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2021 Math Kangaroo

Problem 8

Problem 8 · 2021 Math Kangaroo Easy
Spatial & Visual Reasoning Logic & Word Problems cube-viewscomplementary-counting
Figure for Math Kangaroo 2021 Problem 8
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Answer: E — Diagram E.
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Hint 1 of 2
The grey cubes are exactly the ones that are neither white nor black.
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Hint 2 of 2
Subtract the white shape and the black shape from the full 3×3×3 cube, position by position.
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Approach: grey = full cube minus white minus black
  1. The full cube has 27 unit cubes; the grey ones are those not shown in the white or black diagrams.
  2. Remove the white part and the black part to see which positions are left grey.
  3. Matching that leftover arrangement to the options gives diagram E.
  4. So the answer is E.
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