Three, at least 200 people. Every two people have a problem that neither of them has solved.

On the other hand, if the number of people $n<200$, then approximately $3n<600$, there must be a person $A$ who has solved at least 4 problems. Suppose $A$ has solved the first four problems. If $A$ also solves the fifth problem, then the person who solves the sixth problem has no unsolved problem with him, so $A$ can only solve 4 problems.

Given $n<200$, among the remaining people, there must be a person $B$ who has solved the same four problems. At this point, $A$ and $B$ have no problem that both of them have not solved. This contradiction indicates that the number of people must be $\geqslant 200$.
Three. (50 points) Two know one. - In an exam, there are 6 questions, and each question is solved by exactly 100 people. Moreover, any two participants have at least one question that neither of them solved. How many people at least participated in the exam?