One die is drawn below in three different ways. Find the number opposite 7.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8
A face of a die touches four other faces and is opposite the one face it never touches. Faces seen together in one picture are neighbours, so they can never be opposite each other.
4 is seen next to 5 and 7 in (ii); 3 and 8 in (iii). So 4 touches four faces, and the only face left, 2, is opposite 4
5 is seen next to 2 and 8 in (i); 4 and 7 in (ii). So 5 touches four faces, and the only face left, 3, is opposite 5
7 is seen next to 4 and 5 in (ii). 2 is already opposite 4 and 3 is already opposite 5, so the only face that can be opposite 7 is 8
Why the other options are incorrect
Option (1) 2 — Incorrect. 2 is the face opposite 4, so it cannot also be opposite 7.
Option (3) 3 — Incorrect. 3 is the face opposite 5, so it cannot also be opposite 7.
Option (4) 5 — Incorrect. 5 is seen next to 7 in picture (ii), so it touches 7 and cannot be opposite it.