Observe the dots on a dice (one to six dots) in the following figures. How…

Concept: When two different views of the same dice are shown, any face that occupies the exact same position (say, always on the right) in both views pins down the dice's fixed rotation axis — the axis running through that face and its hidden opposite. The remaining four faces (top, front, bottom, back) then rotate cyclically about this axis between the two views. A direct consequence: the two faces that are NOT common to both views end up opposite each other.

1. In figure (i), the visible faces are: Top = 2, Front = 1, Right = 5.

2. In figure (ii), the visible faces are: Top = 1, Front = 4, Right = 5.

3. Face 5 is common to both figures and stays in the same position (Right) each time, so the dice has been rotated about the Right–Left axis; only the Top, Front, Bottom, and Back faces move.

4. Face 1, which was on the Front in figure (i), has moved to the Top in figure (ii) — this fixes the direction of the cyclic rotation as Front → Top → Back → Bottom → Front.

5. Following that same rotation, the face that was on the (hidden) Bottom in figure (i) rotates into the Front position in figure (ii) — exactly where face 4 now appears.

6. So face 4 physically occupies the Bottom of figure (i), which is directly opposite the Top of figure (i) — and the Top of figure (i) carries 2 dots.

Cross-check: this matches the standard shortcut for such problems — whenever two faces are common between two views of a dice, the two faces that are not common (2 in figure (i) and 4 in figure (ii)) must be opposite each other, confirming the traced rotation.

Result: the face opposite the one showing 4 dots carries 2 dots.