MathDB
What is the largest possible value of k ?

Source:

October 7, 2010
combinatorics unsolvedcombinatorics

Problem Statement

The set XX has 19831983 members. There exists a family of subsets {S1,S2,…,Sk}\{S_1, S_2, \ldots , S_k \} such that: (i) the union of any three of these subsets is the entire set XX, while (ii) the union of any two of them contains at most 19791979 members. What is the largest possible value of k?k ?
Back to ProblemsView on AoPS