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UKMT Cayley Olympiad, 2017

Combinatorics Difficulty 3.0 AMC 10/12 Prove it United Kingdom

In a sports league there are four teams and every team plays every other team once. A team scores 3 points for a win, 1 point for a draw, and 0 points for a loss. What is the smallest number of points that a team could have at the end of the league and still score more points than each of the other teams?

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