A rectangular wall is divided into four squares of equal size where there are two rows each having two squares. The top left square is coloured with green. If, including green, there are three colours available and each square is coloured using any one of these three colours such that no two adjacent squares get painted with the same colour; then how many colour combinations are possible?
- A2
- B4
- C6
- D8
Explanation
Fix the top-left square as green. Its two neighbours (top-right and bottom-left) must each avoid green, giving 2 x 2 = 4 assignments. If the two neighbours take the same colour (2 ways), the bottom-right square can be either green or the third colour (2 ways), giving 4 colourings. If the neighbours differ (2 ways), the bottom-right square must be green to differ from both (1 way), giving 2 colourings. The total is 4 + 2 = 6 possible colour combinations. Hence option C.