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At the end of a soccer tournament in which any pair of teams played between them exactly once, and in which there were not draws, it was observed that for any three teams

A, B

and C, if

A

defeated

B

and

B

defeated

C

, then

A

defeated

C

. Any team calculated the difference (positive) between the number of games that it won and the number of games it lost. The sum of all these differences was

5000

. How many teams played in the tournament? Find all possible answers.

4

Problems(1)