The big match

Back in the days when smoking was popular it was common to find puzzles that involved rearranging matches to form different shapes. Here is a tricky one that Pythagoras would probably have been proud of. I first came across this puzzle in Martin Gardner's superb book "Mathematical Puzzles and Diversions".

The puzzle

Given that a match is one unit long, it is possible to arrange 12 matches on a table in various ways to form polygons with areas that are exactly whole numbers. Two such examples are shown below, a square with an area of 9 square units and a cross with an area of 5 square units. The problem is to use all 12 matches to form the perimeter of a polygon with an area of exactly 4 square units.

Two polygons

Click here for the solution.

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