First, we enumerate ways of describing moves of a standard color scheme 1x1x1 Rubik's cube (an object typically presented as a joke). Rotating any face of the cube of course rotates the entire cube.
Standard move notation: Rotate the {Up, Down, Left, Right, Front, Back} face by a {quarter, half, three-quarter} turn clockwise.
Rotate the {White, Yellow, Blue, Green, Red, Orange} face by a {quarter, half, three-quarter} turn clockwise.
Rotate the cube by a quarter turn so that the {Up, Down, Left, Right, Front, Back, White, Yellow, Blue, Green, Red, Orange} face takes the place of the {Up, Down, Left, Right, Front, Back, White, Yellow, Blue, Green, Red, Orange} face.
Next, a series of puzzle templates of increasing difficulty:
The cube has {U,D,L,R,F,B} face of color {W,Y,B,G,R,O} and {U,D,L,R,F,B} face of color {W,Y,B,G,R,O}. What is the color of the {U,D,L,R,F,B} face? Or, where is the {W,Y,B,G,R,O} face?
The cube has {U,D,L,R,F,B} face of color {W,Y,B,G,R,O} and {U,D,L,R,F,B} face of color {W,Y,B,G,R,O}. We do the following sequence of moves {move possibilities listed above}. After this sequence, what is the color of the {U,D,L,R,F,B} face? Or, where is the {W,Y,B,G,R,O} face?
The cube has {U,D,L,R,F,B} face of color {W,Y,B,G,R,O}. We do the following sequence of moves {move possibilities listed above}. After this sequence, the {U,D,L,R,F,B} face has color {W,Y,B,G,R,O}. We then do another sequence of moves {move possibilities listed above}. After this sequence, what is the color of the {U,D,L,R,F,B} face? Or, where is the {W,Y,B,G,R,O} face?
The constraints could be harder: The {U,D,L,R,F,B} face at time point T1 in this sequence of moves ... has {the same, a different} color as the {U,D,L,R,F,B} face at time point T2. Or dually, the {W,Y,B,G,R,O} face at time point T1 is in {the same, a different} location as the {W,Y,B,G,R,O} face at time point T2.
All of these are easily solvable by considering all 24 possible orientations of the initial cube. Doing 3-dimensional rotations in one's head is the challenge.
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