# Palindromes In Base 11

**Number Theory**Level 3

Let \(n\) be a \(m\)-digit palindromic number (where \(m\geq 2\) is even) in base 10.

What is the units digit of \(n\) when written out in base 11?

If you think the answer depends on the value of \(n\) in base 10, enter -1 as your answer.

**Details and Assumptions:**

The digits allowed in base 11 are digits 0-9 and A where \(\overline{A}_{11}=\overline{10}_{10}\).

If you think the answer depends on the value of \(n\) in base 10, enter -1 as your answer.

If you think the answer is one of the digits 0-9, enter that digit as your answer. If you think the answer is A, enter 10 as your answer.