Coin rolling around a coin

A small coin of radius 1 rolls without slipping all the way around the outside of a fixed coin of radius 3, returning to its start. How many full rotations does the small coin make (relative to the ground)?

Show hints (2)+
  1. The small coin's center traces a circle of radius R+rR+r, not RR.
  2. Rotations =center pathown circumference=R+rr= \frac{\text{center path}}{\text{own circumference}} = \frac{R+r}{r}.

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Asked at: Optiver, SIG

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