Combinatorics · Round robin tournaments · Scoring arguments · Extremal bounds
Eight players took part in a chess tournament, and each of them played exactly one game against every other participant. A win earns \(1\) point, a loss \(0\) points, and a draw \(0.5\) points for each of the two players.
When the tournament ended, no two participants had the same total, and the second-placed player had scored exactly as many points as the last four players scored together.
What was the result of the game between the third-placed and the seventh-placed player?
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Serbian Municipal Competition 2021, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source