Problem 22 · 2012 Math Kangaroo
Hard
Spatial & Visual Reasoning
dice-faces
The diagram shows the 7 positions 1, 2, 3, 4, 5, 6, 7 of the bottom side of a die which is rolled around its edge in this order. Which two of these positions were taken up by the same face of the die?
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Answer: B — 1 and 6
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Hint 1 of 3
Track which face is on the bottom as the die tips from square to square.
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Hint 2 of 3
Each tip moves the bottom face to a neighbour; carefully follow it through the two turns in the staircase path.
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Hint 3 of 3
Label the starting bottom face and update it tip by tip until you see it land face-down again.
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Approach: track the bottom face along the path
- Label the face touching the ground on square 1 and follow it as the die tips along the staircase path 1-2-3-4-5-6-7.
- Updating the bottom face at each tip, the bottoms on the seven squares come out as positions 1, 3, 6, 2, 4, 1, 5 in terms of the original faces.
- The same face is on the bottom on square 1 and again on square 6, so the answer is 1 and 6, B.
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