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# Can You Solve The Mind-Bending Self-Counting Sentence Riddle?

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## Description

"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 ↓↓↓

The puzzle is due to the logician Raphael M. Robinson and it was popularized by Douglas Hofstadter in his book "Metamagical Themas."

My blog post for this video
http://wp.me/p6aMk-4X7

Math Central December 2002 Problem. Proof there are only 2 solutions
http://mathcentral.uregina.ca/mp/archives/previous2002/dec02sol.html

Self descriptive sentences (and two solutions described)
http://www.cut-the-knot.org/ctk/SelfDescriptive.shtml

Unique solution if all occurrences less than 10
http://math.stackexchange.com/questions/19061/puzzle-digit-x-appears-y-times-on-this-piece-of-paper?rq=1

Sketch of proof that there are only 2 solutions

Solving by iterative process
http://web.archive.org/web/20120428023510/http://www.lboro.ac.uk/departments/ma/gallery/selfref/index.html

Variations for self-counting sentences
http://lkozma.net/blog/self-counting-sentences/
http://lkozma.net/blog/self-counting-sentences-ii/

Autogram (self counting with letters)
https://en.wikipedia.org/wiki/Autogram

Variation with letters (autogram)
http://www.braingle.com/news/hallfame.php?path=language/english/sentences/self.ref/self.ref.letters.p&sol=1

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