Problem 19 · 2014 Math Kangaroo
Stretch
Spatial & Visual Reasoning
cube-viewsspatial-reasoning
A 3×3×3 cube is made of 27 small cubes. Some of the small cubes are removed. Looking at the result from the right, from above, and from the front, you see the same shape each time (shown in the picture). How many small cubes were removed?
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Answer: E — 7
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Hint 1 of 2
Each of the three views tells you which columns of small cubes are missing in that direction.
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Hint 2 of 2
Find an arrangement that produces all three silhouettes at once, then count the empty little-cube spots.
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Approach: match all three silhouettes and count the missing cubes
- The three given views show notches: some small cubes must be cleared so the right, top and front outlines all look as drawn.
- Removing cubes only from positions that are missing in every relevant view, the fewest consistent removals reproduce all three pictures.
- Counting those cleared positions gives 7 little cubes removed.
- So 7 little cubes were removed.
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