What is the minimum number of different colours required to paint he given figure such that no two adjacent regions have the same colour ?

Options

A. 3
B. 4
C. 5
D. 6

Answer

A

Explanation

The figure may be labelled as shown.

The regions A, C, E and G can have the same colour say colour .
The regions B, D, F and H can have the same colour (but different from colour 1) say colour 2. The region 1 lies adjacent to each one of the regidas A, B, C, D, E, F, G and H and therefore it should have a different colour say colour 3. A The regions J, L and N can have the same colour different from colour 3) say colour
1. The regions K, Mand O can have the same colour (different fromthe colours 1 and 3). Thus, these regions will have colour
2. The region cannot have any of the colours 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 dolour
3. The region Q can have any of the colours 1 or 2.
`therefore` Minimum number of coloursyequired is 3