Problem 4 · 2016 Math Kangaroo
Easy
Logic & Word Problems
careful-counting
Lisa has mounted 7 postcards on her fridge door using 8 strong magnets (the black dots). What is the maximum number of magnets she can remove without any postcards falling on the floor?
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Answer: C — 4
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Hint 1 of 2
A single magnet placed where two postcards overlap can hold both at once.
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Hint 2 of 2
Find the fewest magnets that still touch every postcard; the rest can be removed.
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Approach: keep the fewest magnets that still touch every postcard
- Every one of the 7 postcards must keep at least one magnet on it, or it falls.
- Where two postcards overlap, a single magnet can hold both at once, so the magnets that sit on overlaps do double duty.
- Keeping just 4 well-placed magnets is enough to pin all 7 cards, so she can remove the other \(8 - 4 = 4\), choice (C).
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