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Niners (Posted on 2002-10-23) Difficulty: 4 of 5
The set of numbers {9, 99, 999, 9999, ...} has some interesting properties. One of these has to do with factorization. Take any number n that isn't divisible by 2 or by 5. You will be able to find at least one number in the set that is divisible by n. Furthermore, you won't need to look beyond the first n numbers in the set.

Prove it.

(from http://www.ocf.berkeley.edu/~wwu/riddles/)

See The Solution Submitted by levik    
Rating: 4.2500 (8 votes)

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re(2): Need some math theory help over here | Comment 13 of 15 |
(In reply to re: Need some math theory help over here by Cory Taylor)

Another reason the problem excludes 2 and 5 is you can prove that the any number of 9s is NOT divisible by 2 or 5. Since n+1 is divisible by 2 and 5, n must not be.
  Posted by Gamer on 2003-05-03 16:44:52

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