7.3. Valera, Seryozha, and Dima received three grades each for three tests, and all the grades turned out to be threes, fours, or fives. Valera said: "I have higher grades for two tests than Seryozha." Seryozha replied: "But I have higher grades for two tests than Dima." Dima countered: "And I wrote two tests better than Valera." Could all the boys be telling the truth? Justify your answer.
Solution: If Valera had grades $5,4,3$, Seryozha - 4, 3, 5, and Dima - 3, 5, 4, then all the boys told the truth: Valera performed better than Seryozha on the 1st and 2nd tests, Seryozha performed better than Dima on the 1st and 3rd tests, and Dima performed better than Valera on the 2nd and 3rd tests.

Note: The given variant is unique up to the permutation of the test numbers; the schoolboys, of course, do not need to prove this.

Answer: They could.

Recommendations for checking:

| is in the work | points |
| :--- | :--- |
| Example showing that all three are correct | 7 points |
| Answer without justification or incorrect answer | 0 points |