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Numbers of letters of numbers of letters of... (Posted on 2006-09-10) Difficulty: 3 of 5
If you take any number you can think of, any integer whatsoever, count the number of letters it takes to write it out fully (with or without any 'and's you may need), then take THAT number and repeat the procedure infinitely, what number (or numbers) does this strange series converge to? Is there a unique solution?

Let's face it, this won't be a challenge. But here's an extra thing or two for you. Do you know if this series converges in every language? If the series converges, what number does it converge to? Do they have a unique solution? Can you tell of any language(s) in which does this series not converge?

Note: What if you converted this series into cardinal numbers instead (34 = thirty fourth [12 letters] then 12 = etc.)? How many possible convergence values are there in English or any other language you know?

No Solution Yet Submitted by Alexis    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Spanish | Comment 8 of 15 |
You get convergence to 5 (CINCO letters) or a loop between 4 (CUATRO letters) and 6 (SEIS letters).
  Posted by Federico Kereki on 2006-09-10 14:30:50
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