A dice is numbered from 1 to 6 in different ways. If 1 is adjacent to 2, 4 and…

Concept: On a cube (a standard six-faced die), every face is adjacent to exactly four other faces and opposite to exactly one face. A face can never be both adjacent to and opposite the same face, and its opposite partner is unique.

1. Face 1 has exactly four neighbours in total. The question already names three of them — 2, 4 and 6 — so only one of the two remaining faces, 3 or 5, can be 1's fourth neighbour; the other must be 1's unique opposite face.

2. Case A: 1 is adjacent to 3, so 5 is opposite 1.

3. Case B: 1 is adjacent to 5, so 3 is opposite 1.

4. Apply the same neighbour-count rule to whichever face sits opposite 1: it is adjacent to every other face except 1. In Case A that face is 5, so 5 is adjacent to 3. In Case B that face is 3, so 3 is adjacent to 5.

5. So in both possible cases, 3 and 5 end up adjacent to each other — the relationship holds no matter which case actually describes the die.

Cross-check: a face has only one opposite, and one of 3/5 is always forced into that role for face 1 in both cases above — so 3 and 5 can never occupy each other's opposite position either, which is why "3 opposite 5" fails. The statements about "2 opposite 6" and "1 adjacent to 3" each hold in only one of the two cases, so they are possible but not necessary; only "3 is adjacent to 5" holds in every valid arrangement.