7. A test paper consists of four multiple-choice questions, each with three options $\mathrm{A}$, $\mathrm{B}$, and $\mathrm{C}$. Several students take the exam, and after grading, it is found that any three students have different answers to at least one question, and no student leaves any question unanswered. Then the maximum number of students who can take the exam is $\qquad$ people.
7.9.

If 10 people take the exam, then for the first question, at least 7 people choose two options; for the second question, at least 5 people among these 7 choose two options; for the third question, at least 4 people among these 5 choose two options; for the fourth question, at least 3 people among these 4 choose two options. Therefore, these 3 people choose only two options for each question, which contradicts the problem statement.

Thus, the maximum number of students taking the exam is 9. Additionally, it is easy to construct a scheme where 9 people take the exam, as shown in Table 1.