Simons Foundation

Mathematical Impressions: The Bicycle Pulling Puzzle

If you pull straight back on the lower pedal of your bicycle, will the bike move forward or backward? This classic puzzle has a surprising twist.

If you pull straight back on the lower pedal of your bicycle, will the bike move forward or backward? This classic puzzle has a surprising twist, so be sure to think about it carefully before watching the answer in this video. The puzzle is discussed in many publications, but none of them present the whole story shown here, as far as I know.

For partial solutions, see Martin Gardner, Mathematical Carnival (Random House, 1975), p. 182, or D. E. Daykin, “The Bicycle Problem,” Mathematics Magazine 45, no. 1 (Jan. 1972), p. 1.

Thank you to Jamie Swan and Rick Jones for providing the bicycle.

More videos from the Mathematical Impressions series.