"In a barn, 100 chicks sit peacefully in a circle. Suddenly, each chick randomly pecks the chick immediately to its left or right. What is the expected number of unpecked chicks?" This question is from the 2017 Raytheon National MathCounts competition that took place today. It took me like 5 minutes to solve it. Congrats to Luke Robitaille who buzzed in under one second and gave the correct answer! Watch the video for a detailed solution and a pedantic discussion of the wording of the question.

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

If you've been watching my videos, you should know how to solve this! This problem is like guessing on a matching test (https://www.youtube.com/watch?v=h2VMMlpEtRU) or figuring out how many shuffled cards do not move position (https://www.youtube.com/watch?v=oUo53pIplhc).

Some people are confused about the linearity of expectation. It works even if the events are not independent. You can read the discussion at Math Stackexchange and see the linearity of expectation proof is correct: https://math.stackexchange.com..../questions/2282622/e

Sources
https://www.nytimes.com/2017/05/15/us/math-counts-national-competition.html?smid=tw-nytimes&smtyp=cur&_r=0

https://twitter.com/i/web/stat....us/86421683552436224

http://www.businessinsider.com..../espn-math-competiti

http://www.prnewswire.com/news....-releases/luke-robit

https://www.mathcounts.org/national-competition

http://www.espn.com/watch/?id=3034800&_slug_=2017-raytheon-mathcounts-national-competition

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My Books

"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.8/5 stars on 27 reviews) https://www.amazon.com/gp/product/1500497444

"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/1523231467/

"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 4.4/5 stars on 13 reviews. https://www.amazon.com/gp/product/1517421624/

"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/1517531624/

"Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 4 reviews) https://www.amazon.com/gp/product/1517596351/

"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.7/5 stars on 12 reviews) https://www.amazon.com/gp/product/1517319307/

"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 4 reviews) https://www.amazon.com/gp/product/150779651X/

"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 3 reviews) https://www.amazon.com/gp/product/1500866148/