A Party is attended by $20$ people. In any subset of $4$ people atleast one knows other $3$. Suppose there exists three people who dont know each other. How many people know all the people in the party?
Options $\to16,17,18$, Can't be determined
Obviously, the people are vertices of the graph and edges exists when they know each other. Since 3 people dont know each other, $18$ is definitely wrong. Moreover each of these $3$ know all the other people.
Not sure how to proceed from here. Any hints appreciated
Let $A,B,C$ don't know each other. Then every $X\notin\{A,B,C\}$ knows $A,B,C$
For every pair $X,Y\notin\{A,B,C\}$ we have $4$-couple $\{A,B,X,Y\}$ and someone knows the other $3$ (clearly that can't be $A$ nor $B$) so $X$ knows $Y$. So in $\{A,B,C\}^C$ everybody knows everybody.
So there are $17$ people knowing all the others.