6. (10 points) An exam consists of 6 multiple-choice questions, with the following scoring rules: Each person starts with 6 points, gets 4 points for each correct answer, loses 1 point for each wrong answer, and gets 0 points for unanswered questions. There are 51 students taking the exam. Therefore, at least ( ) students have the same score.
A. 3
B. 4
C. 5
D. 6
【Analysis】According to this scoring method, the highest possible score is (30 points), and the lowest is 0 points after a deduction of 6 points, totaling $30+1=$ 31 (different scores). Since each wrong answer results in a deduction of: $1+4=5$ points, not answering a question results in a maximum deduction of 4 points, so the highest score is 30 points, the second highest score is: $30-4=26$ points or $30-5=25$ points, thus the scores of 29, 28, and 27 points between 30 points and 26 points cannot be obtained; similarly, 23, 24, and 19 points cannot be obtained either, so there are actually $31-6=25$ (different scores). Then, according to the pigeonhole principle, consider the worst-case scenario to solve the problem.

【Solution】According to this scoring method, the highest possible score is $6 \times 4+6=30$ (points), and the lowest is 0 points after a deduction of 6 points, totaling $30+1=31$ (different scores).

Since each wrong answer results in a deduction of: $1+4=5$ points, not answering a question results in a maximum deduction of 4 points, so the highest score is 30 points, the second highest score is: $30-4=26$ points or $30-5=25$ points, thus the scores of 29, 28, and 27 points between 30 points and 26 points cannot be obtained; similarly, 23, 24, and 19 points cannot be obtained either, so there are actually $31-6=25$ (different scores). Then, $51 \div 25=2 \cdots 1$, so at least 3 people have the same score.

Therefore, the answer is: A.