MathDB
Biggest number of sets

Source: Serbia TST 2009

April 17, 2009
floor functioncombinatorics unsolvedcombinatorics

Problem Statement

Find the largest natural number n n for which there exist different sets S1,S2,…,Sn S_1,S_2,\ldots,S_n such that: 1∘ 1^\circ ∣Si∪Sj∣≤2004 |S_i\cup S_j|\leq 2004 for each two 1≤i,j≤n 1\leq i,j\le n and 2∘ 2^\circ S_i\cup S_j\cup S_k\equal{}\{1,2,\ldots,2008\} for each three integers 1≤i<j<k≤n 1\le i<j<k\le n.
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