There's a curious fact about the number 69: it is the only number whose square and cube contains every digit from 0 to 9 without repetition. But how do we know it's the only number? We can prove it using some good old fashioned logic and some help from Google Bard to generate Python code. Today I Learned Reddit https://www.reddit.com/r/todayilearned/comments/12t2d7z/til_that_69_number_is_the_only_natural_number/ https://www.reddit.com/r/todayilearned/comments/g6s7r/til_that_69_is_the_only_number_whose_square_and/ https://www.reddit.com/r/todayilearned/comments/zh18ub/til_69_is_the_only_number_whose_square_4761_and/ Python Tutor https://pythontutor.com/visualize.html#mode=edit AndyMath IG https://www.instagram.com/p/CsAzVS9J0Bx/ ProofWiki proof https://proofwiki.org/wiki/Number_whose_Square_and_Cube_use_all_Digits_Once Collection of tricks https://www.umassmed.edu/bsrc/tricks/ Google Bard AI https://bard.google.com/ Subscribe: null Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay. If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay. Book ratings are from January 2023. 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 4.3/5 stars on 290 reviews http://amzn.to/1uQvA20 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews http://amzn.to/1o3FaAg "40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews http://amzn.to/1LOCI4U "The Best Mental Math Tricks" rated 4.3/5 stars on 116 reviews http://amzn.to/18maAdo "Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 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 112 reviews http://amzn.to/1GhUUSH "Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews http://amzn.to/1NKbyCs "Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews http://amzn.to/1NKbGlp 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. My Blog https://mindyourdecisions.com/blog/ Twitter https://twitter.com/preshtalwalkar Instagram https://www.instagram.com/preshtalwalkar/ Merch null Patreon https://www.patreon.com/mindyourdecisions Press https://mindyourdecisions.com/blog/press