IMO Shortlist 2009 problem C2


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2. travnja 2012.
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For any integer n\geq 2, let N(n) be the maxima number of triples (a_i, b_i, c_i), i=1, \ldots, N(n), consisting of nonnegative integers a_i, b_i and c_i such that the following two conditions are satisfied:
a_i+b_i+c_i=n for all i=1, \ldots, N(n), If i\neq j then a_i\neq a_j, b_i\neq b_j and c_i\neq c_jDetermine N(n) for all n\geq 2.

Proposed by Dan Schwarz, Romania
Izvor: Međunarodna matematička olimpijada, shortlist 2009