Chapter 19 Quad-Tac-Toe Game
Project by: James Andrews, Ari Blondal, Tu Trinh, and Haohui Zhang.
\(\textbf{Summary:}\) The goal of this project was to remake the old board game Qubic - 3D Tic Tac Toe - into a web game.
The project is based on Hales-Jewett theorem:
Let \(m,k\in \mathbb{N}\) and let \(A\) be an alphabet on \(m\) symbols. There exists an \(n\in \mathbb{N}\) such that whenever \(A^n\) is \(k\)-coloured there exists a monochromatic line.
In the Quad-Tac-Toe game one considers the alphabet \(A=\{0,1,2,3\}\) and the cube \(A^3=\{(x,y,z):x,y,z\in\{0,1,2,3\}\}\text{.}\) Two players are given two different colours and tasked to colour one point \((x,y,z)\in A^3\) at each turn. The player who first completes a monochromatic line wins. Here “a line” means a a set of four collinear points contained in \(A^3\text{.}\)
Observe that there are 76 lines in \(A^3\text{,}\) but that only \(61\) of them are combinatorial lines.
In the current version of the game, the player plays against AI.
\(\textbf{Game:}\) To play the game please go to Quad-Tac-Toe Game.
\(\textbf{GitHub:}\) To access the project files please go to this GitHub repository.