Problem

Source: 2020 Dürer Math Competition Finals E+ 1. 6

Tags: combinatorics, game, game strategy



(Game) At the beginning of the game the organisers place $4$ piles of paper disks onto the table. The player who is in turn takes away a pile, then divides one of the remaining piles into two nonempty piles. Whoever is unable to move, loses. Defeat the organisers in this game twice in a row! A starting position will be given and then you can decide whether you want to go first or second.