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2021 Math Kangaroo

Problem 4

Problem 4 · 2021 Math Kangaroo Easy
Spatial & Visual Reasoning spatial-reasoning

Four identical pieces of paper are placed as shown. Michael wants to punch a hole that goes through all four pieces. At which point should Michael punch the hole?

Figure for Math Kangaroo 2021 Problem 4
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Answer: D — D
Show hints
Hint 1 of 3
The hole has to go through all four pieces of paper at once.
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Hint 2 of 3
So the spot must be covered by every single sheet.
Still stuck? Show hint 3 →
Hint 3 of 3
Look for the dot that sits on top of all four sheets together.
Show solution
Approach: find the common overlap point
  1. A hole through all four sheets must sit where all four sheets overlap.
  2. Checking the marked points, only point D lies in the part shared by every sheet.
  3. So Michael should punch at D.
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