The second tournament
After Arsenal's boring string of scoreless draws in the first tournament, Chelsea, Manchester City and Liverpool disinvited the Gunners and asked Manchester United to replace them. As before, each team played exactly one game against every other team.
Fact 1: There were precisely 9 total goals scored.
Fact 2: Manchester United was held scoreless, losing all 3 games by identical margins.
Fact 3: Chelsea played 1-1 draws against both Manchester City and Liverpool.
Fact 4: Manchester City won the tournament.
What was the final score of the Manchester City-Liverpool game?
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1 solution
Chelsea's two 1-1 draws (Fact 3) account for 4 of the 9 total (Fact 1) goals scored.
Since Man United lost all 3 games they played (fact 2) by identical scores, the number of goals in those games must total a multiple of 3. After subtracting the goals from Chelsea's 1-1 draws, only 5 goals are left. Since 2*3 = 6, which is too many, there must have been only 1 goal scored in every Man Utd game, accounting for 3 more goals. That leaves (5-3) = 2 goals left for the one remaining game, Man City vs.Liverpool.
Since Man City won the tournament (fact 4), they must have beaten Liverpool. With 2 goals available for the game the score has to be either 2-0 or 1-1. A 1-1 result would be a draw, not a win, so the score has to be Man City 2, Liverpool 0.