The Online Math Olympiad is a contest for high school students with challenging problem. This 2016 test had an average score of 9 out of 30. This video is an adaption of problem 16 which is an interesting probability puzzle. At the end of day 0, six magical seeds are planted. On each day following, each seed has a chance to magically transform into an apple tree with a probability of 1/2. Once a seed transforms into an apple tree, it stays an apple tree and survives indefinitely. What is the expected number of days until all six seeds have become apple trees? Can you figure it out?

Thanks to:
Arbitrary Renaissance (https://www.youtube.com/user/ExplosiveBrohoof/) for suggesting the problem and writing up a solution to fill in details from the official solution.

My blog post for this video:
https://wp.me/p6aMk-5oy

Source
Adapted from Fall 2016 OMO Problem 16: http://internetolympiad.org/ar....chive/OMOFall16/OMOF

Online Math Olympaid homepage:
http://internetolympiad.org/

Alex Knudson derivation of solution using Markov chains
http://allmathsconsidered.com/....2018/01/16/a-respons

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