SOLUTION: Please Help Me I'm So Lost and Have no where to Start with this Problem! Tic-Tac-Toe is a game played on a 3 by 3 grid in which players take turns placing an X or an O in the gr

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Question 941347: Please Help Me I'm So Lost and Have no where to Start with this Problem!
Tic-Tac-Toe is a game played on a 3 by 3 grid in which players take turns placing an X or an O in the grid. To win, a player must place three of their symbols along a line horizontally, vertically, or diagonally. One possible win by player O is shown:

a. A player makes a move by placing a symbol in the grid. One move in Tic-Tac-Toe is equivalent to another if there is an isometry that can take the first grid pattern to the other. Consider an empty grid and the first move of the game by player O. There are nine positions in which the player can place an O. Draw all possible moves and indicate which moves are equivalent. How many unique (nonequivalent) moves are there for player O?
b. Once player O makes a move, how many unique moves are possible for player X?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
a. First player (O) can move in the center. Or he can move in any of the four corner squares, which are equivalent since you can rotate the board. Or he can place an O on one of the four "side" squares. There are 3 different moves, up to isometry.

Do the same for part b. You might have to do cases based on where first player goes.