MathDB

5

Part of 1991 Poland - Second Round

Problems(1)

2-element subests of 1-n

Source: Polish MO Recond Round 1991 p5

9/9/2024
P1,P2,…,Pn P_1, P_2, \ldots, P_n are different two-element subsets of {1,2,…,n} \{1,2,\ldots,n\} . The sets Pi P_i , Pj P_j for i≠j i\neq j have a common element if and only if the set {i,j} \{i,j\} is one of the sets P1,P2,…,Pn P_1, P_2, \ldots, P_n . Prove that each of the numbers 1,2,…,n 1,2,\ldots,n is a common element of exactly two sets from P1,P2,…,Pn P_1, P_2, \ldots, P_n .
combinatoricsSubsets