Percentiles and Box Plots · Superchallenge problem

A data set has $n$ different values. $Q_1$ is the median of the lower half (the overall median excluded when $n$ is odd), and the percentile of a number is the percent of the data strictly below it. For how many $n$ with $10 \le n \le 100$ is $Q_1$ exactly at the $25$th percentile?