Two different positions of the same dice with faces Z, G, M, F, H and S are shown below. Select the letter that will be on the face opposite to the one having G.

Correct — B. Z is on top in both views, so hold the vertical axis fixed and turn the cube about it.

With Z on top twice, the four letters seen on the sides — G, M, F and H — all lie in one ring around Z. That leaves S, the letter shown in neither view, as the hidden bottom face opposite Z.

View 1 shows a ring pair, left then right, as G, M. View 2 shows a ring pair as F, H. Turning about a fixed vertical axis preserves the ring order, so both pairs must sit in the same rotational sense.

The one ring of G, M, F, H holding G→M and F→H in the same sense is G, M, F, H. In a ring of four, faces two apart are opposite: G with F, and M with H → option (b).

Why the others are wrong

• (a)
  S — S appears in neither view. It is the sixth letter, and since Z sits on top in both pictures, S must be the bottom face — opposite Z, not opposite G.
• (c)
  H — H sits next to G in the ring, one step away rather than two. Adjacent faces meet along an edge; opposite faces never touch.
• (d)
  M — View 1 shows G and M on the cube at the same time, and two faces you can see together in one picture can never be opposite each other.

A dice item with a letter repeated in both views is the easy kind. Fix that repeated face as the axis and the puzzle collapses into a ring of four side faces.

Here Z is on top in both pictures. The four letters seen beside it — G, M, F and H — therefore form the ring around Z, and the sixth letter S has to be the hidden bottom.

Within a ring of four, neighbours are adjacent and the pair two steps apart are opposite. Matching the ordered pairs read off the two views is all that remains.

Key facts

• The die carries Z, G, M, F, H and S, one letter to a face.
• Z appears on the top face in both views, so G, M, F and H form the ring of side faces around Z.
• S appears in neither view, which places it on the hidden face opposite Z.
• In a ring of four side faces the pairs two steps apart are opposite: G with F, and M with H.

Common traps

• Choosing a letter that appears alongside G in the same picture, which proves the two faces are adjacent
• Assuming the unseen letter S must be opposite G, when it is opposite the repeated face Z
• Reading the two views in opposite rotational senses, which swaps the answer to H

No directly related past PYQ was found.