Problem:
Given that
and are both integers between 100 and 999, inclusive;
is the number formed by reversing the digits of ; and
.
How many distinct values of are possible?
Solution:
Let the hundreds, tens, and units digits of be , and , respectively. Then , and . Since and are between and , inclusive, must be between and , inclusive. Thus there are possible values for .
The problems on this page are the property of the MAA's American Mathematics Competitions