2
$\begingroup$

Moderator Note: This was taken from a contest which ended on 22 Oct 2012.

Suppose we take 3 blocks shaped like equilateral triangles that measure 18 units on a side,and place them centrally upon axles that are themselves the vertices of an equilateral triangle measuring 30 units on a side. Suppose we wrap a durable rubber-band about the three blocks(as depicted by the bold black triangle) and paint a dot on the portion of the band that intersects the top vetex of the "top block". Then the three blocks are rotated at equal speeds- the rubber band rotates with them without slipping or expanding. The question: how far has the dot painted on the band travelled by the time it returns to its original position at the top vertex?

2 Answers 2