Question 141
Ward and Gabrielle are playing a game on a large sheet of paper. At the start of the game, there are 999 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 $\gcd(a, b) = 1$, erase these numbers from the sheet, and write the number $a+b$ on the sheet. The first player who is not able to do so, loses. Determine which player can always win this game.