Task 3. Before the football match between the teams "North" and "South," five predictions were given:

a) there will be no draw;

b) goals will be scored in "South's" net;

c) "North" will win;

d) "North" will not lose;

![](https://cdn.mathpix.com/cropped/2024_05_06_ad0910d2ff8aaa6a488fg-1.jpg?height=315&width=310&top_left_y=910&top_left_x=995)

Fig. 2

e) exactly 3 goals will be scored in the match.

After the match, it turned out that exactly three predictions were correct. What was the final score of the match?
Answer: 1:2.

Solution. Since exactly 3 forecasts are correct, exactly 2 forecasts are incorrect.

First, let's determine which team won. Suppose "North" won. Then 4 forecasts («a», «b», «v» and «g») would be correct, which contradicts the condition.

Suppose the match ended in a draw; then forecasts «a», «v», and «d» are definitely incorrect (since the number of goals scored in a draw is even). Thus, no more than two forecasts are correct, which also contradicts the condition.

Therefore, "North" lost this match. Then forecasts «v» and «G» are incorrect. This means that all the remaining 3 forecasts are correct. Specifically: there was no draw, goals were scored against "South," and exactly 3 goals were scored in the match. Therefore, "South" scored 2 goals. That is, the match ended with a score of $1: 2$.