Problem 5 · 2025 Math Kangaroo
Easy
Spatial & Visual Reasoning
sequence-of-figurestransformations
Thea rotates a painted hexagon clockwise one space at a time. The first rotation can be seen in the picture. Which hexagon does Thea see after the eighth rotation? (The five choices A–E are pictured below the question.)
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Answer: A
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Hint 1 of 2
The hexagon has 6 sectors, so rotating 6 times brings it back to the start.
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Hint 2 of 2
Eight rotations is the same as just 8 − 6 = 2 rotations.
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Approach: rotation repeats every 6 steps
- A hexagon has 6 sectors, so after 6 one-step turns it looks exactly like the start — the pattern repeats every 6 rotations.
- So the 8th rotation looks the same as the 8 − 6 = 2nd rotation; we only need to turn the starting hexagon two steps clockwise.
- Turning the Start picture two sectors clockwise matches choice (A), so that is what Thea sees after the eighth rotation.
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