Solving An INSANELY Hard Viral Math Problem

This seemingly simple viral problem is a lot harder than it looks--it is actually a problem from a university level mathematics textbook! In order to solve the problem, we take a journey through symmetry and group theory which leads to a simple formula for solving these kinds of equations. Thanks to all patrons! Special thanks this month to: Kyle, Michael Anvari, Richard Ohnemus, Shrihari Puranik. 0:00 Problem 1:44 Numerical solution 2:37 Symmetric polynomials 4:15 Power sum polynomials 5:03 Elementary symmetric polynomials 5:46 Deriving Girard-Newton identities 8:14 Girard-Newton identities 9:28 Solution References/alternate methods listed in my blog post https://wp.me/p6aMk-8z8/#sources Multiply by lines and introduction to group theory https://youtu.be/LmVt_KiyDC4 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can't always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to make videos. Be prepared--animation is time consuming and software can be expensive! Why are there comments before the video is published? Get early access and support the channel on Patreon https://www.patreon.com/mindyourdecisions If you buy from the links below I may receive a commission for sales. (As an Amazon Associate I earn from qualifying purchases.) 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 (worldwide links) https://mindyourdecisions.com/blog/my-books/#worldwide My Books (US links) Mind Your Decisions: Five Book Compilation https://amzn.to/2pbJ4wR A collection of 5 books: "The Joy of Game Theory" rated 4.1/5 stars on 45 reviews http://amzn.to/1uQvA20 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 3.5/5 stars on 4 reviews http://amzn.to/1o3FaAg "40 Paradoxes in Logic, Probability, and Game Theory" rated 4.1/5 stars on 14 reviews http://amzn.to/1LOCI4U "The Best Mental Math Tricks" rated 4.7/5 stars on 8 reviews http://amzn.to/18maAdo "Multiply Numbers By Drawing Lines" rated 4.3/5 stars on 6 reviews http://amzn.to/XRm7M4 Mind Your Puzzles: Collection Of Volumes 1 To 3 https://amzn.to/2mMdrJr A collection of 3 books: "Math Puzzles Volume 1" rated 4.4/5 stars on 13 reviews http://amzn.to/1GhUUSH "Math Puzzles Volume 2" rated 4.5/5 stars on 6 reviews http://amzn.to/1NKbyCs "Math Puzzles Volume 3" rated 4.1/5 stars on 7 reviews http://amzn.to/1NKbGlp Connect with me My Blog: https://mindyourdecisions.com/blog/ Twitter: https://twitter.com/preshtalwalkar Newsletter (sent only for big news, like a new book release): http://eepurl.com/KvS0r 2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.