Six letters V, C, R, E, X and Z 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 C.

Correct — D. In both pictures R sits on the same front-right face, so the die has only been spun about the axis through R.

Rule: the face that holds its position is the axis, and the other four faces form a ring turning around it.

Read each view the same way — top face, then front-left. View 1 gives V then C; view 2 gives E then X. All four touch R, so the unseen Z is what lies opposite R.

Only one ring order fits both readings: V → C → E → X. Opposites in a ring of four sit two steps apart, so V faces E and C faces X — option (d).

Why the others are wrong

• (a)
  R — R and C are visible together in view 1, so they share an edge. Two faces seen in the same picture are adjacent and can never be opposite.
• (b)
  Z — Z appears in neither view, so it is the hidden face. It sits opposite R, the letter that holds its position through the turn, not opposite C.
• (c)
  V — V is on top in view 1 while C is on the front-left of that same view. Both are visible at once, so they are adjacent faces.

Two-view dice questions are settled by what stays put. If one symbol occupies the same visible position in both pictures, the die was turned about the axis through that face.

That symbol and the one you never see are then a fixed opposite pair, and the remaining four faces form a ring spinning around them.

Collect the ring from each view in a consistent reading direction, top face first and front-left face second. The single cyclic order that satisfies both views gives every opposite pair, because opposites in a four-ring are two steps apart.

Key facts

• A cube has three opposite pairs, so naming one pair settles nothing about the other two.
• Any two faces visible in the same picture are adjacent, never opposite.
• Here R keeps the front-right face in both views, so R and the unseen Z are the fixed pair.

Common traps

• Pairing faces by their screen position instead of tracking the rotation
• Treating two letters visible in one view as an opposite pair
• Reading the ring in a different direction from each picture, which swaps two of the pairs

No directly related past PYQ was found.