The 100 Prisoners Riddle feels completely impossible even once you know the answer. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription. Special thanks to Destin of Smarter Every Day (https://ve42.co/SED), Toby of Tibees (https://ve42.co/Tibees), and Jabril of Jabrils (https://ve42.co/Jabrils) for taking the time to think about this mind bending riddle. Huge thanks to Luke West for building plots and for his help with the math. Huge thanks to Dr. Eugene Curtin and Dr. Max Warshauer for their great article on the problem and taking the time to help us understand it: https://ve42.co/CurtinWarshauer Thanks to Dr. John Baez for his help with finding alternate ways to do the calculations. Thanks to Simon Pampena for his input and analysis. Other 100 Prisoners Riddle videos: minutephysics: https://www.youtube.com/watch?v=C5-I0bAuEUE Vsauce2: https://www.youtube.com/watch?v=kOnEEeHZp94 Stand-up Maths: https://www.youtube.com/watch?v=a1DUUnhk3uE TED-Ed: https://www.youtube.com/watch?v=vIdStMTgNl0 ▀▀▀ References: Original paper: Gál, A., & Miltersen, P.B. (2003). The Cell Probe Complexity of Succinct Data Structures. BRICS, Department of Computer Science, University of Aarhus. All rights reserved. – https://ve42.co/GalMiltersen Winkler, P. (2006). Seven Puzzles You Think You Must Not Have Heard Correctly. – https://ve42.co/Winkler2006 The 100 Prisoners Problem – https://ve42.co/100PWiki Golomb, S. & Gaal, P. (1998). On the Number of Permutations on n Objects with Greatest Cycle Length k. Advances in Applied Mathematics, 20(1), 98-107. – https://ve42.co/Golomb1998 Lamb, E. (2012). Puzzling Prisoners Presented to Promote North America's Only Museum of Math. Observations, Scientific American. – https://ve42.co/Lamb2012 Permutations – https://ve42.co/PermutationsWiki Probability that a random permutation of n elements has a cycle of length k greater than n/2, Math SE. – https://ve42.co/BaezProbSE Counting Cycle Structures in Sn, Math SE. – https://ve42.co/CountCyclesSE What is the distribution of cycle lengths in derangements? In particular, expected longest cycle, Math SE. – https://ve42.co/JorikiSE The Manim Community Developers. (2021). Manim - Mathematical Animation Framework (Version v0.13.1). – https://www.manim.community/ ▀▀▀ Special thanks to Patreon supporters: RayJ Johnson, Brian Busbee, Jerome Barakos M.D., Amadeo Bee, Julian Lee, Inconcision, TTST, Balkrishna Heroor, Chris LaClair, Avi Yashchin, John H. Austin, Jr., OnlineBookClub.org, Matthew Gonzalez, Eric Sexton, john kiehl, Diffbot, Gnare, Dave Kircher, Burt Humburg, Blake Byers, Dumky, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Josh Hibschman, Timothy O’Brien, Mac Malkawi, Michael Schneider, jim buckmaster, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Stephen Wilcox, Marinus Kuivenhoven, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal ▀▀▀ Written by Derek Muller and Emily Zhang Filmed by Derek Muller and Petr Lebedev Animation by Ivy Tello and Jesús Rascón Edited by Trenton Oliver Additional video/photos supplied by Getty Images Music from Epidemic Sound and Jonny Hyman Thumbnail by Ignat Berbeci Produced by Derek Muller, Petr Lebedev, and Emily Zhang