MathDB

A group of

4046

friends will play a videogame tournament. For that,

2023

of them will go to one room which the computers are labeled with

a_1,a_2,\dots,a_{2023}

and the other

2023

friends go to another room which the computers are labeled with

b_1,b_2,\dots,b_{2023}

. The player of computer

a_i

always challenges the players of computer

b_i,b_{i+2},b_{i+3},b_{i+4}

(the player doesn't challenge

b_{i+1}

). After the first round, inside both rooms, the players may switch the computers. After the reordering, all the players realize that they are challenging the same players of the first round. Prove that if one player has not switched his computer, then all the players have not switched their computers.

Problem Statement