गणित का जादू । एक पहेली जिसका जवाब जानते हुए भी वो समझ नही आती। Smarter Every Day से Destin (https://ve42.co/SED), Tibees से Toby (https://ve42.co/Tibees)और Jabrils से Jabril (https://ve42.co/Jabrils) का धन्यवाद इस दिमाग घुमाने वाली पहेली पर समय देने के लिए । Luke West का धन्यवाद plots बनाने के लिए और गणित में सहायता करने के लिए । Dr. Eugene Curtin और Dr. Max Warshauer का धन्यवाद इस प्रोब्लम पर लिखे इस article के लिए और हमे ये article समझाने के लिए Dr. John Baez का धन्यवाद अलग अलग तरीके से गणना करने में सहायता करने के लिए। Simon Pampena का धन्यवाद अपने योगदान और analysis के लिए । 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/ Patreon supporters का अलग से धन्यवाद: 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