In the illustration
eighteen matches are shown
arranged so that they enclose two spaces, one just twice as large as
Can you rearrange
(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.