MathDB

Serbian MO 2009

Source:

January 24, 2016

SetscombinatoricsSet systemsSerbiaset theorygraph theoryInclusion-exclusion

Problem Statement

Determine the largest positive integer

n

for which there exist pairwise different sets

\mathbb{S}_1 , ..., \mathbb{S}_n

with the following properties:

1

)

|\mathbb{S}_i \cup \mathbb{S}_j | \leq 2004

for any two indices

1 \leq i, j\leq n

, and

2

)

\mathbb{S}_i \cup \mathbb{S}_j \cup \mathbb{S}_k = \{ 1,2,...,2008 \}

for any

1 \leq i < j < k \leq n

Proposed by Ivan Matic

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