## Puzzle #146: The Proud Party Goers

This is a very nice puzzle I got from a site (fivethirtyeight.com) recommended to me by Suman Saraf – thanks Suman.

It’s Friday and that means it’s party time! A group of N people are in attendance at your shindig, some of whom are friends with each other. (Let’s assume friendship is symmetric — if person A is friends with person B, then B is friends with A.) Suppose that everyone has at least one friend at the party, and that a person is “proud” if her number of friends is strictly larger than the average number of friends that her own friends have. (A competitive lot, your guests.)

Importantly, more than one person can be proud. How large can the share of proud people at the party be?

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy partying!

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### 2 Responses to Puzzle #146: The Proud Party Goers

1. Abhinav Jain says:

Share of proud people can be at max N-2

2. Gautam Kumar says:

N-2.
N-2 people being friends with every other person, thus having N-1 friends. Except two, say A and B not being friend with each other and having in total N-2 friends only.