MathDB

3

Part of 2009 Serbia National Math Olympiad

Problems(1)

Serbian MO 2009

Source:

1/24/2016
Determine the largest positive integer nn for which there exist pairwise different sets S1,...,Sn\mathbb{S}_1 , ..., \mathbb{S}_n with the following properties: 11) ∣Si∪Sj∣≤2004|\mathbb{S}_i \cup \mathbb{S}_j | \leq 2004 for any two indices 1≤i,j≤n1 \leq i, j\leq n, and 22) Si∪Sj∪Sk={1,2,...,2008}\mathbb{S}_i \cup \mathbb{S}_j \cup \mathbb{S}_k = \{ 1,2,...,2008 \} for any 1≤i<j<k≤n1 \leq i < j < k \leq n Proposed by Ivan Matic
SetscombinatoricsSet systemsSerbiaset theorygraph theoryInclusion-exclusion