A dice has numbers 1, 2, 3, 5, 6 and 8 on its sides. Two different positions of the same dice are shown below. Select the number that will be on the face opposite to the one having 6.

Correct — C.
Rule: a face is never opposite anything it is seen beside.

The first view shows 6 on the left with 5 on top and 3 on the right.
The second view shows 6 on the left with 2 on top and 1 on the right.

So 6 shares an edge with 5, 3, 2 and 1 — four of the five other faces. The dice carries 1, 2, 3, 5, 6 and 8, so the only face never seen beside 6 is 8, and it must be the opposite one.

That is option (c).

Why the others are wrong

• (a)
  3 — 3 is the right-hand face in the first view while 6 is on the left of the same cube, so the two share an edge and cannot be opposite.
• (b)
  2 — 2 is the top face in the second view with 6 on the left, which makes them adjacent.
• (d)
  1 — 1 is the right-hand face in the second view, sitting directly beside 6, so it is ruled out too.

On a cube every face touches four faces and is opposite exactly one. That gives a clean elimination method for two-view dice.

When a number appears in both views, you get to read its neighbours off directly — two from each picture. Four distinct neighbours account for everything except the opposite face, so the answer is whichever number is left over.

No rotation reasoning is needed in that case, which is why spotting the repeated face first is worth the two seconds it costs.

Key facts

• Every face of a cube is adjacent to four faces and opposite exactly one.
• 6 appears in both views, so its neighbours read off directly as 5, 3, 2 and 1.
• The six numbers printed on this dice are 1, 2, 3, 5, 6 and 8.

Common traps

• Assuming opposite faces add to a fixed total when the numbers are not 1 to 6
• Rotating the cube mentally when the repeated 6 already gives the whole adjacency list

No directly related past PYQ was found.