Determine the minimum possible multiple of the base ten number 2011 that begins with a nonzero digit and contains all the digits from 0 to 9 at least once. What is the next smallest number with this property?

This seems like it would require a computer program. 

Would it be worth looking among pandigital numbers (those with each digit exactly once)?  It seems so.  There are 9*9!=3265920 pandigitals so if 1/2011 of them are multiples of 2011 there should be around 1624 solutions. 

One useful property of pandigitals is they are all multiples of 9 so we can actually look at multiples of 2011*9=18099.  I think this may drop the number of expected solutions by a factor of 9 so maybe there should be around 180 solutions.

If I were to write a program I might have it list the multiples of 18099 beginning with 18099*56548=1024005222  which is just over the first pandigital and check each to see if it is a pandigital.  I do not plan to actually do this.

Posted by Jer on 2011-11-10 13:18:42