MathDB

60

Part of 1989 IMO Longlists

Problems(1)

Intersection of all these sets is empty

Source: IMO Longlist 1989, Problem 60

9/18/2008
A family of sets A1,A2,…,An A_1, A_2, \ldots ,A_n has the following properties: (i) Each Ai A_i contains 30 elements. (ii) Ai∩Aj A_i \cap A_j contains exactly one element for all i,j,1≤i<j≤n. i, j, 1 \leq i < j \leq n. Determine the largest possible n n if the intersection of all these sets is empty.
combinatorics unsolvedcombinatorics