2016 AMC 8 Problems/Problem 11
11. Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is
Solution
We can write the two digit number in the form of ; reverse of
is
. The sum of those numbers is:
We can use brute force to find order pairs
such that
. Since
and
are both digits, both
and
have to be integers less than
. Thus are ordered pairs are
or
ordered pairs