MathDB
TOT 2004 Spring - Junior A-Level p6 game with 2004! on blackboard

Source:

February 25, 2020
combinatoricsgamegame strategy

Problem Statement

At the beginning of a two-player game, the number 2004!2004! is written on the blackboard. The players move alternately. In each move, a positive integer smaller than the number on the blackboard and divisible by at most 2020 different prime numbers is chosen. This is subtracted from the number on the blackboard, which is erased and replaced by the difference. The winner is the player who obtains 00. Does the player who goes first or the one who goes second have a guaranteed win, and how should that be achieved?