Consider a modified version of the very famous tic-tac-toe game in which player 1 moves, then player 2 moves, and then player 3 moves and the game ends. The number of strategies for player 1, 2, and, 3 are respectively:

a.

9, 72, and 504.

b.

None of the available options in this list.

c.

9, 9, and 9.

d.

9, 8, and 7.

Answer: (a). 9, 72, and 504

Explanation:

The number of strategies for player 1, 2 and 3 in the tic - tac - toe game where player 1 moves, then player 2 moves and then player 3 moves can be analyzed below.

For player 1;

The player can choose any of the available 9 positions:

This gives the player 9 strategies.

For player 2;

The player faces a total of 9 nodes as he moves, and at each of the nodes the player has available 8 positions vacant to choose from

Calculating that gives,

Strategies = 9*8 = 72

For player 3;

The player faces a total of 72 nodes as he moves, i. e. 9*8,

Where at each node, 7 available positions are vacant

So, calculating the total strategies for player 3 gives;

Total strategies = 72*7 = 504