MathDB

players can be arranged in a list: $P_1, P_2, P_3,\ldots,P_n$

Source: Moldova EGMO TST 2023

February 4, 2023

combinatorics

Problem Statement

Let there be an integer

n\geq2

. In a chess tournament

n

players play between each other one game. No game ended in a draw. Show that after the end of the tournament the players can be arranged in a list:

P_1, P_2, P_3,\ldots,P_n

such that for every

i (1\leq i\leq n-1)

the player

P_i

won against player

P_{i+1}