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Connected Pentagon

Problem

How many triangles are in a fully connected pentagon?



Solution

By rotational symmetry, all triangles below exist in exactly five other positions.


Making a total of 7 times 5 = 35 triangles in the diagram.

What about a fully connected hexagon?
Can you generalise for n-gons?

Problem ID: 177 (Oct 2004)     Difficulty: 1 Star

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