Question 85
Each player - Andriy and Olesya - has a set of 2019 cards, which contains numbers $1, 2, \ldots, 2019$ (each number is exactly one time for each player). The game follows the following rules. At the beginning of the game there is a card with a number $k \in \{1, 2, \ldots, 2019\}$ on the table. After that, the players take turns (Andriy begins) to change one of their cards to the one that is currently on the table. Besides that, Andriy can change the card on the table to the one he holds, if it has a number that is greater than the number written on the card on the table, and Olesya - on her card with a smaller written number than on the card on the table. A person who cannot make a move is considered to be the loser. Who will win in this game, if everyone wants to win?
(Bogdan Rublyov)
(Bogdan Rublyov)