N is a positive base ten integer having at least 2-digits but at most 4-digits, which is obtained by multiplying the sum of its digits with the product of its digits. It is known that N cannot contain any leading zero.

Determine all possible value(s) of N.

I find 518 unique products, using numbers between 11 and 9999, but excluding any where zero occurs after a non-zero digit (or 519 to allow for a product of zero if non-leading zero allowed)..  

Posted by ed bottemiller on 2010-06-21 15:10:20