\section*{Task 1 - 081211}

At the European Championships for women's rowing in August 1966, the GDR, as the most successful country, received 37 points, and the USSR received 36.5 points. Both countries received exactly one of the three medals awarded in each of the 5 disciplines: Single Sculls, Double Sculls, "Coxed Four," Double Four, and Eight.

How many gold medals, how many silver medals, and how many bronze medals did each of the two countries receive?

The point system is based on the following table.

\begin{tabular}{r|c|c|c} 
& Gold Medal & Silver Medal & Bronze Medal \\
\hline Single Sculls or Double Sculls & 6 & 5 & 4 \\
"Coxed Four" or Double Four & 9 & 7.5 & 6 \\
Eight & 12 & 10 & 8
\end{tabular}

It is also known that the GDR performed better in the Double Sculls than in the Single Sculls and better in the Double Four than in the "Coxed Four." The USSR performed better in the Single Sculls than in the Double Sculls.
}

The USSR has 36.5 points; it must have received a medal in at least one discipline with a non-integer point value. This is only the case for silver medals in the "Coxed Fours" and "Double Fours."

Since there are only two such medals, the GDR can now have received a maximum of one of them. However, this would result in a non-integer total score, but the GDR has 36 points. In the disciplines "Coxed Fours" and "Double Fours," the GDR can only receive a gold or bronze medal. Since it is known that the GDR performed better in the "Double Fours" than in the "Coxed Fours," it follows that the GDR received the bronze medal in the "Coxed Fours" and the gold medal in the "Double Fours."

Thus, the GDR received \(9 + 6 = 15\) points. Therefore, in the remaining three disciplines, the GDR received a total of \(36 - 15 = 21\) points. The maximum possible score here is 24 with three gold medals: \(12 + 6 + 6 = 24\). Since the GDR performed better in the "Double Twos" than in the "Single," it could not have received a gold medal in the "Single," but at most a silver medal, resulting in a maximum score of \(12 + 6 + 5 = 23\).

Since the GDR only has 21 points in the three disciplines, it must have performed worse in (at least) one discipline than "Eights" gold, "Double Twos" gold, "Single" bronze. In the "Eights," the point differences are two points, so exactly one point cannot be lost here. Therefore, it must be exactly one medal worse in "Double Twos" or "Single." If a silver medal had been achieved in the "Double Twos," the GDR would have performed equally well in the "Single," which is not the case. Therefore, a bronze medal must have been achieved in the "Single."

Thus, for the GDR:

Single: Bronze 4

Double Twos: Gold 6

Coxed Fours: Bronze 6

Double Fours: Gold 9

Eights: Gold 12

Total: 3 gold medals, 2 bronze medals, 37 points

For the USSR, considering the impossibility of a gold medal in the disciplines where the GDR has already won, the maximum possible score is \(6 + 5 + 9 + 7.5 + 10 = 37.5\) points.

Since it only has 36.5 points and the point difference of 1 only exists in the "Single" and "Double Twos," it must have been exactly one medal worse in either the "Single" or the "Double Twos."

If it had only the silver medal in the "Single," it would have performed equally well in the "Double Twos," which is not the case. Therefore, the USSR must have received the bronze medal in the "Double Twos."

Thus, for the USSR:

Single: Gold 6

Double Twos: Bronze 4

Coxed Fours: Gold 9

Double Fours: Silver 7.5

Eights: Silver 10

Total: 2 gold medals, 2 silver medals, 1 bronze medal, 36.5 points