Can You Solve This Australian Exam Question?

February 12, 2016 | Elizabeth Knowles

Two dodecagonal (12-sided) coins resting side by side. What is the angle formed between the two coins

It went viral after students were stumped.

This question went viral after it stumped grade 12 students in Australia. There are two ways to think about the problem.

1. x is double an exterior angle

If you think about the exterior angles of the coin (those in blue shown below), they form a total of 360 degrees, as is true for all convex polygons (triangles, squares, hexagons, etc.). In this case, the coin is a dodecagon and thus has 12 sides, 12 corners and 12 equal angles. We can figure out that a single angle is 360/12=30 degrees, so x = 60 degrees.


2. Three dodecagons will leave an equilateral triangle

When dodecagons tile a flat surface, they leave equilateral triangles between them. If we look at the image below, we can see that the angle x is one of the three interior angles of the green equilateral triangle and therefore must be 60 degrees.


dodecahedrons, equilateral triangles in the gaps

Try this puzzle next: Can You Solve The “Connect The Towns” Math Puzzle?

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