IMO 2006 Shortlist C5
An (n,k)-tournament is a contest with n players held in k rounds such that: (i) Each player plays in each round, and eve...
Category: Combinatorics
Problem
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. (Argentina)