Login / Register

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

Thanks! Share it with your friends!


You disliked this video. Thanks for the feedback!

Sorry, only registred users can create playlists.

 Brain Teasers   |   Math
 Find Related Videos  added


"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

Sources and further reading
Douglas Hofstadter "Metamagical Themas" on Google Books:

Math Central December 2002 Problem. Proof there are only 2 solutions

Self descriptive sentences (and two solutions described)

Unique solution if all occurrences less than 10

Sketch of proof that there are only 2 solutions

Solving by iterative process

Variations for self-counting sentences

Autogram (self counting with letters)

Variation with letters (autogram)

If you like my videos, you can support me at Patreon:

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:

Newsletter (sent about 2 times a year):

My Books

"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.9/5 stars on 24 reviews)

"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)

"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.

"Math Puzzles Volume 2" is a sequel book with more great problems. (rated 5/5 stars on 3 reviews)

"Math Puzzles Volume 3" is the third in the series. (rated 5/5 stars on 3 reviews)

"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.8/5 stars on 9 reviews)

"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)

"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)

Post your comment


Be the first to comment