Append the same digit to the left and right of the number 10 so that the resulting four-digit number is divisible by 12.

#
Let the digit $a$ be appended. Then the resulting number will be written in the form $a 10 a$. Since this number is divisible by 12, it must be divisible by both 4 and 3. This, in turn, means that $a$ is divisible by 4, and $2a + 1$ is divisible by 3. This is only possible when $a=4$.

## Answer

4104.