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2013 Math Kangaroo

Problem 9

Problem 9 · 2013 Math Kangaroo Medium
Spatial & Visual Reasoning cube-viewsshadows-projections
Figure for Math Kangaroo 2013 Problem 9
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Answer: E
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Hint 1 of 2
Imagine the pyramid's silhouette from each of the six directions.
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Hint 2 of 2
Which square pattern would need the apex to sit exactly over the centre of the base?
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Approach: project the pyramid along each axis
  1. The apex S is the midpoint of a cube edge, never over the centre of the square base.
  2. So no view puts both base diagonals crossing at the middle.
  3. The full 'X' (both diagonals) view is impossible: E.
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