Problem:
How many three-digit numbers are not divisible by , have digits that sum to less than , and have the first digit equal to the third digit?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Each such three-digit number must have the form , where and are digits and . Such a number will not be divisible by if and only if . If is equal to , or , then any of the ten choices for satisfies the requirement. If is equal to , or , then there are , or choices for , respectively. This results in numbers.
The problems on this page are the property of the MAA's American Mathematics Competitions