Problem:
How many ways are there to write as the sum of twos and threes, ignoring order? (For example, and are two such ways.)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If the sum uses twos and threes, then . Therefore . Both and will be nonnegative integers if and only if is an even integer from to . Thus there are ways to form the sum.
The problems on this page are the property of the MAA's American Mathematics Competitions