An infinite number of participants gathered for the Olympiad, who were registered under the numbers 1,2,…. It turns out that for every n=1,2,… a participant with number n has at least n friends among the remaining participants (note: friendship is mutual). There is a hotel with an infinite number of double rooms. Prove that the participants can be accommodated in double rooms so that there is a couple of friends in each room.Proposed by V. Bragin, P. Kozhevnikov graph theorycombinatoricsKvant