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Quarto games of different sizes

MathsJam Conference 2013 (02/11/2013).

We have a game called Quarto, which uses pieces with four different properties (colour, shape, etc.) and the object is to place four-in-a-row sharing one of the properties on a 4x4 board. Talking about noughts and crosses, we tried to simplify Quarto using a 3x3 setup and found this was impossible. I would like to describe Quarto and the (simple) maths behind which sizes of game do and don't work.

I also showed a naive Quarto player written in python that could play on different sized boards.