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The snapshot shows an example of a square subdivided into (26) squares no two of which are of the same size. It also shows a colouring scheme for the squares such that no two adjacent ones have the same colour. How to carry out such a subdivision? Well look at the papers [1] and [2] for an interesting approach based on an a reformulation of the problem as an electrical circuit problem

The colouring scheme has to do with what was until not very long ago called `the four-colour conjecture':* you need at most four colours to colour any map such that no two adjacent regions have the same colour*. Look up what it is, and is it still a conjecture? What is in the mathematical parlance called a conjecture?