Question 12
The two-digit number $\overline{ab}$ and the number $\overline{ab}+45$ are said to be similar if the sum of the digits of $\overline{ab}$ is the same as the sum of the digits of $\overline{ab}+45$. For example: 15 and $15+45=60$ are similar because the sum of the digits of each number is 6. How many pairs of similar numbers are there?