IMO Shortlist 2004 problem C6


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2. travnja 2012.
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For an {n\times n} matrix A, let X_{i} be the set of entries in row i, and Y_{j} the set of entries in column j, {1\leq i,j\leq n}. We say that A is golden if {X_{1},\dots ,X_{n},Y_{1},\dots ,Y_{n}} are distinct sets. Find the least integer n such that there exists a {2004\times 2004} golden matrix with entries in the set {\{1,2,\dots ,n\}}.
Izvor: Međunarodna matematička olimpijada, shortlist 2004