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How an SAT question became a mathematical paradox. Head to to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.

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Huge thanks to Dr. Doug Jungreis for taking the time to speak with us about this SAT question.
Thanks to Stellarium, a wonderful free astronomy simulator –
Thanks to Newspapers.com, a database of historical newspapers –

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References:
Summary of this problem by MindYourDecisions –
More cool math about this problem by Kyle Hill –
Discussion of a solar day by MinutePhysics –
Murtagh, J. (2023). The SAT Problem That Everybody Got Wrong. Scientific American –
United Press International (1982). Error Found in S.A.T. Question. New York Times –
Yang (2020). What's the hardest SAT math problem that you've seen? Quora –
Coin rotation paradox via Wikipedia –
Simmons, B. (2015). Circle revolutions rolling around another circle. MathStackExchange. –
Sidereal time via Wikipedia –
Solar Time vs. Sidereal Time via Las Cumbres Observatory –

Images & Video:
Zotti, G., et al. (2021). The Simulated Sky: Stellarium for Cultural Astronomy Research -
Newspapers from 1980s - 1990s via Newspapers.com –
SAT Practice Test via the College Board –
Revolution Definition via NASA –
Revolution Definition via Merriam-Webster –
Earth motion animation via NASA –
Satellite animation via NASA –

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Special thanks to our Patreon supporters:
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Directed by Emily Zhang
Written by Emily Zhang and Gregor Čavlović
Edited by Peter Nelson
Animated by Ivy Tello and Fabio Albertelli
Filmed by Derek Muller
Produced by Emily Zhang, Han Evans, Gregor Čavlović, and Derek Muller

Thumbnail by Ren Hurley
Additional video/photos supplied by Getty Images and Pond5
Music from Epidemic Sound

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