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How an SAT question became a mathematical paradox. Head to https://brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription. Special thanks to our Patreon supporters! Join this list to help us keep our videos free, forever: https://ve42.co/PatreonDEB I invented Snatoms, a molecule modeling kit where the atoms snap together magnetically. Try it at https://ve42.co/SnatomsV 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 – https://ve42.co/Stellarium Thanks to Newspapers.com, a database of historical newspapers – https://ve42.co/Newspapers ▀▀▀ References: Summary of this problem by MindYourDecisions – https://www.youtube.com/watch?v=kN3AOMrnEUs More cool math about this problem by Kyle Hill – https://www.youtube.com/watch?v=_zCDbB9wvrc Discussion of a solar day by MinutePhysics – https://www.youtube.com/watch?v=nZMMuv0Ltyo Murtagh, J. (2023). The SAT Problem That Everybody Got Wrong. Scientific American – https://ve42.co/SATSciAm United Press International (1982). Error Found in S.A.T. Question. New York Times – https://ve42.co/SAT-NYT Yang (2020). What's the hardest SAT math problem that you've seen? Quora – https://ve42.co/SATQuora Coin rotation paradox via Wikipedia – https://ve42.co/CoinParadox Simmons, B. (2015). Circle revolutions rolling around another circle. MathStackExchange. – https://ve42.co/CircleRoll Sidereal time via Wikipedia – https://ve42.co/SiderealWiki Solar Time vs. Sidereal Time via Las Cumbres Observatory – https://ve42.co/SiderealLCO Images & Video: Zotti, G., et al. (2021). The Simulated Sky: Stellarium for Cultural Astronomy Research - https://ve42.co/Stellarium Newspapers from 1980s - 1990s via Newspapers.com – https://ve42.co/Newspapers SAT Practice Test via the College Board – https://ve42.co/PracticeSAT Revolution Definition via NASA – https://ve42.co/RevolutionNASA Revolution Definition via Merriam-Webster – https://ve42.co/RevolutionWebster Earth motion animation via NASA – https://ve42.co/OrbitNASA Satellite animation via NASA – https://ve42.co/SatNASA ▀▀▀ Special thanks to our Patreon supporters: Adam Foreman, Anton Ragin, Balkrishna Heroor, Bernard McGee, Bill Linder, Burt Humburg, Chris Harper, Dave Kircher, Diffbot, Evgeny Skvortsov, Gnare, John H. Austin, Jr., john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Lee Redden, Marinus Kuivenhoven, Max Paladino, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, TTST, Ubiquity Ventures ▀▀▀ 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