Question 83
On Facebook, there is a group of people that satisfies the following two properties:
(i) there exists a positive integer $k$ such that any subset of $2k-1$ people in the group contains a subset of $k$ people in the group who are all friends with each other, and
(ii) every member of the group has 2011 friends or fewer.
a. If $k=2$, determine, with proof, the maximum number of people the group may contain.
b. If $k=776$, determine, with proof, the maximum number of people the group may contain.
(i) there exists a positive integer $k$ such that any subset of $2k-1$ people in the group contains a subset of $k$ people in the group who are all friends with each other, and
(ii) every member of the group has 2011 friends or fewer.
a. If $k=2$, determine, with proof, the maximum number of people the group may contain.
b. If $k=776$, determine, with proof, the maximum number of people the group may contain.