Hey jsweston828.

Without any more assumptions, the best case is 1 sample and the worst case is 35 samples.

I assume the format of the data has the student and the score in every observation and that all students names can be identified outside of the data set (even if you don't have the scores, but only the names).

This is if its not assumed to be ordered: if it's assumed to be ordered it will be a lot easier.