In this sentence, the number of occurrences of the digit 0 is __, of the digit 1 is __, of the digit 2 is __, of the digit 3 is __, of the digit 4 is __, of the digit 5 is __, of the digit 6 is __, of the digit 7 is __, of the digit 8 is __, and of the digit 9 is __. The challenge is to fill the blanks with the numerical digits (1, 2, etc.) so that the sentence is true. Can you find the 2 solutions? Sources And Further Reading ↓↓↓\r<br>\r<br>The puzzle is due to the logician Raphael M. Robinson and it was popularized by Douglas Hofstadter in his book Metamagical Themas.\r<br>\r<br>My blog post for this video\r<br>\r<br>\r<br>Sources and further reading\r<br>Douglas Hofstadter Metamagical Themas on Google Books: \r<br>\r<br>Math Central December 2002 Problem. Proof there are only 2 solutions\r<br>\r<br>\r<br>Self descriptive sentences (and two solutions described)\r<br>\r<br>\r<br>Unique solution if all occurrences less than 10\r<br>\r<br>\r<br>Sketch of proof that there are only 2 solutions\r<br>\r<br>\r<br>Solving by iterative process\r<br>\r<br>\r<br>Variations for self-counting sentences\r<br>\r<br>\r<br>\r<br>Autogram (self counting with letters)\r<br>\r<br>\r<br>Variation with letters (autogram)\r<br>\r<br>\r<br>If you like my videos, you can support me at Patreon: \r<br>\r<br>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.\r<br>\r<br>My Blog: \r<br>Twitter: \r<br>Facebook: \r<br>Google+: \r<br>Pinterest: \r<br>Tumblr: \r<br>Instagram: \r<br>Patreon: \r<br>\r<br>Newsletter (sent about 2 times a year): \r<br>\r<br>My Books\r<br>\r<br>The Joy of Game Theory shows how you can use math to out-think your competition. (rated 3.9/5 stars on 24 reviews) \r<br>\r<br>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) \r<br>\r<br>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. \r<br>\r<br>Math Puzzles Volume 2 is a sequel book with more great problems. (rated 5/5 stars on 3 reviews) \r<br>\r<br>Math Puzzles Volume 3 is the third in the . (rated 5/5 stars on 3 reviews) \r<br>\r<br>40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated 4.8/5 stars on 9 reviews) \r<br>\r<br>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) \r<br>\r<br>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 2 reviews)
