Problem 8 · 2023 Math Kangaroo
Medium
Spatial & Visual Reasoning
symmetry
A dark disc with three holes is placed on top of the dial of a watch (see picture). The disc is then rotated about its centre. Which three numbers can be seen through the holes at the same time?
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Answer: A — 4, 6 and 12
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Hint 1 of 2
Rotating the disc keeps the three holes the same distances apart around the circle.
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Hint 2 of 2
Compare the gaps between the three holes with the gaps between the numbers in each answer; only a matching gap pattern can appear.
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Approach: match the angular gaps of the three holes to the gaps between the numbers
- The three holes sit at fixed clock-positions, so the gaps between them (measured in hours) stay the same no matter how you turn the disc: the gaps are 2, 4 and 6 hours.
- Check the gaps for each answer: 4, 6 and 12 are spaced 2, 4 and 6 hours apart — the same pattern.
- None of the other answers has gaps 2, 4, 6, so only this triple can show through the holes at once.
- The answer is A, 4, 6 and 12.
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