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2018 Math Kangaroo

Problem 15

Problem 15 · 2018 Math Kangaroo Hard
Spatial & Visual Reasoning net-foldingdice-faces
Figure for Math Kangaroo 2018 Problem 15
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Answer: E
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Hint 1 of 2
Fold each net mentally and check the three pairs of opposite faces.
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Hint 2 of 2
A valid die needs every opposite pair to be two different colours; find the net where some opposite pair matches.
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Approach: fold each net and test opposite faces
  1. When folded, each net's faces pair up into three opposite pairs.
  2. The rule says opposite faces must be different colours.
  3. Four of the nets fold to dice obeying this; in net E a pair of opposite faces ends up the same colour.
  4. So net E cannot be such a die.
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