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There are six faces and three colours. As there is no restriction on adjacent colours, we can colour each face 3 ways, overall 6^3 ways to paint the cube.Huh, is it this simple? or am I missing something?
The explanation by Venkata seems correct, and as per the explanation, answer should be 3^6, 3 options for each face and there are 6 faces. Correct me if I am wrong !!