Putnam Probability Picture Proof

1989 Putnam A4 asks: How to create irrational probabilities using only fair coin flips? Lets visualize the solution! UPDATE: I have now switched back to thinking that the excellent Michael Penn video    • probably a Putnam probability problem   is actually the same solution as my video, but the probability analysis at the very end of that video matches the "Geometric and use digits of alpha solution" I talk about at the end which you can also read here: https://prase.cz/kalva/putnam/psoln/p... . 0:00 1989 Putnam A4 and Michael Penn 1:16 Uniform Random Variable Solution 2:20 Make the Uniform out of Fair Coin flips 5:42 Approximate using finitely many coin flips 6:31 Bounds by asking is U on the left/right? 7:56 Bounds using partial sums 10:25 Example where we need more flips 13:50 Final algorithm to solve problem 14:50 Equivalence to the shorter flip-until-first-heads solution Music: Sneaky Adventure Kevin MacLeod Licensed under Creative Commons: By Attribution 3.0 License http://creativecommons.org/licenses/b...