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Game on blocking off the way from the bottom left to top right cell

Source: 2020 Caucasus Mathematical Olympiad

March 16, 2020
combinatoricsgame

Problem Statement

Positive integers nn, k>1k>1 are given. Pasha and Vova play a game on a board n×kn\times k. Pasha begins, and further they alternate the following moves. On each move a player should place a border of length 1 between two adjacent cells. The player loses if after his move there is no way from the bottom left cell to the top right without crossing any order. Determine who of the players has a winning strategy.