Problem 2 · 2025 Math Kangaroo
Easy
Spatial & Visual Reasoning
transformationssymmetry
Isabelle plays with a hexagonal sheet of paper. With each move she rotates the hexagon by the same angle in the same direction. The illustration shows the sheet at the start and after the first move. After how many moves does the sheet look the same as it did at the beginning?
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Answer: A — 6
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Hint 1 of 2
The single dotted wedge acts as a marker — track where it lands after one move.
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Hint 2 of 2
Find the rotation angle of one move, then see how many moves complete a full turn back to the start.
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Approach: track the marker wedge under repeated equal rotations
- The colouring has no rotational symmetry, so the sheet only looks identical after a whole turn brings every wedge home.
- Comparing the start and the first move, the unique dotted wedge has shifted by one position — a 60° rotation.
- A 60° step needs \(360^\circ \div 60^\circ = 6\) moves to return to the original picture, which is (A).
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