2007 Alabama ARML TST Problems/Problem 5

Problem

How many positive 5-digit odd integers are palindromes?

Solution

The units digit must be odd, and the ten-thousands digit must be equal to the units digit. So there are 5 possible choices there. Then there are ten choices for the tens and hundreds digits, but the thousands digit is fixed. Therefore there are 5*20*20=500 5-digit odd palindromes.