This ancient paradox, which is brought to us courtesy of Esther Inglis-Arkell at io9.com, involves two different-sized wheels, one inside another. The two wheels travel in sync over a certain distance as in this animation below:
But should the smaller inside wheel rotate over the same distance as the larger external wheel? As Ms Inglis-Arkell states: If you look at the animated gif above, both wheels use their entire circumference to trace the same amount of distance – the red line. Clearly one circumference is smaller than the other. Either that means that the wheels have the same circumference, which they don’t, or that different circumferences “unroll” to the same length, which they can’t.
What is the solution to this puzzle?
prior probability 
The outside wheel rotates faster than the inside wheel.
Good answer, but why would the speed of the rotation have any effect on the distance travelled between two points?