The Optimal Solution to an Impossible Problem

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Join the channel to get exclusive and early videos, original music, lecture videos, and more! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Check out my math fashion brand: https://mathshion.com/ More Math Chats: https://www.youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO Business Inquiries: [email protected] We discuss the optimal solution to the famous 100 prisoners problem. One hundred prisoners all on death row are numbered 1-100. One by one they enter a room with a cupboard of 100 drawers. Each drawer is numbered 1-100 and contains a number 1-100. Each prisoner has the opportunity to open 50 of the 100 drawers to try to find their number. If every prisoner finds their number within 50 drawer openings, they are all pardoned and will live. If even a single prisoner fails, they all die. The optimal solution will take us through permutations and cycles as well as counting and probability. #mathematics #mathproblems #mathpuzzle Textbooks I Like! Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Abstract Algebra: https://amzn.to/3IjoZaO Linear Algebra: https://amzn.to/43xAWEz Calculus: https://amzn.to/3PieD1M Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/4d5HbUQ Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★DONATE★ ◆ Support Wrath of Math on Patreon: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu 0:00 Intro 2:08 Naive Strategy 3:47 Permutations 6:18 The Strategy 7:45 Cycles 10:23 Counting Problematic Cycles 19:27 Probability of Survival 20:40 Final Thoughts