MathDB

3n - 2

participants took part in the chess festival, some of them played one game of chess with each other. Prove that at least one of the following statements holds:
(A) One can find

n

chess players

A_1 , A_2 , . . . , A_n

suchthat Ai has played a game with

A_{i+1}

for all

i = 1, ...,n -1

.
(B) Seven chess players can be found in

B_1 , . . . , B_7

, who have not played with each other, except perhaps three pairs

(B_1, B_2)

(B_3, B_4)

and

(B_5, B_6)

, each of whom may or may not have played a game of chess.

Problem Statement