## Task 2 - 050922

28 students of a class participated in a sports festival. Each one takes part in at least one of the three disciplines: shot put, long jump, and 100-meter dash.

The number of those who participate in both shot put and long jump, but not in the 100-meter dash, is equal to the number of those who only participate in shot put, and is greater than 1.

No participant competes only in the long jump or only in the 100-meter dash.

Six students compete in the two disciplines of shot put and 100-meter dash and do not participate in the long jump.

The number of those who compete in both the long jump and the 100-meter dash is five times the number of those who compete in all three disciplines.

The number of those who compete in all three disciplines is even, but not zero.

How many students compete in each of the three individual disciplines?
If the number of participants in all three disciplines is denoted by $y$, and the number of those who only participate in the shot put by $x$, then $x$ and $y$ must satisfy the following equation:

$$
2 x+5 y+6=28, \quad \text { so } \quad 2 x+5 y=22
$$

Therefore, $y$ must be even. Since it is also given that $y \neq 0$ and $x>1$, (1) is only satisfied for $y=2$ and $x=6$. Thus, the number of participants is:

In the shot put $2 \cdot 6+2+6=20$ students, in the long jump $5 \cdot 2+6=16$ students, and in the 100-m dash $5 \cdot 2+6=16$ students.