This graph will tell you if a number is divisible by 7. Start at the circle YES. Move a number of black arrows equal to the first (leftmost) digit of the number. Then move one green arrow to get to the next digit. Repeat this for each digit (except don't move a green arrow for the last digit). If you end up at YES, then the number is divisible by 7. Blog post (with proof): http://mindyourdecisions.com/blog/2015/07/26/divisibility-by-7-test-using-a-graph-why-does-it-work-sunday-puzzle/#.VbV4SvlVhBc Sources Tanya Khovanova's Math Blog, Guest Blogger David Wilson http://blog.tanyakhovanova.com/2010/08/divisibility-by-7-is-a-walk-on-a-graph-ii-2/ http://blog.tanyakhovanova.com/2009/08/divisibility-by-7-is-a-walk-on-a-graph-by-david-wilson/ http://www.quora.com/What-is-the-process-of-creating-this-automata-for-checking-divisibility-by-7 http://math.stackexchange.com/questions/413296/how-does-the-divisibility-graphs-work If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog: http://mindyourdecisions.com/blog/ Twitter: http://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965 Google+: https://plus.google.com/108336608566588374147/posts Pinterest: https://www.pinterest.com/preshtalwalkar/ Tumblr: http://preshtalwalkar.tumblr.com/ Instagram: https://instagram.com/preshtalwalkar/ Patreon: http://www.patreon.com/mindyourdecisions Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 4/5 stars on 23 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 1 review) 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 4.5/5 stars on 11 reviews. https://www.amazon.com/gp/product/1517421624/ "Math Puzzles Volume 2" is a sequel book with more great problems. https://www.amazon.com/gp/product/1517531624/ "Math Puzzles Volume 3" is the third in the series. https://www.amazon.com/gp/product/1517596351/ "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 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 3 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 1 review) https://www.amazon.com/gp/product/1500866148/