[Illustration]
In the illustration eighteen matches are shown arranged so that they
enclose two spaces, one just twice as large as the other. Can you
rearrange them (1) so as to enclose two four-sided spaces, one exactly
three times as large as the other, and (2) so as to enclose two
five-sided spaces, one exactly three times as large as the other? All
the eighteen matches must be fairly used in each case; the two spaces
must be quite detached, and there must be no loose ends or duplicated
matches.