Question

In how many ways can the four walls of a room be painted with three colours such that no two adjacent walls have the same colour?

• A. 2
• B. 9
• C. 18
• D. 24

Hint:

At high temperatures, the heat capacity of a solid follows the Dulong-Petit law.

Answer 1

The Correct Option is D

Let walls be A, B, C, D (forming a closed loop). Since no two adjacent walls can have the same colour: - Wall A: 3 choices - Wall B: 2 choices (not same as A) - Wall C: 2 choices (not same as B) - Wall D: Not same as both C and A, still 2 choices possible So, total ways = \(3 \times 2 \times 2 \times 2 = 24\)