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SciTech Daily Review

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By Russel Dear

Matches have been in common use for over 100 years but it is not known who first thought of using them for puzzles. Maxey Brooke, matchstick puzzlist extraordinaire and author of Tricks, Games and Puzzles with Matches (Dover 1971), thinks the earliest published matchstick puzzle was in douard Lucas's Récréations Mathématiques, written somewhere between 1884 and 1891. Now, of course, they commonly appear on the back of match boxes and in the "childrens' corner" of newspapers and magazines.

A new matchstick problem, devised from an idea by New Zealand teacher Bob Carr, asks you to lay them non-overlapping on a flat surface to form convex polygons, that is, ones having all their corners pointing outwards. If each n-sided polygon is worth n points, the challenge is to lay them to gain the most number of points.

For example, the following arrangement of six matches scores three points for the triangle, four for the square and five for the pentagon, a total of 12.

What is the maximum score you can obtain from six matches?


The best score I've made from six matches is 26 with the configuration at left. Remember, the polygons have to be convex.
2*3 + 1*4 + 2*5 + 1*6 = 26

The fact that so much space is taken up by the thickness of the matches seems to preclude there being a solution for the general case. What if line segments are used instead of matches -- is there a solution for the general case then, I wonder?

Russell Dear is a Mathematician living in Invercargill