MathDB

Let

n

and

k

be two integers with

n>k\geqslant 1

. There are

2n+1

students standing in a circle. Each student

S

has

2k

neighbors - namely, the

k

students closest to

S

on the left, and the

k

students closest to

S

on the right.
Suppose that

n+1

of the students are girls, and the other

n

are boys. Prove that there is a girl with at least

k

girls among her neighbors.
Proposed by Gurgen Asatryan, Armenia

C5