Problem 19 · 2020 Math Kangaroo
Medium
Spatial & Visual Reasoning
Logic & Word Problems
cube-viewsspatial-reasoningcareful-counting
Irene made a "city" using identical wooden cubes. Beside the problem there is a view from above and a side view of this "city." We do not know which side of the "city" the side view shows. What is the smallest number of cubes Irene could have used to build it?
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Answer: E — 15
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Hint 1 of 2
The top view tells you which floor cells have at least one cube; the side view tells you the heights seen in a row.
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Hint 2 of 2
Add the smallest heights at each occupied cell that still match both views — the orientation is unknown.
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Approach: combine the two views for a minimum
- The top view marks which ground cells are occupied; the side view limits the column heights.
- Choosing the least cube count at each cell that is still consistent with both views (over the unknown orientation) gives a minimum.
- That smallest total comes to 15 cubes, choice E.
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