## Task 1 - 240731

During the Peace Race, the following race situation occurred on one stage:

Exactly 14 riders, none of whom were from the GDR, had fallen behind the main field. Exactly $90 \%$ of the riders who had not fallen behind formed the main field; some, but not all, of the GDR riders were among them.

The riders ahead of the main field formed a leading group; it included exactly one twelfth of all the riders in the stage. In the leading group, the Czechoslovak team was the weakest represented, and the Soviet team was the strongest represented.

Determine whether the teams and the number of riders in the leading group can be uniquely determined from these data!

If this is the case, provide these numbers!
If exactly $x$ drivers participated in the stage, then exactly $x-14$ drivers did not fall back, and exactly $10\%$ of these, i.e., $\frac{1}{10}(x-14)$ drivers, formed the leading group. Since this was also $\frac{x}{12}$ drivers, it follows that

$$
\frac{1}{10}(x-14)=\frac{x}{12} \quad \Rightarrow \quad x=84
$$

Thus, since $84: 12=7$, the leading group consisted of exactly 7 drivers.

Among them were also GDR drivers, and at least 2, as there were also Czechoslovak drivers in the leading group, but at least one fewer than GDR drivers.

If there had been at least 3 GDR drivers, then at least 4 Soviet drivers, in contradiction to the fact that among the 7 drivers in the leading group, not only the GDR and Soviet teams were represented.

Thus, it can be uniquely determined: In the leading group, there were exactly 2 GDR drivers, (1) and exactly 1 Czechoslovak driver. (2)

Furthermore, it follows that the Soviet team was represented by 3 or 4 drivers. If it had been exactly 3, then the contradiction would arise that another team had exactly one driver in the leading group, so the Czechoslovak team would not have been the weakest represented there. Thus, it is uniquely determined: In the leading group, the teams of the USSR, GDR, and Czechoslovakia were represented, among them (apart from the drivers mentioned in (1), (2)) exactly 4 Soviet drivers.