Chat Six

Discrete Mathematics Level 5

Chat Six is an application that allows you to invite 6 friends to chat in your private chat room online. Your friend then can create his or her new chat room and invite any 6 friends (including you) into it. Therefore, it is possible for you and your online friend to have at most 5 mutual friends in 2 different chat rooms.

As the community grows larger, every member eventually has 1 chat room of their own (each consisting of 7 persons), and if we pick any 2 persons out of this network (friends or not), they will have 2 mutual friends in common.

If \(n\) is a number of people in this entire social network, what is the least possible value of \(n\)?

Assume there is no deletion of any room or member along the way.


Problem Loading...

Note Loading...

Set Loading...