There are five possibilities to get a * * * score after answering these two questions: 1. Both questions are correct: 4 points.

2. I didn't do either question: 2 points.

3. Both questions are wrong: 0.

4. Didn't do a question: 3 points.

5. One question is correct: 1.

According to "at least six students have the same score in each question", we should take the score of each question as the drawer and the students as the entry. There are 3×3=9 kinds of scores, that is, there are 9 drawers. It is known that at least one of the nine drawers has at least six items, and it is concluded that there are at least 9x (6- 1)+ 1 = 46 people.

Please read the questions clearly: the score of each question is the same, that is, the scores of the two questions are the same. There are five kinds of scores: 0, 1, 2, 3, 4. There are nine combinations of scores: 00,01,02, 10, 1 1.

Eight of the nine situations have five people in common, and any situation of 1 has six people in common. 5*8+6=46.

3.？ There are three possibilities for each question. So there are nine possibilities, so if there are only nine people, it is possible that everyone is different. If there are five people, it is possible that only five people are the same. If there is one more person, he must be the same as the first five, then 46 people will be enough.

4.？ From the point of "at least six students have the same score in each question", we should regard the score of each question as a drawer and the students as the object. If (a, b) is used to represent the score of each question, where A and B represent the scores of the first and second questions respectively, then there are (2,2), (2, 1), (2,o), (1, 2), (1, 660. The question becomes: It is known that at least one of the nine drawers has at least six kinds of articles, so how many kinds of articles are there? Using the pigeon hole principle in reverse, we get at least: 9×(6- 1)+ 1=46 (person).