Percentiles and Box Plots · Superchallenge problem

A data set consists of ten different whole numbers. Its five-number summary (minimum, $Q_1$, median, $Q_3$, maximum) is $1, 6, 10, 15, 30$, where $Q_1$ and $Q_3$ are the medians of the lower five and upper five values. How many different data sets are possible?