The hexagon game involves two players, who construct an undirected graph with 6 verticies. Player 1 adds solid edges, whereas Player 2 uses dashes. Game starts with a graph with empty edges. Player 1 makes the first move. At each move, a player has to add a new edge between two vertices that are not connected by any old edge – edges can intercept with each other. Figure 1 shows initial state of the game; Figure 2 shows game in progess; Figure 3 shows that player 1 won.