Dissection Puzzles 117available measured 9 inches in breadth by 16 inches in length. How did he
cut it into only two pieces that would exactly fit the hole? The answer is based
on what I call the "step principle," as shown in the diagram. If you move the
piece marked B up one step to the left, it will exactly fit on A and form
a perfect square measuring twelve inches on every side.
-.--------------12. - -in. -------------,
:
.~I I
,
(() ,
4-in. , I B
,
,
I
A,
16 In.This is very simple and obvious. But nobody has ever attempted to explain
the general law of the thing. As a consequence, the notion seems to have got
abroad that the method will apply to any rectangle where the proportion of
length to breadth is within reasonable limits. This is not so, and I have had
to expose some bad blunders in the case of published puzzles that were sup-
posed to be solved by an application of this step principle, but were really
impossible of solution. * Let the reader take different measurements, instead
of 9 in. by 16 in., and see if he can find other cases in which this trick will work
in two pieces and form a perfect square.
[* See Dudeney's Amusements in Mathematics, Problem 150, where he catches Sam Loyd in
such a blunder.-M. G.)