MathDB

10.3

Part of 2023 All-Russian Olympiad Regional Round

Problems(1)

Every 30 sets intersect, then all intersect

Source: ARO Regional stage 2023 10.3=11.3

2/16/2023
Given are 5050 distinct sets of positive integers, each of size 3030, such that every 3030 of them have a common element. Prove that all of them have a common element.
combinatoricsRussia