That's How You Prevent A Fork

Logic Level 1

It is O O 's move in the Tic-Tac-Toe game (above). Which of the moves gave above (1, 2, 3, 4, 5) is the best move for O O ?

Assume both players intend to win the game and plays optimally.


Source: University of South Carolina High School Math Contest, 1991


The answer is 5.

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3 solutions

Ashish Menon
Mar 25, 2016

CASE 1 \text {CASE 1} :-
If O O plays 1 1 . Then X X who plays optimally would play 5 5 . Then O O would definitely lose because , in the next turn it can play either 2 2 or the square to the right of the bottom X X . But, in the next turn, X X would definitely win.


CASE 2 \text {CASE 2} :-
If O O plays 2 2 . Then X X who plays optimally would play in the square right of the bottom X X . Then O O would definitely lose because , in the next turn it can play either 3 3 or 5 5 . But, in the next turn, X X would definitely win.


CASE 3 \text {CASE 3} :-
If O O plays 3 3 . Then X X who plays optimally would play 5 5 . Then O O would definitely lose because , in the next turn it can play either 2 2 or the square to the right of the bottom X X . But, in the next turn, X X would definitely win.


CASE 4 \text {CASE 4} :-
If O O plays 4 4 . Then X X who plays optimally would play in the square left of the bottom X X . Then O O would definitely lose because , in the next turn it can play either 3 3 or 5 5 . But, in the next turn, X X would definitely win.


CASE 5 \text {CASE 5} :-
If O O plays 5 5 . Now, the optimal player X X can't do anything to defeat the optimal player O O because now X X would not succeed in forming a two path trap (like the ones in the above cases).


So, the best move for O O is 5 \boxed{5} .

You're case 2 is a little off. I think you meant to say right of the bottom X

Luke Nelson - 5 years, 2 months ago

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Yeah, thanks, i have edited it. :-)

Ashish Menon - 5 years, 2 months ago

Always look for your opponent's intent. Which move of your opponent gives them the best shot at winning? Lets give our squares coordinates ey?

(1 , 1) : (2 , 1) : (3 , 1)

(1 , 2) : (2 , 2) : (3 , 2)

(1 , 3) : (2 , 3) : (3 , 3)

Coordinates of your opponent's 'X' are (1 , 1) and (2 , 3) To give the the best opportunity to win, they need to play (2 , 1) or (1 , 3) common squares for their 3 in a row or column. Since (2 , 1) is taken, they'll try (2 , 3) next. That is why you need to play that move

If x is put in the positions 2 &5 you can see there'll be two way path for x.Again if o is put in 2 still there's a two way path.So you have to put o in the position of 5.

What is a "two way path for x"?

Calvin Lin Staff - 7 years, 1 month ago

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A guaranteed win

Curious Caterpillar - 1 month, 2 weeks ago

X will check mate O if O will put his turn to 1~4 imagine it.

Roi Vinson Abrazaldo - 7 years, 1 month ago

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