Discussion
A dice is marked from A to F in different ways. If A is adjacent to B, D and F, then which of the following statements is necessarily true?
Answer: A
The statement that must be true is C is adjacent to E.
Each face of a cube touches four others and is opposite one. A touches B, D and F, so its fourth neighbour and its opposite face are C and E in some order. Whichever of C and E is opposite A, the other is one of A's neighbours, and a face opposite A touches all four of A's neighbours. So C and E are always adjacent.
'C is opposite E' is therefore impossible. 'B is opposite F' and 'A is adjacent to C' may or may not hold, depending on how the remaining faces are placed.
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