Problem 3 · 2023 Math Kangaroo
Easy
Spatial & Visual Reasoning
clock-calendarspatial-reasoning
A dark disc with two holes is placed on top of the dial of a watch, as shown. The dark disc is now rotated so that the number 8 can be seen through one of the holes. Which numbers could one see through the other hole now?
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Answer: A — 4 and 12
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Hint 1 of 2
The two holes keep a fixed angular gap as the whole disc turns.
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Hint 2 of 2
Find which two clock numbers sit the same angular distance apart as the two holes.
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Approach: use the fixed angular spacing between the two holes
- In the picture the two holes sit over the 1 and the 5, so they are a fixed 4 hours apart on the disc.
- If 8 shows in the hole that was over the 1, the disc turned 7 hours, so the other hole (was over 5) now shows 5 + 7 = 12.
- If 8 shows in the hole that was over the 5, the disc turned 3 hours, so the other hole (was over 1) now shows 1 + 3 = 4.
- So the other hole shows 4 or 12, which is option A.
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