Problem:
How many two-digit numbers have digits whose sum is a perfect square?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The sum of the digits of a two-digit number is at most . This means the only possible perfect square sums are and . Each square has the following two-digit possibilities:
There are two-digit numbers in all.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions