Question

How many $7$ -digit palindromes (numbers that read the same backward as forward) can be formed using the digits $2, 2, 3, 3, 5, 5, 5?$

$6$

$12$

$24$

$36$

$48$

Answer: A

Concepts:palindrome permutations parity

Difficulty rating: 1170

Solution:

A $7$ -digit palindrome has the form with the middle digit used once and the outer three digits each used twice. Only $5$ appears an odd number of times, so $5$ must be the middle digit.

The remaining digits $2,3,5$ fill the first three positions in some order and mirror to the last three. There are $3!=6$ such orderings.

Thus, the correct answer is A.

2009 AMC 10B Problem 11

Answer: A

Difficulty rating: 1170

Solution:

Problem 11 in Other Years