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Dots and Cubes

Here is a game to challenge your spatial visualization ability. You are probably familiar with the game known as Dots and Squares. The game usually involves two players and is normally played on a square array of points or dots. Each player, in turn, connects an adjacent, non-diagonal pair of dots with a line until a square is formed. The player who completes the square claims it. Of course, strategies may develop that make it desirable for a player not to accept every opportunity to complete a square and, thereby, make greater gains later on. When all possible squares have been formed, the player with the most squares wins the game (Figure 1). An example of dots and squares: (a) original array of dots; (b) Player 1, then Player 2; (c) At this stage of play, Player 1 has just put in line DE, giving Player 2 the opportunity to complete squares ABED and BCFE; (d) at the completion of play, Player 1 has won.