Question 71
Let $\overline{ab}$ be a two-digit integer. A positive integer $n$ is a relative of $\overline{ab}$ if:
i) the units digit of $n$ is also $b$.
ii) the other digits of $n$ are nonzero and sum to $a$.
For example, the relatives of 31 are 31, 121, 211, and 1111. Find all two-digit numbers that divide every one of their relatives.
i) the units digit of $n$ is also $b$.
ii) the other digits of $n$ are nonzero and sum to $a$.
For example, the relatives of 31 are 31, 121, 211, and 1111. Find all two-digit numbers that divide every one of their relatives.