Data & Statistics · Superchallenge problem

Five numbers, in increasing order, have a median of $12$ and an IQR of $10$ (here $Q_1$ is the $2$nd value and $Q_3$ is the $4$th). The $2$nd and $4$th values are equally spaced from the median. Find those two values. Then, given that the minimum is $4$ and the mean of all five numbers is $12$, find the maximum.