Six letters S, T, M, P, R and C are written on different faces of a dice. Two positions of this dice are shown in the figures below. Find the letter on the face opposite to M.

Correct — B.

Rule: T is on top in both views, so the cube has only been spun about the vertical axis and the four side letters stay in one ring around T.

A quarter-turn one way would carry S round to the right-hand face; a quarter-turn the other way would carry M round to the left-hand face. The second view shows neither S nor M, so the cube has been turned a half-turn, 180 degrees.

A half-turn replaces every side face with the face opposite it. The right-hand face read M and now reads R, so M is opposite R — option (b).

Why the others are wrong

• (a)
  C — C is drawn in neither view, which makes it the hidden face opposite the top letter T. It is the one letter the two views never place beside M.
• (c)
  S — S and M are drawn on adjacent faces of the first view, meeting along the front vertical edge. Faces that share an edge can never be opposite.
• (d)
  P — The half-turn brings P to the left-hand face, where S had been, so P is opposite S. The letter arriving where M stood is R, not P.

Two views pin down opposite faces only when you can say how the cube moved between them.

Because T sits on top in both drawings, the movement is a rotation about the vertical axis, and the four side letters S, M, P and R stay in a single ring around T.

A quarter-turn always leaves one of the two visible side faces still visible. Neither S nor M reappears in the second view, so the turn has to be a half-turn, and a half-turn swaps each side face for its opposite.

That gives M opposite R and S opposite P. T, which appears in both views, is left with the only letter never drawn: C.

Key facts

• The six letters are S, T, M, P, R and C, and C appears in neither view.
• Faces drawn together in one view share an edge, so S is not opposite M and P is not opposite R.
• A 180-degree turn about the vertical axis leaves the top face unchanged and replaces every side face with its opposite.

Common traps

• Assuming C must be opposite M just because C is never shown.
• Guessing between the two surviving pairings instead of settling how far the cube turned.

No directly related past PYQ was found.