999 integers 2 player game
Source: 2020 Dutch IMO TST 2.2
November 22, 2020
combinatoricsgamewinning strategygame strategy
Problem Statement
Ward and Gabrielle are playing a game on a large sheet of paper. At the start of the game, there are ones on the sheet of paper. Ward and Gabrielle each take turns alternatingly, and Ward has the first turn.
During their turn, a player must pick two numbers a and b on the sheet such that , erase these numbers from the sheet, and write the number on the sheet. The first player who is not able to do so, loses.
Determine which player can always win this game.