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 $5 \cdot 10 \cdot 10=\boxed{500}$ 5-digit odd palindromes.

See also

2007 Alabama ARML TST (Problems)
Preceded by:
Problem 4
Followed by:
Problem 6
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