MIND-BENDING LOGIC PUZZLE - The Self-Counting Sentence

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
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The puzzle is due to the logician Raphael M. Robinson and it was popularized by Douglas Hofstadter in his book Metamagical Themas.\r
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My blog post for this video\r
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Sources and further reading\r
Douglas Hofstadter Metamagical Themas on Google Books: \r
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Math Central December 2002 Problem. Proof there are only 2 solutions\r
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Self descriptive sentences (and two solutions described)\r
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Unique solution if all occurrences less than 10\r
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Sketch of proof that there are only 2 solutions\r
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Solving by iterative process\r
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Variations for self-counting sentences\r
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Autogram (self counting with letters)\r
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Variation with letters (autogram)\r
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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
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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
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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
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40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated 4.8/5 stars on 9 reviews) \r
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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)