Two positions of a dice are shown below. When number 1 is on the top, what…
2024
Two positions of a dice are shown below. When number 1 is on the top, what number will be at the bottom?
- A.
2
- B.
3
- C.
5
- D.
can't determine
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept: When two positions of a cube/dice share one common face in the same position (here, 6 on top in both), compare the other visible side faces. If one side-face value appears in both views but switches sides (right in one view, left in the other), the two faces that do NOT repeat between the views must be a pair of opposite faces of the cube.
Position | Top face | Left face | Right face |
|---|---|---|---|
(i) | 6 | 1 | 4 |
(ii) | 6 | 4 | 5 |
The top face (6) is common to both positions, so both views are anchored to the same vertical axis.
The value 4 is also common to both positions, but it moves from the right side in position (i) to the left side in position (ii).
Because the repeating face (4) switches sides while the top stays fixed, the two side faces that do NOT repeat between the two positions — 1 and 5 — must be the pair of faces opposite each other on the cube.
Cross-check: Arranging the three known side faces in the rotational order read off the two views gives the cyclic sequence 1 → 4 → 5 → (the unseen fourth side face) around the vertical axis through the top and bottom faces. In a ring of four side faces, faces that are two positions apart in the cycle are opposite each other — that places 1 opposite 5, and 4 opposite the unseen face, matching the pairing found above.
Result: Since 1 and 5 are opposite faces, when 1 is turned to the top, 5 must be at the bottom.