9

Part of 2017 NZMOC Camp Selection Problems

Problems(1)

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

Source: New Zealand NZMOC Camp Selection Problems 2017 p9

k

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

n

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