Three different positions of the same dice are given. Find the number on the face opposite to the face showing ‘2’.

Correct — C. The three views read, as top / left / right: 3, 5, 4 — then 3, 4, 6 — then 2, 1, 6.

Dice 2 and dice 3 both carry 6 on the right, so between them the cube has only turned about the 6-axis.

Rule: when one face holds its position, the other four run in a fixed ring around it.

Reading top-then-left in each: dice 2 gives 3 then 4, dice 3 gives 2 then 1. The ring is therefore 3 → 4 → 2 → 1.

In a ring of four, faces two steps apart are opposite. So 2 pairs with 3 → option (c).

Why the others are wrong

• (a)
  6 — 6 shares a view with 2 — dice 3 shows 2 on top and 6 on the right — and faces seen together are adjacent, never opposite.
• (b)
  4 — 4 sits one step from 2 in the ring 3 → 4 → 2 → 1, not two. It is 1 that lies opposite 4.
• (d)
  1 — 1 stands beside 2 in dice 3, on the left while 2 is on top, so the two are adjacent faces.

Two rules settle almost every dice item. First, faces that appear together in one view are adjacent, so they can never be opposite.

Second, when two views share a face in the same position, the cube has turned about that face and the remaining four sit in a fixed cyclic order around it.

Collect the adjacencies first. Here 3 meets 5, 4 and 6, while 6 meets 1, 2, 3 and 4 — four neighbours, which already forces 6 opposite 5.

Key facts

• Faces printed in the same view are adjacent, so a number is never opposite one it is shown beside.
• When two views share one face in the same position, the other four faces run in a cyclic ring around it.
• In a four-face ring the opposite pairs are the entries two steps apart.
• The full pairing on this die is 1 with 4, 2 with 3, and 5 with 6.

Common traps

• Assuming opposite faces add to seven — on this die they add to 5, 5 and 11
• Using only two of the three views and guessing the final pair
• Reading the ring in opposite directions in the two views, which reverses the pairing

No directly related past PYQ was found.