IMO Shortlist 2006 problem C5

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Dodao/la: arhiva
2. travnja 2012.
An (n, k) - tournament is a contest with n players held in k rounds such that:

(i) Each player plays in each round, and every two players meet at most once.
(ii) If player A meets player B in round i, player C meets player D in round i, and player A meets player C in round j, then player B meets player D in round j.

Determine all pairs (n, k) for which there exists an (n, k) - tournament.
Izvor: Međunarodna matematička olimpijada, shortlist 2006