2023 Waseda Junior High School "Investigation"

Problem
Four teams, A, B, C, and D, play a round-robin tournament. The winning team receives 3 points, each team receives 1 point in the event of a draw, and the losing team receives 0 points. After all the round-robin matches were completed, the managers of each team made the following statements. How many points did B, C, and D each score?

• Manager of A "My team's total was 7 points. If we had beaten D, we would have won all our matches."

• Manager of B "My team had no draws."

• Manager of C "The sum of the points of all 4 teams was 16 points."

• Manager of D "My team had a lower score than C."

※Information regarding use
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Solution method