A move in the game is equivalent to deleting an edge from a graph with n vertices where there's an edge between consecutive numbers. 1-2-3...-n. There is no edge in between n and 1 because deleting it creates no new graphs. The number of edges id v - 1, where v is the number of vertices. The number of edges reduces by 1 in every move. If the number of edges is even (0 included), Player 2 wins.
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