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2015 Math Kangaroo

Problem 10

Problem 10 · 2015 Math Kangaroo Medium
Spatial & Visual Reasoning net-foldingfolding

Julia folds the paper net pictured on the right into a cube. Which number is on the face that is opposite to the face with the number 3?

Figure for Math Kangaroo 2015 Problem 10
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Answer: E — 6
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Hint 1 of 2
Find the straight strip of three squares that contains the 3.
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Hint 2 of 2
In a strip of three faces, the two end faces fold to opposite sides.
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Approach: use the straight three-square strip of the net
  1. The faces 3, 5 and 6 lie in a straight vertical strip of the net.
  2. When a strip of three faces is folded, the two ends become opposite faces.
  3. So 3 and 6 end up on opposite faces of the cube.
  4. The face opposite 3 carries 6.
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