IMC 2007 Q22
22. The diagram shows an ordinary die in which the scores on opposite faces always total 7. It is placed on a horizontal table with the ‘1’ face facing East. The die is moved four times, rotating it each time through 90° about an edge. The faces in contact with the table are first 1, then 2, then 3, then 5. In which direction is the ‘1’ face facing after this sequence of moves?
- A West
- B East
- C North
- D South
- E Up
Intermediate Mathematical Challenge 2007, Question 22. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A West
The table shows the number on the face in contact with the table at the various stages described and also the numbers on the three faces of the die visible from the viewpoint in the question.
| In contact with the table | 5 | 1 | 2 | 3 | 5 |
| Facing South | 3 | 3 | 3 | 5 | 4 |
| Facing East | 1 | 2 | 6 | 6 | 6 |
| Facing Up | 2 | 6 | 5 | 4 | 2 |
As the ‘6’ face is now facing East, the ‘1’ face will be facing West.
Solution © UK Mathematics Trust, from the IMC 2007 solutions.