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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Need some math theory help over here | Comment 12 of 15 |
(In reply to Need some math theory help over here by Bryan)

I agree entirely with your analysis. This is one of those problems that is (or seems to be) obvious at first glance, the the problem is the actual proof. Not being a proof guy myself, I'll tell you I thought about the same method, and left it at that.
  Posted by Cory Taylor on 2003-03-06 04:57:23

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