The six faces of a dice have been marked with alphabets A, B, C, D, E and F…
2025
The six faces of a dice have been marked with alphabets A, B, C, D, E and F respectively. This dice is rolled three times, and the three resulting positions are shown as:
Find the alphabet opposite A.
- A.
C
- B.
D
- C.
E
- D.
F
Attempted by 2 students.
Show answer & explanation
Correct answer: C
In a "three positions of a dice" puzzle, each picture shows three faces meeting at one corner, and those three faces are always mutually adjacent to one another; adjacent faces can never form an opposite pair. Every face of a cube has exactly one opposite face and exactly four adjacent faces, so once four distinct faces have been confirmed adjacent to a given face, the sixth remaining face must be its opposite.
From view (i): A, B and C are mutually adjacent, so B and C are both confirmed adjacent to A.
From view (ii): D, C and E are mutually adjacent, so C and E are both confirmed adjacent to D, and C and D are both confirmed adjacent to E.
From view (iii): F, E and B are mutually adjacent, so E and B are both confirmed adjacent to F, and F and B are both confirmed adjacent to E.
Collecting every face confirmed adjacent to E: C and D (from view (ii)) and F and B (from view (iii)) - four distinct faces in all.
Since these four faces already account for all of E's adjacent faces, the only face never confirmed adjacent to E is A, so A must be E's opposite face.
Faces confirmed adjacent to B: A and C (view (i)), and F and E (view (iii)) - four distinct faces, so D, the only face left, is opposite B.
Faces confirmed adjacent to C: A and B (view (i)), and D and E (view (ii)) - four distinct faces, so F, the only face left, is opposite C.
That leaves only A and E unpaired, which independently confirms the same result: A is opposite E.
Therefore, the alphabet opposite A is E.