What is the minimum number of colours required to fill the spaces in the given diagram without any two adjacent spaces having the same colour?
The space P, Q and R have to be shaded by three different colors definitely because these three spaces are adjacent to other two.
Now, in order that no two adjacent spaces have same colour, the space T, U and S must be shaded with the color of P, Q and R respectively.
Also the space X, V and W must be shaded with the color of the spaces S, T and U respectively i.e with the colors of the spaces R, P and Q respectively. Thus, minimum three colors are required.
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