Miraculous Solution To HARD Test Problem

This one stumped me! This problem is part of the AIME, a qualifying test for the US Mathematical Olympiad team. The talented students who take the AIME only average about 20 percent--it's a hard test! Plus no calculators are allowed. Can you figure out this problem from the 1987 test? Learn the trick which results in a miraculous solution. Thanks to all patrons! Special thanks this month to: Michael Anvari, Shrihari Puranik, Richard Ohnemus, Kyle. Art of problem solving proof https://artofproblemsolving.com/wiki/index.php/1987_AIME_Problems/Problem_14 Sophie Germain's story is worth reading (the video has a hyphen in her name by mistake) https://en.wikipedia.org/wiki/Sophie_Germain Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g This is the only channel to feature math topics suggested by people around the world. Support on Patreon to inspire mathematical discovery and make the world a better place: https://www.patreon.com/mindyourdecisions If you buy from the links below I may receive a commission for sales. This has no effect on the price for you. Show your support! Get a mug, a t-shirt, and more at Teespring, the official site for Mind Your Decisions merchandise: https://teespring.com/stores/mind-your-decisions My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 4.0/5 stars on 38 reviews) http://amzn.to/1uQvA20 "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 3.5/5 stars on 4 reviews) http://amzn.to/1o3FaAg "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. http://amzn.to/1GhUUSH "Math Puzzles Volume 2" is a sequel book with more great problems. (rated 4.5/5 stars on 6 reviews) http://amzn.to/1NKbyCs "Math Puzzles Volume 3" is the third in the series. (rated 4/5 stars on 6 reviews) http://amzn.to/1NKbGlp "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.4/5 stars on 13 reviews) http://amzn.to/1LOCI4U "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.8/5 stars on 5 reviews) http://amzn.to/18maAdo "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 4.3/5 stars on 6 reviews) http://amzn.to/XRm7M4 Connect with me My Blog: https://mindyourdecisions.com/blog/ Twitter: https://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965 Pinterest: https://www.pinterest.com/preshtalwalkar/ Tumblr: https://preshtalwalkar.tumblr.com/ Instagram: https://instagram.com/preshtalwalkar/ Patreon: https://www.patreon.com/mindyourdecisions Newsletter (sent only for big news, like a new book release): http://eepurl.com/KvS0r