7. A test paper consists of 4 multiple-choice questions, each with three options $(A),(B),(C)$. Several students take the exam, and after grading, it is found that: any 3 students have 1 question whose answers are all different, and no student leaves any question unanswered, then the maximum number of students who can take the exam is $\qquad$ people.
If 10 people take the exam, then for the 1st question, at least 7 people choose only two of the options; for the 2nd question, at least 5 of these 7 people choose only two of the options; for the 3rd question, at least 4 of these 5 people choose only two of the options; for the 4th question, at least 3 of these 4 people choose only two of the options. Thus, these 3 people choose only two options for each question, which contradicts the problem statement. Therefore, the maximum number of students taking the exam is 9. The answer sheet for 9 students is constructed as follows:
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline & Jia & Yi & Bing & Ding & Wu & Yi & Geng & Xin & Ren \\
\hline 1 & $A$ & $A$ & $A$ & $B$ & $B$ & $B$ & $C$ & $C$ & $C$ \\
\hline 2 & $A$ & $B$ & $C$ & $A$ & $B$ & $C$ & $A$ & $B$ & $C$ \\
\hline 3 & $A$ & $B$ & $C$ & $C$ & $A$ & $B$ & $B$ & $C$ & $A$ \\
\hline 4 & $A$ & $B$ & $C$ & $B$ & $C$ & $A$ & $C$ & $A$ & $B$ \\
\hline
\end{tabular}