MathDB

Let

n

be a positive integer. Morgane has coloured the integers

1,2,\ldots,n

. Each of them is coloured in exactly one colour. It turned out that for all positive integers

a

and

b

such that

a<b

and

a+b \leqslant n

, at least two of the integers among

a

b

and

a+b

are of the same colour. Prove that there exists a colour that has been used for at least

2n/5

integers. \\ \\ (Vincent Jugé)

Problem Statement