One die is drawn below in three different ways. Find the number opposite 8.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5
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.
2 is seen next to 4 and 8 in (ii); 5 and 9 in (iii). So 2 touches four faces, and the only face left, 1, is opposite 2
4 is seen next to 1 and 5 in (i); 2 and 8 in (ii). So 4 touches four faces, and the only face left, 9, is opposite 4
8 is seen next to 2 and 4 in (ii). 1 is already opposite 2 and 4 is already opposite 9, so the only face that can be opposite 8 is 5
Why the other options are incorrect
Option (1) 4 — Incorrect. 4 is seen next to 8 in picture (ii), so it touches 8 and cannot be opposite it.
Option (3) 9 — Incorrect. 9 is the face opposite 4, so it cannot also be opposite 8.
Option (4) 1 — Incorrect. 1 is the face opposite 2, so it cannot also be opposite 8.