Harary's Generalized Ticktacktoe

            Chapter thirty seven talks about Harary’s Generalized Ticktacktoe. When I first read the title of the chapter I thought it was going to be about the ticktacktoe that you played when you were little kids and tried to align either three X’s or three O’s in a line to win, but there is more to it that Harary explains. One different way for doing ticktacktoe is draw it how you normally would but instead of squares connect the lines with dots so that you have nine dots total and you play with colors instead of X’s and O’s, and the person to make a line out of the same color wins.

            This is how you could play ticktacktoe and this is how most people play it, nut Harary took a different approach to it. The squares that you put the X’s and O’s in when playing ticktacktoe he referred to these as polyominoes.  So if you had to polyominoes you would have two squares next to each other. All the polyominoes have to be touching one another, but you can rearrange them in any order you would like. For example, if you had three squares you could make a straight line or an L shape. Once you knew what cells you were using you had to know the name of it, which he referred to this as animal cells. So first of all you have to know what the animals’ board number is and you find this out by the length of the smallest square in which the first player can win. If there is a number then the animal is called a winner and if not then it is called a loser. If you start out with a loser then the second player can never win, but he may be able to have a draw with the other person.

            Next you have to find out what b and m are as what he called them. B is side length of the board while m is the number of moves it takes to win. On a monomino, which is just one cell while polyominoes are multiple cells, both b and m are equal to 1 so that board is a winner. Not all boards are like this though it just depends on how they are assembled. Like a mentioned before if you have three cells you can either make a straight line or an L, but when you do this b is not the same because in the straight line it is four while in the L it is only 3. There is an animal cell called Fatty which is just a two-by-two square which is known as the smallest basic loser, because no matter where player one puts his two cells or domino player two can always take the other cell of the domino, which is why Fatty is always a loser.

            There are also other variations to this game in which both players try to make an animal cells. When you play this game with more than two people it becomes a lot more complex than what it already is. Also instead of playing with squares you can try playing with triangles or hexagons, but doing so will not be an easy task. I believe that Harary's version is a lot harder than regular ticktacktoe and is more confusing to me. I am not really sure what makes a animal cell a winner or loser necessarily which is one of the main points in his version, so maybe once I knew that I would better understand how to play the game.