MathDB

201

Part of 1951 Moscow Mathematical Olympiad

Problems(1)

MMO 201 Moscow MO 1951 20 problems to 20 students

Source:

8/7/2019
To prepare for an Olympiad 2020 students went to a coach. The coach gave them 2020 problems and it turned out that
(a) each of the students solved two problems and (b) each problem was solved by twostudents.
Prove that it is possible to organize the coaching so that each student would discuss one of the problems that (s)he had solved, and so that all problems would be discussed.
combinatorics