[ Tournaments and tournament tables ]  [ Mathematical logic (other) ]

Authors: Fedulkin L.E., Fedulchina E.M.

Before the football match between teams "North" and "South," five predictions were made:

a) there will be no draw;

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

c) "North" will win;

d) "North" will not lose;

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

After the match, it turned out that exactly three of the predictions were correct. What was the final score of the match?
Suppose "North" won. Then 4 predictions ("a", "b", "c", and "d") would be correct, which contradicts the condition.

Suppose the match ended in a draw. Then the predictions "a", "c", and "d" (in a draw, the total number of goals is even) are definitely incorrect, which also contradicts the condition.

Therefore, "North" lost the match. Then predictions "c" and "d" are incorrect, and the remaining 3 predictions are correct. Specifically: there was no draw, goals were scored against "South", and exactly 3 goals were scored in the match. Therefore, the match ended with a score of $1: 2$.

## Answer

$1: 2$.