Solution
Upset in the Round Robin
Show the problem again
Four teams (Rovers, United, City and Albion) each played every other team once. A win is worth 3 points, a draw 1 point and a loss 0. The final points were: Rovers 6, United 5, City 4, Albion 1. No other information survives. Which team beat Rovers?
Worked solution
There are six games, and the points total is $6 + 5 + 4 + 1 = 16$. A decided game gives 3 points and a draw gives 2, so with $w$ decided games and $d$ draws, $3w + 2d = 16$ and $w + d = 6$, giving $w = 4$ and $d = 2$. Each team plays three games, and the only ways to score the given totals are: Rovers 6 = win, win, loss; United 5 = win, draw, draw; City 4 = win, draw, loss; Albion 1 = draw, loss, loss. The two draws use four team-slots: United has two, City one, and Albion one, so the draws are United-City and United-Albion. United's remaining game, against Rovers, must be its win. So United beat Rovers. (The rest is forced too: Rovers beat City and Albion, and City beat Albion, giving 6, 5, 4 and 1 points.) The answer is United.
Source: Original puzzle written for AxiomIQ; reconstructing results from a league table is a standard recreational exercise.