Tick Tack Toe #1

Logic Level 1

If it's O \color{#3D99F6}\text{O} 's turn, can O \color{#3D99F6}\text{O} force a win?

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17 solutions

Munem Shahriar
Oct 6, 2017

Relevant wiki: Tic Tac Toe

Hence O can force a win \color{#3D99F6} \boxed{\text{O can force a win}}

The question was not clear....it seemed to infer that the “o” could force a win... in the next move. It would have been clearer to specify that this could only happen in the NEXT moves, not just in the immediate upcoming one.

Jacques Carrier - 3 years, 7 months ago

This problem makes recall the moments of having boring days at school warming the last benches and Doing "Tic,Toc , Tic"

Naren Bhandari - 3 years, 7 months ago

This is one of the few tic-tac-toe situations where a win can be forced. The only other one I know is if O starts in a corner and X then starts in a mid-side box. They're both pretty artificial, as they rely on the opponent doing something dumb ie not going into the centre or a corner.

Katherine barker - 3 years, 7 months ago

That's true(just pointing out).Because it only depends on where the opponent would put their X, so edit your options and add 'It is impossible' or 'It depends on the moves of the opponent'

Lim Xiangying - 3 years, 7 months ago

“O” has seven positions at which it can be placed. That gives it 7 chances to force a win, out of which only 6 are possible! Giving “O” a 6/7 (85%) chance to force a win!

Suren Kumar - 3 years, 7 months ago

These are not just possible moves, but also depict the winning strategy. That is to say, if X X deviates from the sequence of moves you have shown at any point, there is still a way for O O to win!

Agnishom Chattopadhyay - 3 years, 7 months ago

In move 4, player will play for defeating the other player

Sankalp Nayyar - 3 years, 7 months ago
Alec Situ
Oct 9, 2017

Relevant wiki: Tic Tac Toe

First put O in any corner. Then, X is forced to be in the opposite corner. Now, put O in any other corner. Because there are now one row and one diagonal missing one, any one X picks will remain the other row or diagonal missing one.

Any other corner wouldn't do. It has to be the other corner in the same column as the first O (or the second, rather).

Stewart Gordon - 3 years, 7 months ago

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Well... if O picks the two top corners he's OK. He could win using the top row. He just cannot pick the two bottom corners.

Richard Desper - 3 years, 7 months ago

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He can't, because once he's taken one of the top corners X will have two in a row, which O will then need to block.

Stewart Gordon - 3 years, 7 months ago

I just realized you were responding to his second move in the solution, not the first. Good point.

Brian Egedy - 3 years, 7 months ago

Any of the corners or sides allow O to force the win. The only potential draw is the top center.

Brian Egedy - 3 years, 7 months ago

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Any move is a potential draw, since O is under no obligation to follow through with the best move. But the top centre is the only move that leads to a draw if both players play perfectly from that point forward.

Stewart Gordon - 3 years, 7 months ago

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The only potential draw with best play, I should have said. Thank you.

Brian Egedy - 3 years, 7 months ago

I can block anyone in this game and make it a tie everytime

GJevon Covington - 3 years, 7 months ago

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Yes, but not if you start from a configuration in the game which is already at a disadvantage.

Agnishom Chattopadhyay - 3 years, 7 months ago

This is a stupid question. You cant expect everyone to do a complete risk or chance analysis of tiktaktoe. If you want that just look at the wiki page.....the number of comments proves i am right.

Geert Nijs - 3 years, 7 months ago

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Firstly, this is a game of strategy, not chance.

Secondly, the problem doesn't ask anybody to do a complete analysis. It just asks you to give the outcome of one specific opening sequence. Even so, there's no need to analyse the full game tree - just one sequence of moves that guarantees a win for O would do.

Stewart Gordon - 3 years, 7 months ago

There are no stupid questions, just stupid answers

Dave Moreau - 3 years, 7 months ago

This is not a stupid question. This is only an easy question. Please be nice and polite on Brilliant.

Agnishom Chattopadhyay - 3 years, 7 months ago
Stewart Gordon
Oct 16, 2017

O can go in any corner. Obviously, X is forced to block the win. If O went in a top corner, he is forced to go in the bottom corner in the same column, thereby creating a fork. If O went in a bottom corner, he can force a win by playing in either of the other two cells in the same column.

Yet another way to win is to take the left or right edge cell and then an adjacent corner. In other words, O can force a win by going anywhere except the top.

Side comment: I was taught as a child that O goes first, but a lot of resources take the position that X goes first (or that there's no set rule about it). This is one of the few instances I've seen in recent times of O going first. (I wonder if there's any correlation between this and whether people call the game "noughts and crosses", "tic-tac-toe" or some other name.)

I have always referred to the game as "noughts and crosses". irrespective of who is supposed to go first. O goes first in this case because his first move is already done. Hence it is O's turn to make the next move, whatever the game is referred to as.

Paul Townsend - 3 years, 7 months ago
Zain Majumder
Oct 16, 2017

The trick is to create a situation where there are two ways for O to win, but X can only block one. For instance, imagine O plays the following move:

Now X is forced to play in the bottom left to prevent a three in a row:

Now O plays this move:

If X puts their move on square 1, O plays their move on square 2. If X puts their move on square 2, O plays their move on square 1. Therefore, O forced X into a loss.

Victor Dumbrava
Oct 16, 2017

The answer is YES , because if the first player (the O) moves to any of the upper corners, regardless of the side, the other player (the X) is forced to defend, hence leaving the attacker (O) two choices. Here is a visual representation:

First Move First Move

Second Move Second Move

Third Move Third Move

Now it is pretty obvious that O has two ways to win the game, thus there is nothing left to do for the defender.

Great job of explaining how the play goes!

Agnishom Chattopadhyay - 3 years, 7 months ago

Nice solution. ¨ \ddot \smile

Munem Shahriar - 3 years, 7 months ago

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Thanks! I aimed to get a more "visual" representation of how things go.

Victor Dumbrava - 3 years, 7 months ago
Annie Li
Oct 16, 2017

It is possible but sometimes, it depends on the other players moves.

Moderator note:

The question is asking if the player "can force a win".

"Can" means there is some circumstances where it will happen, not "no matter what moves the player does they will win". It's the same distinction we commonly see in math problems with "always" and "sometimes" -- it's not "always" true for every sequence of moves O win will, but "sometimes" is enough in this case.

"Force" means it will happen no matter what the other player does in response. Since optimal moves for O means the opponent has no recourse even in optimal counter-moves, O can force a win.

this one doesn't matter where your opponent goes.

max boys - 3 years, 7 months ago

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Yep, that is why a win can be forced.

Agnishom Chattopadhyay - 3 years, 7 months ago

Actually, O can force a win with any second move other than the top center.

Brian Egedy - 3 years, 7 months ago

The O will always win, unless it the O is placed in the top center. Other than that, the other players moves don’t matter at all

Josiah Borgstede - 3 years, 7 months ago

Either your opponent will move to block you, in which case you'd trap him/her, or won't and you'll win even quicker.

Sam Maxwell - 3 years, 7 months ago
Matin Naseri
Feb 22, 2018

If both palyers are playing optimally the game , O \color{#3D99F6}{O} will be win the game.

Because O \color{#3D99F6}{O} select the central cell of the game . Central cell is the strategical cell of (Tic tac toe) \text{(Tic tac toe)}

Two case will be support the O \color{#3D99F6}{O} .

One case is in below :

Divyansh Saxena
Oct 21, 2017

There is just one move...just put O on any corner...and no matter how much you try O will always win...

Jeff Umbrell
Oct 19, 2017

If O goes into either space to the right or left, X has to block. O then goes to the appropriate corner, X can only block one of two possible moves.

Al Dynak
Oct 18, 2017

Whoever moves first can always win in tic-tac-toe. The second move by the first player controls where the second player makes their second move.

Patrick Beranek
Oct 17, 2017

Put O anywhere, and then form a triangle next turn in such a way that there are two ways to win. This is a force win, and there is no way to prevent it.

Marcel Johe
Oct 17, 2017

Put O on either side of the middle row. Then place an O either above or below it. You have forced a win.

Diane Neglia
Oct 17, 2017

1.O choses the Lower left corner. 2. X Must counter with upper right corner. 3. Then o goes in Middle left. 4a. If x goes in top left then o wins horizontal middle. 4b. If x goes middle right then o wins left vertical

I assumed the problem was implying that given this scenario could you force a win with this one move excluding and moves afterwards XD

William Kennedy - 3 years, 7 months ago

As long as Circle's next move is on the corner, it is going to win.

Any corner?

Agnishom Chattopadhyay - 3 years, 7 months ago

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Any corner works.

A Former Brilliant Member - 3 years, 7 months ago
Pedro Hm
Oct 17, 2017

There's an even quicker solution: put an O on the top left corner, which forces X to be put on the lower right corner. In turn that forces O to be put in the lower left corner, assuring the win for O.

Jay Denney
Oct 16, 2017

As long as 'O' does not go into the top centre square with its next move, it should be able to win.

Terry Smith
Oct 16, 2017

In TicTacToe the first player must take the center or they will lose. The second player must take a corner or THEY will lose.

Wrong. The first player can safely start in any cell. In each case, with perfect play the game is drawn. Specifically:

  • If player 1 takes the centre, player 2 must take a corner
  • If player 1 takes a corner, player 2 must take the centre
  • If player 1 takes an edge, player 2 must take one of the cells in the same row or column.

Stewart Gordon - 3 years, 7 months ago

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This is the most interesting comment so far.! I wonder if in the case of this specific problem there is/are way/s for the X player to definatelly block O from winning.. This would be for me more interesting (like a chess "avoid check&mat in 2 moves" problem)..:):)

george soilis - 3 years, 7 months ago

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