MathDB

a student who is friends with everyone else in a class of n students

Source: New Zealand NZMOC Camp Selection Problems 2017 p9

September 19, 2021

combinatorics

Problem Statement

Let

k

and

n

be positive integers, with

k \le n

. A certain class has n students, and among any

k

of them there is always one that is friends with the other

k- 1

. Find all values of

k

and

n

for which there must necessarily be a student who is friends with everyone else in the class.