Problem 24 · 2023 Math Kangaroo
Stretch
Geometry & Measurement
spatial-reasoning
A game marker in the shape of a regular tetrahedron has one marked face. That face is placed on the triangle marked START. The marker is then moved within the diagram always to the next adjacent triangle by rolling it around an edge. On which triangle is the marker when it is on the marked side again for the first time?
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Answer: E — E
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Hint 1 of 2
Roll the tetrahedron one edge at a time and track which face is touching the table.
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Hint 2 of 2
Follow the marked face until that same face lands face-down again, and read where the marker sits on the net.
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Approach: simulate the tetrahedron rolling across the net
- Place the marked face on START and roll the marker from triangle to triangle over shared edges.
- Tracking the orientation, the marked face first returns to the table after the marker has travelled around the net.
- At that moment the marker is on triangle E.
Mark:
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