Question

If there are 48 different pairs of people, who know each other at the party of 20 people, then show that some person has 4 or fewer acquaintances.

Answer 1

@satellite73

Answer 2

must be pigeonhole week

Answer 3

Ok but how ?

Answer 4

idk

Answer 5

Will I get explanation on OS ?

Answer 6

well i think it has to do with graphs maybe
does that ring a bell?

Answer 7

you will assume that each person has 5 or more acquaintances, then arrive at a contradiction
say make a graph , people are connected if they know each other
the each person has 5 or more connections, so the sum of all these will be at least 100

Answer 8

does this sound familiar at all? there is going to be some reason that if the number of edges in the graph will be half of that, namely 50, but since there are only 48 people that is a contradiction

Answer 9

Thank you @satellite73

Answer 10

yw, not really complete, but i hope you get the idea