The six faces of a dice have been marked with the letters A, B, C, D, E and F. If A is adjacent to B, C and E, then which of the following statements is definitely true?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → D is adjacent to F
On a cube each face touches four faces and is opposite the fifth. A face also touches every face that touches the face opposite it.
A touches B, C and E, so A’s fourth neighbour and its opposite face are D and F, in some order.
Whichever of D and F is opposite A touches all four of A’s neighbours, and the other of the two is one of them.
So D and F always touch each other: D is adjacent to F in every possible dice.
Why the other options are incorrect
Option (1) B is adjacent to E — Incorrect. Two of A’s four neighbours can be opposite each other, so B and E may be opposite faces.
Option (3) A is adjacent to D — Incorrect. D may be the face opposite A, with F as A’s fourth neighbour.
Option (4) F is adjacent to A — Incorrect. F may be the face opposite A, with D as A’s fourth neighbour.