Involutions and bijections
Source: Kvant Magazine No. 1 2020, 50th Anniversary, M1069
March 10, 2023
combinatoricsfunctionKvant
Problem Statement
Every day, some pairs of families living in a city may choose to exchange their apartments. A family may only participate in one exchange in a day. Prove that any complex exchange of apartments between several families can be carried out in two days.Proposed by N. Konstantinov and A. Shnirelman