MathDB

There is a queue of

n{}

girls on one side of a tennis table, and a queue of

n{}

boys on the other side. Both the girls and the boys are numbered from

1{}

n{}

in the order they stand. The first game is played by the girl and the boy with the number

1{}

and then, after each game, the loser goes to the end of their queue, and the winner remains at the table. After a while, it turned out that each girl played exactly one game with each boy. Prove that if

n{}

is odd, then a girl and a boy with odd numbers played in the last game.
Proposed by A. Gribalko

Problem Statement