8.3. On a test, the teacher gave five problems and graded the test with a score equal to the number of problems solved. All students, except for Petya, solved the same number of problems, while Petya solved one more. The first problem was solved by 9 people, the second by 7 people, the third by 5 people, the fourth by 3 people, and the fifth by one person. How many fours and fives were received on the test?
Answer: None. Suppose Petya got no less than a four, then the others solved no less than 3 problems each, and the total number of problems solved by all students is no less than $3 \cdot 9=27$ (from the condition it is clear that the number of students is no less than 9). But, on the other hand, this number is equal to $9+7+5+3+1=25$. Contradiction.