Who Doesn't Start In The Middle?

Logic Level 1

You are playing a game of Tic-tac-toe. You are playing as $\color{#3D99F6}O$ while your opponent plays as $\color{#D61F06}X$ . The game plays as shown:

Which of the three labelled boxes should you put your next $\color{#3D99F6}O$ in to save yourself from losing?

Assume your opponent plays optimally, that is your opponent always try to win and always try to save themselves from losing.

A B C

1 solution

Nihar Mahajan
Apr 8, 2016

Note that if opponent places $X$ on uppermost left corner, he will win since he gets two boxes open to win. i.e the $A$ box and the lowermost left corner box. So in order to defend myself, I should put $O$ on box $A$ to force the opponent to put $X$ on lowermost left corner box, thus defending effectively.

Moderator note:

Technically, you should continue with the analysis to show that in any eventual outcome, $O$ can still "prevent from losing". It is not immediately apparent that just because he escapes this trap, that he can escape all future traps.

While these weren't among the given options, placing the next $O$ in either of the corners on the left side of the grid would lead to a draw as well.

Brian Charlesworth - 5 years, 2 months ago

Oh good point. May I ask how do I rephrase the directive of this question? Like

"Which of the following moves should you put your next $\color{#3D99F6}O$ in order to save yourself from losing?"

Pi Han Goh - 5 years, 2 months ago

What you have presently is quite clear. Another option would be "Which of the three labelled boxes should you put your next $O$ in to save yourself from losing?"

Brian Charlesworth - 5 years, 2 months ago

@Brian Charlesworth – Great! I've made the relevant edits!

Pi Han Goh - 5 years, 2 months ago

Who Doesn't Start In The Middle?

1 solution

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