Not so common a problem.
The curve traced by a point on the circumference of a circle which rolls without slipping on a flat surface in a straight line is known as a cycloid.
In terms of the radius of the circle , what is the length of the path traced by the point in one complete revolution of the circle?
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1 solution
The circle rolls along a path 2 × p i × R long, therefore the start and endpoints must be this distance apart, and the path of the point must be greater as it's not a straight line. 8 × p i is the only answer that satisfies this. If there'd been two answers greater than 2 × p i × R , I would have been stuffed...