Problem From The Hardest Test - Use A Coin To Simulate Any Probability

How can you simulate any probability from a fair coin? What if you had an unfair coin? This is a great problem from the the Putnam Exam, which has legendary difficulty: the average (median) score is usually 1 out of a possible 120 points. No calculators allowed though, and you have to prove everything very carefully. My blog post for this video http://wp.me/p6aMk-50o Thanks to all patrons! Special thanks to: Kyle Shrihari Puranik If you like my videos, you can support me at Patreon:   / mindyourdecisions   Sources 1989 Putnam exam, problem A-4 http://www.math.hawaii.edu/~dale/putn... Sorta Insightful http://www.alexirpan.com/2015/08/23/s... Not really blogging https://amakelov.wordpress.com/2013/1... Janko Gravner's course Math 189 problem set 11 https://www.math.ucdavis.edu/~gravner... Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog: http://mindyourdecisions.com/blog/ Twitter:   / preshtalwalkar   Facebook:   / 168446714965   Google+: https://plus.google.com/1083366085665... Pinterest:   / preshtalwalkar   Tumblr:   / preshtalwalkar   Instagram:   / preshtalwalkar   Patreon:   / mindyourdecisions   Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.9/5 stars on 26 reviews) https://www.amazon.com/gp/product/150... "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 2 reviews) https://www.amazon.com/gp/product/152... "Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 12 reviews. https://www.amazon.com/gp/product/151... "Math Puzzles Volume 2" is a sequel book with more great problems. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/151... "Math Puzzles Volume 3" is the third in the series. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/151... "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.8/5 stars on 9 reviews) https://www.amazon.com/gp/product/151... "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 3 reviews) https://www.amazon.com/gp/product/150... "Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 2 reviews) https://www.amazon.com/gp/product/150...