Problem: Circle A has 1/3 the radius of circle B, and circle A rolls one trip around circle B. How many times will circle A revolve in total?

1982 SAT Question
In the figure above, the radius of circle A is one third the radius of circle B. Starting from position shown in figure, circle A rolls around circle B. At the end of how many revolutions of circle A will the center of circle A first reach its starting point?

(a) 3/2
(b) 3
(c) 6
(d) 9/2
(e) 9

Blog post summary: http://mindyourdecisions.com/b....log/2015/07/05/every

Sources:
http://www.donaldsauter.com/rolling-circles.htm
http://www.nytimes.com/1982/05..../25/us/error-found-i

Also see the Coin Rotation Paradox
https://en.wikipedia.org/wiki/....Coin_rotation_parado

Update: some people have made really cool interactive worksheets at Geogebra. You should check these out!

Rolling Circles: http://tube.geogebra.org/m/787131
Rolling coin paradox: http://tube.geogebra.org/m/112822
A question about a rolling circle: http://tube.geogebra.org/m/107691

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