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2010 Math Kangaroo

Problem 1

Problem 1 · 2010 Math Kangaroo Easy
Spatial & Visual Reasoning path-tracing
Figure for Math Kangaroo 2010 Problem 1
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Answer: E
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Hint 1 of 2
The road piece has to join the cat to the milk and the mouse to the cheese, yet keep those two routes from ever touching.
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Hint 2 of 2
Look at which sides of the missing square each road must enter and leave, then find the piece whose roads connect exactly those sides without crossing.
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Approach: match the road piece to the required connections
  1. The cat must reach the milk, and the mouse the cheese, but the two animals' paths must stay separate.
  2. So the missing piece needs two roads that link the correct opposite sides while never meeting in the middle.
  3. Only the curved piece E carries the two routes past each other without letting them join.
  4. So the piece is E.
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