Question 182
The Facebook group Olympiad Training has at least five members. There is a certain number $k$ with the property: for every $k$ members it holds that at least one member of those $k$ is friends with the other $k-1$. (Friendship is mutual: if $A$ is friends with $B$, then $B$ is also friends with $A$.)
a) Suppose $k=4$. Can you say with certainty that the Facebook group has a member who is friends with all other members?
b) Suppose $k=5$. Can you say with certainty that the Facebook group has a member who is friends with all other members?
a) Suppose $k=4$. Can you say with certainty that the Facebook group has a member who is friends with all other members?
b) Suppose $k=5$. Can you say with certainty that the Facebook group has a member who is friends with all other members?