Problem:
How many three-digit numbers satisfy the property that the middle digit is the average of the first and the last digits?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The first and last digits must be both odd or both even for their average to be an integer. There are odd-odd combinations for the first and last digits. There are even-even combinations that do not use zero as the first digit. Hence the total is .
The problems on this page are the property of the MAA's American Mathematics Competitions