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Pasha and Vova play the game crossing out the cells of the $3\times 101$ board

Source: Caucasus MO 2023

July 16, 2023
combinatorics

Problem Statement

Pasha and Vova play the game crossing out the cells of the 3×1013\times 101 board by turns. At the start, the central cell is crossed out. By one move the player chooses the diagonal (there can be 1,21, 2 or 33 cells in the diagonal) and crosses out cells of this diagonal which are still uncrossed. At least one new cell must be crossed out by any player's move. Pasha begins, the one who can not make any move loses. Who has a winning strategy?
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