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 found it easier to relate this trivial topic to games I already knew. When beginning to read this chapter I thought of the game Dots and Boxes, except the goal for that game is to connect four lines and create a box of your color. However instead of using the boxes to color, Harary’s version uses triangles. The winner of each of these games has his or her color most represented on the board, which makes the two games similar. Also, you try to optimize the number of boxes you get, and decrease the amount your opponent gets. The second game I connected this to was Connect 4. You place the checkers in certain places to get four in a row. Like in Harary’s extreme ticktacktoe, the four checkers have be connected. Thinking of the generalized ticktacktoe in reference to the games I knew made understanding this chapter a lot easier.
ReplyDeleteI think my favorite part of this chapter was reading what his made up names for these “animals” were; my favorite being Snaky. However I think if I ever wanted to play this game, I would need some other kind of tutorial to learn to play it properly.
I’m not sure Haray’s ticktacktoe is like the game dots and line at all; the book explains that you do not actually draw the lines but you color in the dots instead. I understand why it might look like that but how you play is different from my understanding. I’m confused as to why Haray makes his game seem different from regular ticktacktoe, because it seems like players just use colored dots instead of X’s and O’s while playing. I’m still a little confused on some of the arrangements of animal cells and how you could play Haray’s game with them. I don’t really understand how you can determine the length of a side on the board or how they can determine if the board is a winner or not. I did, however, find it interesting how they had specific names for all the animal cells and the names have no correlation with each other which is kind of cool. Another confusing topic for me was the concept of m; I didn’t quite understand how you could determine it. Is m determined as the fewest moves to takes to win or the most? Overall though I think learning Haray’s version of ticktacktoe would be interesting!
ReplyDeleteWho knew the simple game of ticktacktoe could be so complicated? When first reading this I also had an image of what ticktacktoe looked like, the same way as Devin had. I was very surprised to see the ticktacktoe the chapter was describing was not the game I played to pass time in class with a classmate. There is no more X's and O's but rather colored dots. One confusing factor of this chapter for me was the fact that the author was comparing Harary's version of ticktacktoe to animals. I am not sure how that analogy came about and I am very confused on how the game could be played with them. As I read further into the chapter I picked up on the animal names just being different names of pentominoes but I am not certain if that is correct.The pentominoes were also a confusing aspect for me, because I am not quite sure how they come into play with this ticktacktoe with colored dots. I would be very interested in playing this version of ticktacktoe, however, because it seems quite fun and different from the ticktacktoe I am used to. This game seems similar to many other paper and pencil games I have played so I would be extremely interested in seeing how all of this plays out.
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