Six letters X, T, S, M, R and O 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 R.

Correct — A.

Both views show X on top, so the dice has only been spun about its vertical axis. X is therefore opposite the sixth letter, O, and T, S, M, R are the four side faces.

Rule: when the top face repeats, the four side faces keep their cyclic order.

View 1 reads left face T, right face S. View 2 reads left face M, right face R.
Reading both the same way, the side ring runs T, S, M, R — S follows T and R follows M.

In a ring of four, opposite faces are two apart: T is opposite M, and S is opposite R.
So the face opposite R is S → option (a).

Why the others are wrong

• (b)
  M — M and R are visible together in view 2, so they share an edge. Two faces seen in the same picture can never be opposite.
• (c)
  O — O appears in neither view, which is exactly what makes it the face opposite X, the letter on top in both pictures. It is already spoken for.
• (d)
  T — T and R are never seen together, so adjacency alone does not rule T out — but the side ring runs T, S, M, R, which places T only one step from R.

Two views of a dice give you adjacency, and adjacency on its own is often not enough. Here T-S and M-R are the only pairs seen together, which leaves two possible pairings of opposites.

What breaks the tie is that X is on top in both pictures. A repeated top face means the dice has turned only about the vertical axis, so the four side faces keep their cyclic order.

Read each picture the same way — left face, then right face — and the two readings join into one ring: T, S, M, R. Faces two apart in a ring of four are opposite.

Key facts

• X on top in both views forces X opposite O, the letter shown in neither view.
• The side ring is T, S, M, R, read as left face then right face in each picture.
• In a ring of four side faces the opposite pairs are T-M and S-R.

Common traps

• Concluding from adjacency alone, which leaves two consistent pairings here
• Reading one picture left-to-right and the other right-to-left, which reverses the ring and swaps the answer

No directly related past PYQ was found.