'Tic-tac-toe' or 'cross & noughts'

Logic Level 2

Two amateur people are playing a game of tic-tac-toe. Each person places his/her mark, either X \color{#D61F06} X or O \color{#3D99F6}O . We do not know who started first.

After the first player has placed his/her second mark, the players will always place his or her mark in a line that already contains

(a) two of his/her own marks,
(b) two of his/her opponent's marks,
(c) giving priority to (a) over (b).

Only the last mark to be placed in the game shown in the figure has not been given. Who will win the game, X \color{#D61F06} X or O ? {\color{#3D99F6}O}?

O X Can't be determined

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4 solutions

Let the no. in each block represent the location of a mark. Then, from rule 3, the seventh mark must be placed in block 5. And from rule 2, the seventh mark wins for both X and O.

Since lines 1-4-7 and 7-8-9 have 2 opponent marks, this tells us that the 6th mark must either be in block 7 or block 9. However, placing the 6th mark in block 7 would contradict rule 3c, where O would rather play it in block 5 and win the game. Thus, the sixth mark was placed in block 9 and it was 'X'.

Accordingly, the 7th or the final mark must be 'O' and O \boxed {O} wins the game.

Nope, I could not find a possible way that "O" started this game and all rules were followed, for the answer to be "O" , the player who started made the mark "O". give more clear solution please

Shubham Diwe - 5 years, 8 months ago

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2-1-7-4-8-9 is a valid sequence that satisfies the conditions.

Calvin Lin Staff - 5 years, 8 months ago

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In response to Calvin Lin : The 7-4 move is a deadlock i.e., after the "O" is made in 7, the other player would not bother making a mark in 4. But yes the rules apply after 2nd move so that is a possible combination.

Shubham Diwe - 5 years, 8 months ago

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@Shubham Diwe The rules did not say "The other player will not bother marking in a deadlock."

Calvin Lin Staff - 5 years, 8 months ago

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@Calvin Lin Yes therefore I find you all need to have a little look at logic and ask yourself “do I reallly know this?” Please gentlemen thank you

Echo Pippin - 4 months ago

Edit: This comment is false.


As pointed out in the reports, all that you know is "The last play of X is 9". You do not know that it was the 6th move. For example, we could have 1-8-4-7-9-2 as a valid play.

Calvin Lin Staff - 5 years, 9 months ago

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But, how can the sixth mark be at 2. Shouldn't it be at 5 (to prevent X from winning).

Dinesh Nath Goswami - 5 years, 9 months ago

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Well you still need to show that this steps are constructable. There are four possible configurations in which this scenario can take place.

Pi Han Goh - 5 years, 9 months ago

Sorry about that. I agree that your reasoning is correct.

I have updated the answer back to O.

I have edited your solution slightly for clarity.

Calvin Lin Staff - 5 years, 9 months ago

@Calvin: sir, 2-1-7-4-8-9 is too amateur-ish, don’t you think? 4 after 7 is a complete waste of move!

Devansh Trivedi - 2 years, 11 months ago

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The problem doesn't say that the game cannot be "amateur-ish". It just states that the game has to be played accordingly to the given rules.

Calvin Lin Staff - 2 years, 11 months ago

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You are right, sir. Thanks for the reply! 😅

Devansh Trivedi - 2 years, 11 months ago
Cool Jet
Dec 29, 2018

Assume one of the players goes first. Try to reason through all options and imagine a real-life situation where you and your friend are playing a game. Since this is supposed to be a logic puzzle, think about the possibilities of what he would do. Though there are many possible game like 1,8,4,7,9,2. 2,1,4,7,8,9 , using the rules given, it would be O winning the game.

Akshay Krishna
Oct 4, 2018

The last move concludes the game; which directly depicts it's O's move in the middle cause O follows all three rules and X does not.

C .
Aug 21, 2018

Whoever played first, they still have a threat on board, so their opponent's 3rd move needs to have been made to prevent another threat. Supposing X played first, O's 3rd move must have been in the lower-left corner, but this would mean that O already had a threat on board, which X should've countered, according to rule (b). Or which O should've preferred, according to rule (c). So X couldn't have played first to reach this state, according to the stated rules.

Therefore, O played first (and will thus win on the next move), and their 3rd move must've been to the middle of the bottom row. X chose to counter in the corner instead of in the center. The previous moves could've happened in any of the 4 possible ways.

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