Combinatorics · Tournaments · Round robin · Extremal example · Double counting
Sixteen teams take part in a basketball tournament played as a double round robin: every two teams meet exactly twice. The eight best-placed teams qualify for the next tournament. Teams are ranked by the number of games they won, and if several teams have the same number of wins, their order among themselves is decided by drawing lots.
What is the smallest number of wins that is certain to secure a team's qualification?
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Serbian Regional Competition 2017, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source