Problem

Source: 2019 China North MO, Problem 4

Tags: combinatorics



A manager of a company has 8 workers. One day, he holds a few meetings. (1)Each meeting lasts 1 hour, no break between two meetings. (2)Three workers attend each meeting. (3)Any two workers have attended at least one common meeting. (4)Any worker cannot leave until he finishes all his meetings. Then, how long does the worker who works the longest work at least?