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© Copyright 2001, Jim Loy
Part II
Go back to David Coles' Triangle Puzzle (Part I)
7,10: I began to experiment with asymmetry, because
symmetry often produces parallel lines. See part III, where most of the
solutions are highly symmetric. With asymmetry, these former parallel lines
will meet, and maybe produce more triangles. These three figures are not
equivalent to each other. The third one comes from a pentagram (5-pointed
star). The others were experiments in distorted 5-point stars.
8,14 and 9,18: Continuing with asymmetry, above. It is hard to guess if these are optimal or not, except that they are improvements over previous attempts. These were produced with a kind of free-hand drawing technique that doesn't work very well for much more complicated figures. And so, you will see some symmetry later.
10,22: Here is what I mean by symmetry. The first figure in
the diagram on the left is Mr. Coles' solution, which produces 20 triangles. It
was hard to beat that. But hours of experimentation with asymmetry resulted in
the better solution (second figure in the diagram) with 22 triangles.
11,27: On the right is my most difficult experiment with
asymmetry, so far. I have painted every other triangle, to make it easier to
count triangles. Mr. Coles' solution has 26 triangles.
This article is continued in David Coles' Triangle Puzzle (Part III).