30
votes
Accepted
Titanic Tic-Tac-Toe
The first player can always force a win.
I wrote this Python script to analyze the tree of possible game states reachable from an empty starting board. No matter what the second player does, the ...
- 6,409
19
votes
Accepted
Noughts and Crosses puzzle
The position is as follows:
No two of Eques's counters occupy the same line of 3 (satisfying the never-threatening requirement), and no matter where Knott (O) places their next O, Eques (X) has a ...
- 121k
18
votes
Accepted
Blindfold Tic-Tac-Toe
You can't do this going second:
The strategy going first is:
Interestingly,
- 144k
14
votes
Accepted
A Tic-Tac-Toe variant with three marks - winning strategy and chances
Solution
Step-by-step deduction
If A plays first, then
Proof: the crucial realisation is that B can always force A to play in a specific square. WLOG, say A's first move is an $X$.
If A's first ...
- 115k
14
votes
Tic-Tac-Toe problem
The answer is no, no one can force a win. Suppose Niels goes first. Henrik can stop Niels from winning as follows: whenever Niels goes in a triangle, Henrik goes in the corresponding coloured triangle:...
- 9,185
13
votes
Accepted
Tic-Tac-Toe Without a Predefined Board
X plays, O plays, X plays as follows:
X O
X
We're now locked on this plane, albeit not uniquely (the O can be in the central or rightmost column). Either way, O ...
- 1,003
12
votes
Accepted
What is my favorite brand of pen?
I don't know what it was about the last hint that finally got me to the solution but I have it now.
Here's how I moved forward from Stiv's partial solution:
finally gives
Many thanks to Stiv for ...
- 1,108
12
votes
What is my favorite brand of pen?
A partial answer to explain the 'Given...' section.
There are several clues in this puzzle to tell us that we should be focussing not on tic-tac-toe, but on the game of...
One other important element ...
- 121k
11
votes
Accepted
Buzzword Bingo Boss Battle!
So, we are playing misère Tic-tac-toe with the option of taking more than one turn in a row. Seems quite interesting, so let's take a stab at it.
The flow of the narrative here is a bit messy, because ...
- 72.4k
9
votes
Accepted
Pigpen Tic-Tac-Toe
The game:
So the winner is...
First lets deduce what the words must be:
And now we can fill in the grid, turn by turn:
And from here, calculating the scores will find that
- 54.6k
6
votes
Accepted
Another Tic-Tac-Toe problem
A wins if $n=2$:
No matter what B plays on their first turn, there will be a flat plane passing through the first X, which contains at most one O. A can create a 2 by 2 square on that plane while ...
- 33.4k
6
votes
Accepted
Tic Tac Toe Recursive
Alice wins.
She starts by playing in the center square of the center board (which we'll call board C). Bob sends Alice over to another board, and she plays in the center of that one. Eventually, Bob ...
- 144k
5
votes
Accepted
Noughts and Crosses and... there's more?
First, as clued in the hint,
Looking at the grids in the first row, we note that
Interpreting
Looking at the bottom row of grids
- 15.1k
5
votes
Accepted
Tic-Tac-Toe on a Rubik's Cube
They are literally winning words because..
We can see that..
We can list down them as,
Now using the same logic for remaning two matches we get..
from where we can identify the other two winning ...
- 4,779
5
votes
Decision Paralysis
The one with the winning strategy is quite surprisingly
First, let us note that
First options
Case 1
Case 2
Case 2.1
- 8,038
5
votes
Optimal running-time tic-tac-toe algorithm
"Asymptotic complexity" is a notion that only makes sense when you have some notion of "problem size" that can increase to infinity.
The game of tic-tac-toe is always played on a 3x3 board and never ...
- 116k
4
votes
What is the optimal first move in tic-tac-toe?
There is a nice article analyzing the Tic Tac Toe first move strategy at https://paperandpencilgames.com/2019/02/tic-tac-toe-strategy-tutorial.html
To address the reviewers comments, here is the ...
- 417
3
votes
What is the ideal strategy in this randomised-goal tic-tac-toe variant?
I spent entirely too much time thinking about this when it was posted, but I still only have a partial answer.
Also, this whole answer (and all of its underlying thoughts) were assuming that the game ...
- 2,213
3
votes
Accepted
Harary's generalized Tic-Tac-Toe; Winning strategy for Skinny on a 7 x 7 board?
Daniel Mathias has solved this question in a comment on the MSE post, so for completeness I will summarize the entire strategy here.
X starts by claiming the center. Up to symmetry, O's response is ...
- 31.8k
2
votes
N-dimensional Tic-Tac-Toe variant
I don't know the answer exactly, but roughly speaking it should scale with $N$.
Suppose the answer is a line of length $n$, and suppose that the O player is able to contain the X player in a ...
- 22.4k
2
votes
N-dimensional Tic-Tac-Toe variant
I don't know solution for any N, but may be investigation of more general problem can be helpful.
Let's say we have N dimensional space and for each X turn O has M turns. Call the result (max length ...
- 16k
2
votes
What is the optimal first move in tic-tac-toe?
From experience of playing against kids that don't have the game solved (daughters, ages 5 and 7 at the time of play), starting in the corner gave about 1/3 chance to win and starting in the center ...
- 2,050
2
votes
Tic-Tac-Toe Without a Predefined Board
Yes, as long as I didn't interpret you wrong, I believe that player 1 has a forced win:
Diagram:
Diagram explantion and reasoning:
2.
3.
4.
- 4,105
1
vote
What is the optimal first move in tic-tac-toe?
One way to answer this is to consider all 255,168 possible games of tic-tac-toe and record if they result in a win, draw or loss for the starting player and analysing where the first move was for each ...
- 127
1
vote
Titanicker Tic-Tac-Toe
There can't be a draw because if the board is full, either you can move the board and get new places to play, or you can't because all positions you can go where already used, and you lose.
So the ...
- 804
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