3D Tic-Tac-Toe

Logic Level 1

In $3D$ Tic-Tac-Toe, the game is not played on a board but in $3D$ space using $27$ cubicles in a $3 × 3 × 3$ format (It’s like filling the insides of an empty rubiks cube)

$\color{#D61F06}{\text{Player 1}}$ will inject the colour $\color{#D61F06}{\text{red}}$ into one cubicle followed by $\color{#2222ff}{\text{Player 2}}$ who will inject $\color{#2222ff}{\text{blue}}$ into a cubicle of his/her choice and so on.

An already filled cubicle can not be injected.

A player wins if they are able to make a consecutive line of three blocks in their colour.

If $\color{#D61F06}{\text{Player 1}}$ is to start first, who will win if both players play optimally?

\color{#D61F06}{\text{Player 1}}

\color{#3D99F6}{\text{Player 2}}

\color{#20A900}{\text{Draw(neither can win)}}

4 solutions

Agent T
Apr 6, 2021

I'm a tic tac toe champion so it was quite easy for me to guess :P

Player 1 can start with any corner.That will guarantee his win in the 3rd move irrespective of the 2nd player's move.

Sayantan Ray - 1 month, 3 weeks ago

I think u r missing something .... If he starts with corner player 2 goes center Then I assume u take a adjacent corner to ur first move so player 2 takes the one in between.but now player 2's first 2 crosses are lined so u cant attack and need to defend.hence u cant win till move 5

vatsal negi - 1 month, 2 weeks ago

I know what's missing ....it ....is ....the..... Answer itself

Agent T - 1 month, 1 week ago

Jonathan Xiang
Mar 7, 2021

player 1 can make the checkmate move at move 3

How can they do that? I've only found solutions for 4 moves.

Sebastian Krieg - 3 months ago

The checkmate move happens at move 3, the win happens at move 4, so both of you are right

Jason Gomez - 3 months ago

I'd like to see someone making a visual solution to this.

Veselin Dimov - 3 months ago

F Zs
Jun 7, 2021

Here's my logic:

Player 1 takes the center
Player 2 takes anything
Player 1 can force Player 2 in a move by taking either cubes adjacent to the center (i.e. either cubes). Player 1 has to take care not to force Player 2 in a winning combination.
Player 2 plays the forced move, to prevent Player 1 from winning.
Player 1 can create a triangular shape in any plane that has two possible winning combinations, making impossible for Player 2 to prevent both.

That is, something like this ( x is Player 1, o is Player 2, and * s mark Player 1's winning positions):
```
x x *
_ x _
_ o *
```

Also note that this strategy also works in 2D tic tac toe, however, it will lead to draw against a perfectly playing opponent (there's no way to always win in the 2D one).

Steven Adler
May 31, 2021

Player 1 takes the center of the middle layer.

If player 2 takes corner of upper or lower layer, player 1 takes middle of same layer. Player 2 must then block in middle of opposite layer. Player 1 then takes side or 2 of 3 corners of opposite layer. FORK!

If player 2 takes middle of upper or lower layer, player 1 takes corner of same layer. Player 2 must block on opposite corner of opposite layer. Player 1 then plays adjacent corner of opposite layer. FORK!

If player 2 takes side of upper or lower layer, player 1 takes adjacent side of same layer. Player 2 must block on side of opposite layer. Player 1 then plays adjacent corner of opposite layer. FORK!

If player 2 takes corner or side of middle layer, player 1 takes middle of upper or lower layer. Player 2 must block in middle of opposite layer. Player 1 then plays any corner of opposite layer. FORK!

There are no other possibilities for player 2’s first move. So player 1 always wins on his 4th move.

3D Tic-Tac-Toe

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