Problem:
A palindrome between and is chosen at random. What is the probability that it is divisible by ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Each four-digit palindrome has digit representation abba with and . The value of the palindrome is . Because is divisible by and is not, the palindrome is divisible by if and only if or . Thus the requested probability is .
The problems on this page are the property of the MAA's American Mathematics Competitions