Chapter 29 Schur's Theorem: A Game
Project by: Revika Jain and Sahil Modak.
\(\textbf{Summary:}\) Our project is a based on Schur's theorem:
If the set of positive integers is finitely coloured, then there exists positive integers \(x\text{,}\) \(y\text{,}\) and \(z\) having the same colour and such that \(x+y=z\text{.}\)
The game can be played by 2–5 players. The game has numbers from 1 to 20. The game allows players to choose to have 2 or 3 colour options, and one of the two equations: \(x+y=z\) and \(x+y=2z\)
At each turn, a player can use any colour on any number on the game board. The player should colour numbers in a. way so that the chosen equation does not have a monochromatic solution.
To play the game go to Revika Jain's Github site.
Instructions: You can go to the terminal, and run python install pygame. After pygame gets installed, you can go into the folder where you have out game downloaded and then say Python UI.py. If you use VSCODE, then there is a run icon on the top right (that is usually where it is). That should open up a pop for you to play the game.
Watch the demo video: