4. In the class, there are 30 students: excellent students, average students, and poor students. Excellent students always answer questions correctly, poor students always make mistakes, and average students answer the questions given to them strictly in turn, alternating between correct and incorrect answers. All students were asked three questions: "Are you an excellent student?", "Are you an average student?", "Are you a poor student?". 19 students answered "Yes" to the first question, 12 to the second, and 9 to the third. How many average students are there in this class?
Answer: 20 C-students

Solution. Let $a$ be the number of excellent students, $b$ be the number of poor students, $c$ be the number of C-students who answered the first question incorrectly, answered the second question correctly, and answered the third question incorrectly (we will call these C-students of the first type), and $d$ be the number of C-students who answered the first question correctly, answered the second question incorrectly, and answered the third question correctly (we will call these C-students of the second type).

To the first question, "Yes" was answered by excellent students, poor students, and C-students of the first type, so $a+b+c=19$. To the second question, "Yes" was answered by poor students and C-students of the first type, that is, $b+c=12$. To the third question, "Yes" was answered only by C-students of the first type, so $c=9$. Then from the second equation, we get that $b=3$, and from the first equation: $a=7$. There are 30 students in the class, so $d=30-19=11$, therefore, the total number of C-students:

$9+11=20$.

Grading criteria.

“+" - a complete and well-reasoned solution is provided

“ $\pm$ " - a generally correct reasoning is provided, containing minor gaps or inaccuracies

“耳” - it is indicated in the provided reasoning that C-students can be of two types, but there is no further progress or a computational error is made.

"-" - the problem is not solved or solved incorrectly