MathDB

36

Part of 1983 IMO Longlists

Problems(1)

What is the largest possible value of k ?

Source:

10/7/2010
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 ?
combinatorics unsolvedcombinatorics