Problem
COM-B1-M09-P012 Degrees from \(0\) to \(5\)
#12
★★☆☆☆ Level 2 of 5
In a group of \(6\) people, can the numbers of acquaintances be \(0,1,2,3,4,5\)?
A person of degree \(5\) knows everyone, while degree \(0\) knows no one.
If there is a person who knows all \(5\) others, then every other person knows at least that person. Thus no person can have \(0\) acquaintances. Therefore the degree set \(0,1,2,3,4,5\) is impossible.
Graph version of pigeonhole for degrees.