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 Niners (Posted on 2002-10-23)
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.

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

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 re(4): | Comment 7 of 15 |
(In reply to re(3): by TomM)

I was a little quick with my explanation of Case 2. It is also possible that n can be split into two factors such that one is a factor of N(j-i) and the other is a factor of (10^i), but this would still mean that n is divisible by either 2 or 5 which casewas excluded from the puzzle.
 Posted by TomM on 2002-10-24 01:42:03

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