems

124 Geometrical Problems

352. PROBLEM OF THE EXTRA CELL

Here is a fallacy that is widely known but imperfectly understood. Doubt-
less many readers will recognize it, and some of them have probably been not
a little perplexed. In Figure A the square resembling a chessboard is cut into

8

...... 1'3

8

..... ......

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J

II

I

Iffi#mtH

B

A

four pieces along the dark lines, and these four pieces are seen reassembled
in diagram B. But in A we have sixty-four of these little square cells, whereas
in B we have sixty-five. Where does the additional cell come from?
Examine it carefully and see if you can discover how that extra square
creeps in, and whether it is really possible that you can increase the size of
a slice of bread and butter by merely cutting it in pieces and putting them to-
gether again differently.

353. PROBLEM OF THE MISSING CELL

Can you arrange the four pieces of the previous puzzle in another way so
that instead of gaining a square we have lost one, the new figure apparently
containing only 63 cells?

354. A HORSESHOE PUZZLE

Here is an easy little puzzle, but we

have seen people perplexed by it for

some time. Given a paper horseshoe,

similar to the one in the illustration,

can you cut it into seven pieces, with

two straight clips of the scissors, so

that each part shall contain a nail

hole? There is no objection to your