# 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

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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:

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Rotate so that 2 faces down:

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Rotate so that 3 faces down:

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Rotate so that 5 faces down:

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As the '6' face is now facing East, the '1' face will be facing West.