Problem 22 · 2020 Math Kangaroo
Stretch
Spatial & Visual Reasoning
cube-views
John built a structure of equal-sized wooden cubes whose front, right-side and top views are shown, using as many cubes as possible. His sister Ana wants to remove as many cubes as she can without changing any of these three views. At most, how many cubes can she remove?
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Answer: B — 12
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Hint 1 of 2
The three views (front, side, above) must all stay the same after removing cubes.
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Hint 2 of 2
Keep only the cubes forced by all three silhouettes; count how many of the fullest build can be taken away.
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Approach: compare the fullest build with the minimum that keeps all views
- Build the most cubes giving those three views, then strip out any cube not needed by all three silhouettes.
- Each removed cube must leave the front, side and top outlines unchanged.
- The largest number she can remove while preserving every view is 12.
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