Cube Container Rotation Check
A cube-shaped equipment container has six faces marked with lifting-point codes. The rigging plan states: code A is opposite D, B is opposite E, and C is opposite F. In the stored orientation, A is on top, B faces north, and C faces east. To fit a sling, the crew must rotate the container 90 degrees clockwise as viewed from above, then tip it forward 90 degrees so that the face that was top moves to the north side. A crane attachment must be on the face that ends up on top. The crew leader believes the top face will be D because D was on the bottom originally. You must verify the final orientation and identify which code is on top, which faces north, and which faces east. No diagram is available; the markings are painted and cannot be read from the crane cab. The container is symmetric, so only the painted codes reveal orientation.
1. Determine the code on the top face after both rotations. Show each step and name the face that ends up north and the face that ends up east.
Read the worked answer
Start with a complete orientation. Top A, bottom D, north B, south E, east C, west F. Opposite pairs are A-D, B-E, C-F, which matches the plan.
Step 1: rotate 90 degrees clockwise as viewed from above. The top and bottom stay put. Looking down, clockwise moves north to east, east to south, south to west, and west to north. So: top A, bottom D, north F, east B, south C, west E.
Step 2: tip forward 90 degrees so the old top goes north. The east and west faces stay on the same sides. The top A moves to north; the north F moves to bottom; the bottom D moves to south; the south C moves to top. Final orientation: top C, north A, east B, south D, west E, bottom F.
Check with opposites: top C must be opposite bottom F, which holds. North A must be opposite south D, which holds. The final top code is C, not D.
2. The crew leader says the top face will be D because D was originally on the bottom. What is the error in that reasoning, and what simple physical check could confirm the final top face without a diagram?
Read the worked answer
The error is treating a face's original position as its final position. A 90-degree tip moves the bottom face to a side, not to the top. In this sequence, D starts on the bottom, stays on the bottom through the clockwise turn, and then moves to the south side when the container is tipped forward. The face that moves to the top is the old south face, which after step 1 is C. The leader also overlooks that the first rotation changes which face is south before the tip.
A simple check is to mark the starting orientation on a small box: write A on top, B on the north side, and C on the east side. Perform the same two rotations physically, then read the top, north, and east faces. The result should be top C, north A, east B. A second check is to verify opposite pairs at the end: C and F must be opposite, and A and D must be opposite. If someone claims D is on top, then A would have to be on the bottom, but A ends on the north side, so D cannot be top.
3. If the crew instead tipped the container backward 90 degrees after the same clockwise rotation, how would the final top and north faces differ?
Read the worked answer
After step 1 the orientation is top A, bottom D, north F, east B, south C, west E. Tipping backward 90 degrees means the top moves south, the south moves to bottom, the bottom moves to north, and the north moves to top. East and west remain unchanged. The final orientation would be top F, south A, bottom C, north D, east B, west E. Compared with the forward tip, the top changes from C to F, and the north face changes from A to D. The east face remains B in both cases because the tip axis runs east-west. This comparison shows why the direction of the tip, not just the amount, determines the answer: the same starting orientation and the same 90-degree clockwise turn produce different top faces depending on whether the container is tipped forward or backward.