7.3. Three eleventh-graders played tic-tac-toe against two ninth-graders (in each match, an eleventh-grader played against a ninth-grader). It is known that Veronika won against Rita, then Yulia won against Svetlana, and Veronika - against Maria, and finally, Maria won against Yulia. What were the names of the eleventh-graders? (Find all possible answers and prove that there are no others)
Solution. Veronica won against Rita and Maria. This means Rita and Maria are from the same class. Maria won against Yulia, so Yulia is not in the same class as Maria, which means she is with Veronica. Similarly, Yulia won against Svetlana, so Svetlana is also with Maria. Therefore, we get that Veronica and Yulia are in one class, and Rita, Maria, and Svetlana are in another. Since there are three 11th graders by the condition, these are Rita, Maria, and Svetlana.

Criteria. Only the answer - 1 point.

Only the answer with a check that it is correct - 2 points.

Solution 2. Let's draw a picture connecting the girls who played against each other with lines. It is clear that in this chain, the classes of the girls alternate. Then Rita, Maria, and Svetlana are from the same class, and Veronica and Yulia are from another. From this, we find the 11th graders.

![](https://cdn.mathpix.com/cropped/2024_05_06_d2a53bb54b6f92af142eg-2.jpg?height=326&width=688&top_left_y=117&top_left_x=1255)

Criteria. (for the solution with a picture) The picture is drawn - 3 points. Noted that two adjacent girls cannot be classmates, so in this chain, the classes alternate - 2 points.

Answer - 2 points.