Question

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 1

Answer is option A)

since first player can select any of the 9 positions available,

So he has 9 strategies.

Now the second player moves, & he face total 9 nodes,

& At each node, he can select any of the 8 positions vacant .

So total strategies = 8*9 = 72

( 8 strategies at each of 9 nodes)

Now P3 moves ,

Now he faces total 8*9 = 72 nodes

At each node, he have 7 positions vacant,

So 7 strategies available at each of 72 nodes

Total strategies = 7*72

= 504