Problem:
Find the least positive integer such that no matter how is expressed as the product of two positive integers, at least one of these two integers contains the digit .
Solution:
The number can be expressed as the product of and , neither of which contains the digit 0 for . Since , and all other pairs of positive integers whose product is contain at least one trailing , the requested value of is .
The problems on this page are the property of the MAA's American Mathematics Competitions