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 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 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 . Does the player who goes first or the one who goes second have a guaranteed win, and how should that be achieved?