# The triangular football

The boys of my school formed three teams to play a triangular football tournament in which each team faced only once against the other teams. As usual, two points were awarded to the winner of the match, one in case of a tie and zero to the loser.

There was the curious circumstance that each team scored a single goal throughout the tournament and yet the classification was as follows:

The red team scored 3 points, the green team 2 and the blue team 1.

What was the result of the match that faced the green team with the blue one?

#### Solution

The result was: Green team 1, blue team 1.

The explanation is as follows: To get 3 points the red team had to win a match and tie another one and as it only scored a goal in the entire tournament, it had to win a 1-0 match and tie the other match 0-0.

The blue team that got a single point had to tie one game and lose the other so the results should be 1-1 for the draw and 0-1 for the game that lost. This means that the draw had to be achieved with the green team, which had to tie zero with the red team so the result of the match that faced the green team with the blue was 1-1.

 Match Outcome Red vs green 0 - 0 Red vs blue 1 - 0 Green vs Blue 1 - 1