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 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
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