In a standard league system (with teams), each team has played one match after the first weekend.
Is it always true that the team in 1st place played the team in th place; the team in 2nd place played the team in th place etc.?
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The statement is not always true because of the third criterion for ranking, Goals For. A simple counterexample would be the following: Team A beats Team X by a score of 4:3, while Team B beats Team Y by a score of 2:1. Neither of the first two criteria will separate Teams A & B, nor teams X & Y; then applying the third criterion, Team A would rank ahead of Team B, but Team X would rank ahead of Team Y.