Problem 1 · 2023 Math Kangaroo
Medium
Spatial & Visual Reasoning
clock-calendar
A dark disc with two holes is placed on the dial of a watch as shown in the diagram. The dark disc is now rotated so that the number 10 can be seen through one of the two holes. Which of the numbers could one see through the other hole now?
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Answer: A — 2 and 6
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Hint 1 of 2
The two holes stay a fixed angular distance apart no matter how the disc turns.
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Hint 2 of 2
Find the gap (in hours) between the two holes from the starting picture, then apply it to the 10.
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Approach: use the fixed angular spacing between the two holes
- In the starting position the two holes reveal numbers a fixed number of hours apart on the dial.
- That same gap is preserved after any rotation of the disc.
- When one hole shows 10, applying the gap lands the other hole on the numbers 2 and 6.
- So the other hole could show 2 and 6.
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