Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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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.


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