Two different positions of the same dice with faces R, P, T, S, M and B are shown below. Select the letter that will be on the face opposite to the one having S.

Correct — D.

Rule: a face is never opposite a face it is seen beside.

The first view shows T on top, R on the left and S on the right, so S touches T and R.

The second view shows M on top, P on the left and S on the right, so S also touches M and P.

That accounts for four of the five other letters. Only B never appears next to S, so B is the face opposite S: option (d).

Why the others are wrong

• (a)
  M — M is visible together with S in the second view, so the two faces meet along an edge. Adjacent faces are never opposite.
• (b)
  R — R stands beside S in the first view. A letter you can see at the same time as S must border it, so R cannot be the hidden opposite face.
• (c)
  T — T sits on top in the first view while S faces you, so T borders S. Only a letter absent from both views can be opposite S.

A cube has six faces. Each one has four neighbours and exactly one opposite, and you can never see a pair of opposite faces at the same time.

So collect neighbours instead of rotating the die in your head. Every letter that appears alongside S in either view is eliminated.

When four letters have gone, the sixth is forced. Counting neighbours is enough whenever the two views between them expose four different letters beside the face you are asked about.

Key facts

• A cube face has four adjacent faces and exactly one opposite face.
• Two faces visible in the same view of a die are adjacent, never opposite.
• If four letters are seen beside a face, the one remaining letter is opposite it.

Common traps

• Assuming the letter drawn diagonally across from S is the opposite face
• Rotating the die mentally when simply listing neighbours already settles it
• Treating the two pictures as two different dice rather than one die turned

No directly related past PYQ was found.