Gaming article "Nine Squares"
Martin Gardner, a famous advocate of science and author of entertaining math books, called this paper activity the "pearl of logic games". The playground is a 3x3 square grid composed of 16 points. Game-play begins as one player joins two vertically/horizontally lined points to create a segment. The object is to create squares by connecting the four necessary points. Players move in turn, connecting the dots until one player finally encloses one or two single squares. Once, the player has created a square, he/she continues his/her turn until the end of the game or until his/her next line doesn't form a square. After all possible segments & squares are drawn, points are calculated. Players receive points for forming a square. The player who encloses the most squares wins. Because we have nine squares total, there will never be a tie game.
In Nine Squares we have a 3x3 game-board, for added difficulty. There are many possibilities for combination attacks, like in chess, when a more experienced player gives his/her opponent a chance to enclose one or more squares and then makes his/her opponent move at a loss. The aim of this game is winning by "wait-and-see" move. Unfortunately, I haven't tested the game, and don't know which player has the winning strategy. My best guest would be the second player.
Let's see the position in the Fig. 1. Here the players have already exhausted a few moves, which enclose the squares, and the game - using the chess terminology - comes to an ending stage. The playground is divided into two fields, consisting of two and seven possible square formations.
It is clear that, if the player makes a move in the lower field, he'll lose for sure, as his rival will enclose seven squares. The second player has to give Player 1 the opportunity to enclose the two squares at the top of the board. But it isn't obvious how to do this. You should move quickly and pass the turn back to Player 1 when only seven possible square formations are left. If the second player connects a4 to b4, and the first player connects b4 to c4, then two squares are available for the taking. Connecting b3 to b4 leads to the most predictable victory. We can observe the same idea in Fig. 2:
After the obvious moves c4 to d4 and d3 to d4, the second player encloses the square and continues the game by joining a4 to b4. The first player can enclose all four squares, but he/she will end up losing. The correct moves are a3 to b3, a2 to b2 and b1 to c1! You shouldn't move a2 to b2.
Now we come to more complicated situations. In the situation depicted in Fig. 3, you can win only with the help of the combinatory move b2 to c2, c1 to c2, c2 to c3 or c2 to d2. The rival can take or turn down square, but in any case he has to give up five squares below. In this position it isn't important who enclosed two squares above.
Considering the symmetry, there aren't too many different positions available on a 3x3 board. Experienced players are aware of the moves they're making and the moves they want to make after their own, and after their opponents. In Figures 4-10 situations are given where numerous decisions can be made where one move is not necessarily the winning move. I hope this display will help the readers interested in Nine Squares to appreciate the beauty, and master secrets of this game.