Dicey Directions
An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?
Problem
Image
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 facing after this sequence of moves?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: the '1' face will be facing West
Rotate so that 1 faces down:
Image
Rotate so that 2 faces down:
Image
Rotate so that 3 faces down:
Image
Rotate so that 5 faces down:
Image
As the '6' face is now facing East, the '1' face will be facing West.