Question

Show that in any set of six classes, each meeting regularly once a week on a

particular day of the week, there must be two that meet on the same day,

assuming that no classes are held on weekends.

Answer 1

There are six classes (pigeons), but only five weekdays (pigeonholes). Therefore, by the pigeonhole principle, at least $\lceil\dfrac{6}{5}\rceil=2$ classes must be held on the same day.