1. A gathering has 1982 people attending, and among any 4 people, at least one person knows the other three. How many people at this gathering know all the attendees?
We prove that there are at least 1979 people who know all the attendees. In other words, at most three people do not know all the attendees.

Using proof by contradiction. Assume that at least four people do not know all the attendees. Let $A$ be one of them, and $A$ does not know $B$. At this point, apart from $A$ and $B$, there is still $C$ who does not know all the attendees. If $C$ does not know $D$, and $D$ is not $A$ or $B$, then among $A$, $B$, $C$, and $D$, each one does not fully know the other three, which contradicts the given condition. Therefore, the people $C$ does not know must be $A$ or $B$. At this point, apart from $A$ and the previous reasoning for $C$, the people $D$ does not know must be $A$, $B$, or $C$. At this point, among $A$, $B$, $C$, and $D$, each person does not fully know the other three, which still contradicts the given condition.

It is possible that exactly 1979 people know all the attendees. For example, among 1982 people, $A$ does not know $B$ and $C$, and apart from this, every two people know each other. Then, in any four people, at least one person knows the other three, and exactly 1979 people know all the attendees.