Six letters M, N, O, P, Q and R are written on different faces of a dice. Two positions of this dice are shown in the figure below. Find the letter on the face opposite to O.

Correct — A. Read the two drawings as one cube.

The first shows M on top, N in front and O on the right face. The second shows P on top, Q in front and O again on the right face.

Rule: two faces visible in the same drawing share an edge, so they are adjacent — and adjacent faces are never opposite.

O collects M and N as neighbours from the first drawing and P and Q from the second. That is four of its five possible neighbours, so the letter left over, R, is the face opposite O — option (a).

Why the others are wrong

• (b)
  P — P is drawn alongside O in the second view, so the two faces meet along an edge. An adjacent face cannot be the opposite one.
• (c)
  Q — Q also shares the second view with O, which rules it out for the same reason.
• (d)
  M — M shares the first view with O, so M is one of O's four neighbours rather than its opposite face.

A cube has six faces in three opposite pairs, and every face touches exactly four others.

That gives the fastest dice rule there is: anything you can see at the same time as a face is adjacent to it. Collect the letters that share a drawing with your target face, and whatever is left over is the opposite.

Here O appears in both drawings, so it gathers four neighbours without any rotation reasoning at all.

Key facts

• A cube's six faces form three opposite pairs, and each face is adjacent to four others.
• Two faces visible in one drawing of a cube are adjacent, never opposite.
• O is visible in both drawings, so M, N, P and Q are all adjacent to it.

Common traps

• Matching the two drawings by face position instead of by letter.
• Rotating the cube mentally when a repeated face already settles the answer.
• Choosing a letter that shared a drawing with the target face.

No directly related past PYQ was found.