The 4 walls of a square room are painted using 3 available colours, each wall one colour. Walls that meet at a corner must have different colours. How many colourings are possible?

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Accepted Answer

18. Walls 1 and 3 face each other, as do 2 and 4. Case 1 & 3 same colour (3 ways): 2 & 4 each avoid it, 2×2=4, giving 12. Case 1 & 3 different (3×2=6): 2 & 4 must both be the third colour, 1 way, giving 6. Total 12+6=18.

The 4 walls of a square room are painted using 3 available colours, each wall one colour. Walls that meet at a corner must have different colours. How many colourings are possible?

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