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Torus Patterns

Age 16 to 18
Challenge Level

An insight to this problem will most likely be gained by physically trying to colour in various regions of the squares on paper, where you can get a feel for how everything fits together.

Start by working out which parts of the squares are connected together. If you colour one region of the square, you will see that the colours of certain other regions of the square immediately follow by considering connected parts of the square.