Stories of Magic: Witches and Burning Schools Part 3: Binarily Searching for the Culprit

Another building housing the girls just burned down, this one at a slightly earlier time because they have guards hanging out during the times the previous buildings burn.  Still no fire extinguisher.  However, due to a growing shortage of housing, forms 1 and 3 (the forms that don't take national exams) have been sent home.  If they keep splitting the number of girls in half like this and housing the halves in different dorms, they will be able to isolate the arsonist in O log n time.