Case 15 · spatial reasoning · Medium · About 8–12 minutes
An archive's demonstration cube carries one number on each face. A guide rolls it through a short route without picking it up. At the end, two faces matter for a combination.
You can track the cube on paper or use any small box with temporary face labels. Ordinary dice conventions are not required.
The cube starts with these faces pointing in the stated fixed room directions:
- Top: 1; bottom: 6.
- North: 2; south: 5.
- East: 3; west: 4.
North is the top of your page, east is right, south is down, and west is left. These directions stay fixed throughout.
Roll the cube one face-width in each direction, in this exact order:
North, east, east, south, west, north.
Each roll is a quarter-turn over the corresponding bottom edge. There are no slides, spins on the floor, or turns about a vertical axis. For example, on a northward roll the old top becomes the north-facing side, and the old south-facing side becomes the new top.
Which number is on top after the sixth roll, and which number faces north?
The positions of the cube on the floor do not matter. Track its orientation. The illustration is decorative and does not define any starting face numbers.
Hint 1 - reveal when you want a nudge
After the first north roll, the top is 5 and the north face is 1. East and west faces have not changed.
Hint 2 - reveal when you want a nudge
Track three perpendicular faces, or all six, after every roll. After the two east rolls, the top is 2, north is 1, and east is 4.
Reveal the solution and explanation
The final top is 2, and the final north face is 4.
Here is an orientation check using the top, north, and east faces after each roll:
| Stage | Top | North | East |
|---|---|---|---|
| Start | 1 | 2 | 3 |
| North | 5 | 1 | 3 |
| East | 4 | 1 | 5 |
| East | 2 | 1 | 4 |
| South | 1 | 5 | 4 |
| West | 4 | 5 | 6 |
| North | 2 | 4 | 6 |
The opposite pairs remain 1–6, 2–5, and 3–4. These pairs let you recover the three unlisted faces at every stage. At the end, bottom is 5, south is 3, and west is 1.
A common mistake is treating east as the cube's personal right after turning. Here east always means the room's east. Since the start and every quarter-turn are completely specified, each new orientation is forced and the result is unique.
Solve another: The Cabinet of Fifty Mysteries · Browse all 50 cases
