A NEW MATCH PUZZLE.
(
Patchwork Puzzles)
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.
Answer:
1. The easiest way is to arrange the eighteen matches as in Diagrams 1
and 2, making the length of the perpendicular AB equal to a match and a
half. Then, if the matches are an inch in length, Fig. 1 contains two
square inches and Fig. 2 contains six square inches--4 x 11/2. The second
case (2) is a little more difficult to solve. The solution is given in
Figs. 3 and 4. For the purpose of construction, place matches
temporarily on the dotted lines. Then it will be seen that as 3 contains
five equal equilateral triangles and 4 contains fifteen similar
triangles, one figure is three times as large as the other, and exactly
eighteen matches are used.
[Illustration: Figures 1, 2, 3, 4.]
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