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?
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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.
Answer: the '1' face will be facing West
Rotate so that 1 faces down:
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![Dicey Directions Dicey Directions](/sites/default/files/styles/large/public/thumbnails/content-id-5771-dicey%252520directions%252520solution%2525201.png?itok=cs3R0nE2)
Rotate so that 2 faces down:
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![Dicey Directions Dicey Directions](/sites/default/files/styles/large/public/thumbnails/content-id-5771-dicey%252520directions%252520solution%2525202.png?itok=eLIzsYEa)
Rotate so that 3 faces down:
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![Dicey Directions Dicey Directions](/sites/default/files/styles/large/public/thumbnails/content-id-5771-dicey%252520directions%252520solution%2525203.png?itok=t0-w-jdL)
Rotate so that 5 faces down:
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![Dicey Directions Dicey Directions](/sites/default/files/styles/large/public/thumbnails/content-id-5771-dicey%252520directions%252520solution%2525204.png?itok=jupmx9UU)
As the '6' face is now facing East, the '1' face will be facing West.