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?
Age
14 to 16
Challenge level
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Dicey Directions
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 facing after this sequence of moves?

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.