Problem:
How many digit palindromes (numbers that read the same backward as forward) can be formed using the digits ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because the digit appears three times, must be the middle digit of any such palindrome. In the first three digits each of , and must appear once and the order in which they appear determines the last three digits. Since there are ways to order three distinct digits the number of palindromes is .
The problems on this page are the property of the MAA's American Mathematics Competitions