Problem 18 · 2014 Math Kangaroo
Stretch
Spatial & Visual Reasoning
dice-facesspatial-reasoning
The faces of a die are labelled 1, 2, 3, 4, 5, 6. Faces 1 and 6 share an edge. So do faces 1 and 5, faces 1 and 2, faces 6 and 5, faces 6 and 4, and faces 6 and 2. Which number is on the face opposite face 4?
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Answer: A — 1
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Hint 1 of 2
Opposite faces of a die never share an edge.
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Hint 2 of 2
List every face that face 4 shares an edge with; the one number missing from that list is opposite to 4.
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Approach: find face 4's neighbours; the leftover face is opposite
- From the listed common edges, face 4 shares an edge only with face 6.
- Face 1 shares edges with 6, 5 and 2, but never with 4, so 1 is not next to 4.
- Working through the edges, faces 2, 3, 5 and 6 all end up next to 4, leaving 1 as the only non-neighbour.
- So the face opposite 4 is 1.
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