# Problem B. 4690. (February 2015)

**B. 4690.** 9 mathematicians of a university went to a conference together. Since the presentations were boring, they fell asleep several times, each of them at most 4 times. For any pair of mathematicians, there was a time when they were both sleeping. Show that there was a time instant when at least three of them were sleeping.

(5 pont)

**Deadline expired on March 10, 2015.**

### Statistics:

82 students sent a solution. 5 points: 56 students. 4 points: 8 students. 3 points: 3 students. 2 points: 4 students. 1 point: 6 students. 0 point: 5 students.

Problems in Mathematics of KöMaL, February 2015