Five football teams held a tournament - each team played against each other once. 3 points were awarded for a win, 1 point for a draw, and no points for a loss. Four teams scored 1, 2, 5, and 7 points respectively. How many points did the fifth team score?

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Each team played 4 games. It is clear that the first team drew once and lost the rest of the games. The second team has two draws and two losses. The third team could not have scored five points with draws alone, so it must have won once, in addition to having two draws and one loss. The fourth team won twice (otherwise, it would have scored no more than 6 points). This team also has one draw and one loss. In the end, the first four teams won 3 times and lost 7 times. However, the number of wins should equal the number of losses. Therefore, they lost 4 times to the fifth team, and that team has 12 points.

Example of a tournament with such a distribution of points: the fifth team won against everyone, the fourth team won against the first and second, the third team won against the first, and all other games ended in draws.

## Answer

12 points.