Problem:
Find the sum of all positive two-digit integers that are divisible by each of their digits.
Solution:
Let represent the tens digit and the units digit of an integer with the required property. Then must be divisible by both and . It follows that must be divisible by , and that must be divisible by . The former condition requires that for some positive integer , and the latter condition implies that or or . Thus the requested two-digit numbers are , and . Their sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions