MathDB

At a party there were some couples attending. As they arrive each person gets to talk with all the other persons which are already in the room. During the party, after all the guests arrive, groups of persons form, such that no two persons forming a couple belong to the same group, and for each two persons that do not form a couple, there is one and only one group to which both belong. Find the number of couples attending the party, knowing that there are less groups than persons at the party.

Problem Statement