Problem 11 · 2025 Math Kangaroo
Medium
Spatial & Visual Reasoning
dice-facescube-views
On a standard die, the sum of the number of points on opposite sides is always 7. We want to tilt the die shown several times along its edges so that all six sides are on top once. Which of the given sequences of top numbers is not possible?
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Answer: B — 3-2-5-1-6-4
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Hint 1 of 2
Each tilt moves to a face sharing an edge with the current top; opposite faces (summing to 7) can never be consecutive in the list.
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Hint 2 of 2
Check each sequence: two faces that are opposite must not appear next to each other.
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Approach: adjacent tops cannot be opposite faces
- Tilting over an edge sends the top to a face that shares that edge, i.e. an adjacent face — never to the opposite face (its 7-partner).
- So in a valid sequence no two consecutive top numbers may sum to 7; scan each option for such a forbidden step.
- In sequence B, the step 2 then 5 has \(2+5=7\), an impossible move, so B is the one that cannot occur.
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