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UKMT Pink Kangaroo, 2026

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

In the first round of a chess tournament, each player plays against every other player exactly once. A player gets 3, 1 or $-1$ points respectively for winning, drawing or losing a match. At the end of the first round, the sum of the scores of all the players is 90. How many players are there in the tournament?

(A) $10$ (B) $11$ (C) $12$ (D) $13$ (E) $14$

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