Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [tic-tac-toe]

Tic-tac-toe is a paper-and-pencil game for two players, $X$ and $O$, who take turns marking the spaces in a $3 \times 3 $ grid.

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A non-losing strategy for tic-tac-toe $\times$ tic-tac-toe

Consider a $9 \times 9$ matrix that consists of $9$ block matrices of $3 \times 3$. Let each $3 \times 3$ block be a game of tic-tac-toe. For each game, label the $9$ cells of the game from $1$ to $9$ with order from left to right, from above to…
mez
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Is the aim of this Tic-Tac-Toe puzzle possible to achieve?

I was playing Tic-Tac-Toe with my friend when I came up with a puzzle. I might have to put this on the Puzzling Stack Exchange, but I do not know if the aim of the puzzle can be achieved. I am aware that math(s) is incorporated, so that is why I am…
Mr Pie
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Bidding Tic Tac Toe

In regular tic tac toe, both the players get alternate chances. This is a variant of that. Player $A$ has $\$x$ amount and player $B$ has $\$y$ amount as initial balance. Assume that $y>x$. Both the players bid some amount from the available amount…
Nimit
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Winning strategies in multidimensional tic-tac-toe

This question is a result of having too much free time years ago during military service. One of the many pastimes was playing tic-tac-toe in varying grid sizes and dimensions, and it lead me to a conjecture. Now, after several years of mathematical…
Joonas Ilmavirta
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Prove that a game of Tic-Tac-Toe played on the torus can never end in a draw. (Graph theoretic solutions only.)

Here's a problem I assigned to my graph theory class. The only caveat is that I insisted that their solutions be entirely graph theoretic. Have fun with it. Prove that a game of Tic-Tac-Toe played on the torus can never end in a draw. The idea…
Doc
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Prove that $5 \times 5 \times 5$ tic-tac-toe ends in a draw

I am pretty sure that when played perfectly, $5 \times 5 \times 5$ tic-tac-toe will end in a draw. Is anyone able to prove this?
suomynonA
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Tic-Tac-Toe on the Real Projective Plane is a trivial first-player win in three moves

Consider a $3 \times 3$ Tic-Tac-Toe board with opposite sides identified in opposite orientation. We play Tic-Tac-Toe in the Real Projective Plane. More precisely, consider a $3 \times 3$ Tic-Tac-Toe board on the unit square $[0,1]^2$. We glue the…
Desura
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Optimal Tic Tac Toe algorithm without lookahead

Is there any algorithm for tic tac toe that does not rely on a lookahead algorithm that is perfect for any sized boards? Edit: For boards larger than $3 \times 3$, we have to find the best move for a $k$ in a row where $k < n$ and we have a $n…
picakhu
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What are the symmetries of a tic tac toe game board?

What are the symmetries of the tic tac toe board game? In other words, what are the ways you can rotate, reflect, and/or flip the tic tac toe board, such that the next best move to a board (before it was rotated, reflected, etc) is still the next…
Jeff
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Two players put fill $1$ and $0$ in a $3\times 3$ matrix and compute its determinant when it is full. Can Player $0$ win if $1$ starts at the center?

In Determinant Tic-Tac-Toe, Player 1 enters a 1 in an empty 3 × 3 matrix. Player 0 counters with a 0 in a vacant position, and play continues in turn until the 3 × 3 matrix is completed with five 1’s and four 0’s. Player 0 wins if the determinant is…
global05
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Why does the strategy-stealing argument for tic-tac-toe work?

On the Wikipedia page for strategy-stealing arguments, there is an example of such an argument applied to tic-tac-toe: A strategy-stealing argument for tic-tac-toe goes like this: suppose that the second player has a guaranteed winning strategy,…
templatetypedef
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Game combinations of tic-tac-toe

How many combinations are possible in the game tic-tac-toe (Noughts and crosses)? So for example a game which looked like: (with positions 1-9) A1 -- B1 A2 -- B2 A3 -- -- [1][3][4][6][7] would be one combination
Danield
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On which simple graphs (no loops, no multi-edges) is tic-tac-toe winnable, where is it a draw?

Tic-tac-toe can be certainly won in 2D (on a 2-dimensional square grid including diagonals) already if the field is just slightly larger: 4x4 (while 3x4 still is a draw). There is an excellent video by 'PBS infinite series' -see references- that…
Michael T
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Probability of draw with random play on $N\times N$ Tic Tac Toe

I was coding a tic tac toe game where $2$ players play tic tac toe randomly on a given $N$ board size $(N\times N)$. $X$ starts first. If one side gets $N$ consecutive (horizontal/vertical/diagonal) of their symbols, they win. If no one won and…
Minot
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Tic Tac Toe on an infinite grid

Imagine playing tic tac toe, but rather than the standard 3 by 3 grid, the board extends indefinitely in every direction. When playing the usual game, one player must get three squares in a row to wind the game. However, with an infinite grid, three…
PiGuy314
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