Puzzles and logic › Tournaments and games › Counting matches
Maximum rounds guaranteeing a four-team condition
University · ●●●●● 200 pts
There are 18 teams in a single round-robin tournament. In each round the 18 teams are divided into 9 pairs, and the two teams in each pair play one match. The teams are regrouped from round to round, and over 17 rounds each team plays exactly one match against each of the other 17 teams. Suppose that after rounds, played according to any feasible schedule, there always exist 4 teams that have played exactly 1 match among themselves in total. Find the maximum possible value of .