Question 154
There are numbers $1, 2, 3, \ldots, 100$ on the board. Each is written exactly once. Petryk and Ivasyk are playing in the following game (Petryk starts): each player erases one number from the board. If after player's turn the sum of all erased numbers (by both players) cannot be represented as a difference of squares of integers, the player loses. Who will win in this game if both players want to win?