A white cube(with six faces) is painted red on two different faces. How many different ways can this be done (two paintings are considered same if on a suitable rotation of the cube one painting can be carried to the other)?


a)$2$ b)$15$ c)$30$


different ways can this be done is $2$ i.e one adjacent and one opposite.

As painting choosed will be same no matter what we choose

Am I right in my approach?Please correct me if I am wrong?

  • 2
    $\begingroup$ That seems correct to me. The first one can be anywhere and if the second is not opposite it has to be adjacent and each of those are equivalent by rotation. $\endgroup$ – John Douma Nov 14 '15 at 2:17
  • 1
    $\begingroup$ Your count is correct. For the colours on non-opposite faces, I can put a red face down on a table and rotate until the other red face is facing me. $\endgroup$ – André Nicolas Nov 14 '15 at 2:22

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