Question

Seti held a party. He says, ‘There were 11 people at my party, and everyone had 3 friends there.’ Is this possible? Explain your answer

Answer 1

Yes, it is possible

Explanation:

Think the people as points in space and the friendship between two people as a line connecting two points.

Then the question is equivalent to asking whether it is possible for all 11 points being connected by lines such that every point is connected to exactly three other points.

Clearly this is possible, since we always have, for each point, ten other points to connect it to, so we can select any three of the ten.