Consider this classic scheduling problem: for a certain lecture room, we are given the start and end times of a set of classes that could be assigned to the room. We wish to create a schedule that maximizes the number of classes offered in the room, so that none of them overlap in time. (The remaining classes are assigned to other rooms.) Note that there may be more than one optimal schedule! A bold 376 classmate claims to have come up with an algorithm that will always produce an optimal schedule, which works as follows