Three positions of a cube are shown below. Which number will be opposite to…

In a puzzle showing multiple views of a cube, two faces shown together in the same view always share an edge, so they are adjacent and can never be opposite each other. Consequently, if two different views both display the same pair of faces, the one face left over in each of those views is that face's true opposite — this is the Two-Common-Faces Rule.

1. The first view shows faces 1, 2, and 5, while the third view shows faces 5, 2, and 3 — both views share the same pair, 2 and 5.

2. By the rule above, the face left over in the first view (1) must be opposite the face left over in the third view (3).

3. Independently, the first view places 1 next to 2 and 5, and the second view places 1 next to 6 and 4 — so 1 is adjacent to all four of the other faces (2, 4, 5, 6). A face with four adjacent neighbours has only one face left to be its opposite, which confirms 1 is opposite 3.

So the face opposite the one marked 3 is 1.