Question

Four soccer teams compete in a tournament. Each team faced each other exactly once with no ties allowed. A team received 1 point for each win.

The results
Team 1 had 1 point
Team 2 had 3 points
Team 3 had 1 point
How many points did team 4 have?

Answer 1

1 point

Explanation:

The number of games in the tournament is:

₄C₂ = 6

Another way to look at it: Team 1 plays 3 games against Team 2, 3, and 4. Then, Team 2 plays 2 games against Team 3 and 4 (Team 2 already played Team 1). Finally, Team 3 plays a game against Team 4. So the total is 3 + 2 + 1 = 6.

If there's a total of 6 games, then there's a total of 6 points. So if x is the number of points Team 4 has:

x + 1 + 3 + 1 = 6

x + 5 = 6

x = 1

Team 4 has 1 point.