The tournament
Chelsea, Liverpool, Manchester City and Arsenal play a small tournament, each team playing one game against each of the other three.
You are given the following information:
Fact 1. Arsenal did not score a goal but did not lose a game.
Fact 2: 5 total goals were scored.
Fact 3: Manchester City scored 2 total goals and finished with 3 draws.
Fact 4: Liverpool won the tournament.
What was the final score of the Liverpool-Chelsea game?
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1 solution
By fact 1, all three of Arsenal's games finished 0-0.
By fact 3, Manchester City's opponents finished with exactly 2 goals scored, since Man City has 2 goals scored and drew every opponent.
This accounts for every game except Liverpool vs. Chelsea, and 4 of the (by fact 2) 5 goals scored. That leaves 1 goal for the Liverpool-Chelsea game, and since Liverpool won the tournament, they must have scored it..