In the first round of the FIFA World Cup, there are groups of 4 teams, which play each other in order to qualify to the second round. It is generally said that if a team wins its two first matches, it is assured its qualification. Is this true?
Some notes for non-soccer fans... The two top teams (points-wise, or after tie-breaking rules are applied) in each group qualify for the next round. Each team plays the three others. A win gives three points; a draw, one, and a loss, zero.
Assume A beats B, B beats C, C beats A, and everybody beats D: three teams (A, B, and C) would finish with 6 points, needing tie-breaking, and D would have 0 points. (Everybody tying with D would also work: A, B, and C would have 4 points, and D just 3.)
1st day: A beats D, B beats C.
2nd day: A beats B, C beats D.
3rd day: C beats A, B beats D.
A won its two first matches, but could not qualify because of tie-breaking rules.
Spoiler
