MathDB

There were 20 participants in a chess tournament. Each of them played with each other twice: once as white and once as black. Let us say that participant

X{}

is no weaker than participant

Y{}

X{}

has won at least the same number of games playing white as

Y{}

and also has won at least the same number of games playing black as

Y{}

. Do there exist for sure two participants

A{}

and

B{}

such that

A{}

is not weaker than

B{}

?
Boris Frenkin

Problem Statement