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.

(In reply to a d1 answer (+background) by Ady TZIDON)

This is an excellent solution.

It is the requisite background knowledge - mostly #5 - that made me think the problem was more of a D2

Posted by Jer on 2013-05-29 12:37:31