Q1: What is the minimum number of different colours required to paint he given figure such that no two adjacent regions have the same colour?

ANS:A - 3

The figure may be labelled as shown. The regions A, C, E and G can have the same colour say colour 1. 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 regions A, B, C, D, E, F, G and H and therefore it should have a different colour say colour 3. The regions J, L and N can have the same colour (different from colour 3) say colour 1. The regions K, M and O can have the same colour (different fromthe colours 1 and 3). Thus, these regions will have colour 2. The region P 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 colour 3. The region Q can have any of the colours 1 or 2. Minimum number of colours required is 3.