Just to show you how hard the SATs were, here’s a question (sent by reader Bryan) that I got wrong. I guessed three, assuming that the circumference of the smaller circle (1/3 of the larger), would translate into rotations needed to get around the circumference of the larger circle. How I got a perfect score in 1966 on the math part of the SAT defies me!
At any rate, the correct answer was not one of the SAT’s choices, so nobody got the question right.
Stop the video at 55 seconds in, make your guess, and then watch on.
An explanation of the correct answer for two circles is in the Wikipedia entry for “coin rotation paradox”. You can demonstrate this for yourself by using two coins of equal size.
This trick will make you the hit of any cocktail party—that is, if the cocktail party is full of academics.
ADDENDUM: This gif shows you that a coin rotates twice going around a coin of equal radius. Follow the blue dot from where it starts: you’ll see that it’s gone around once when it’s halfway around the central coin.