What is the minimum number of different colours required to paint the figure given above such that no two adjacent regions have the same colour?
A) 3
B) 4
C) 5
D) 6
Correct Answer: A
Solution :
We shall label the various regions in the given figure as shown. The regions A, C, E and G can have the same color say color 1. The regions B, D, F and H can have the same color (but different from color 1, say color 2. The region I lies adjacent to each one of the regions A, B, C, D, E, F, G and H and therefore it should have a different color say color 3. The regions J, L and N can have the same color (different from the color 1 and 3). Thus, these regions will have color 2. The region P cannot have any of the colors 1 and 2 as it lies adjacent to each one of the regions J, K, L, M, N and O and so it will have color 3. The region Q can have any of the colors 1 or 2. \[\therefore \]Minimum number of colors required is 3.
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