Determine all possible values of a positive integer N such that the product of the nonzero digits in the baseN representation of 2009 (base ten) is equal to 18 (base ten).
(In reply to
computer solution (spoiler) by Charlie)
In retrospect, it looks as if an analytic solution might be based on factoring 2009 in various possible ways and coming up with polynomials that could be solved a base, though this might still lead to a large number of polynomials to solve given that the order is important, and you don't know how many 0's or 1's to include.

Posted by Charlie
on 20100613 14:45:57 