Problem 23 · 2024 Math Kangaroo
Stretch
Spatial & Visual Reasoning
spatial-reasoningcomposition
Kanga wants to build a figure out of these three cube parts (shown at the top). He may rotate or flip the parts. Which of the five pictured figures (A)–(E) can he NOT build?
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Answer: E
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Hint 1 of 3
First count the cubes in the three given parts added together — every figure Kanga can build must have exactly that many cubes.
Still stuck? Show hint 2 →
Hint 2 of 3
For each choice, try to colour it in three groups, one matching each part, turning or flipping the parts as needed.
Still stuck? Show hint 3 →
Hint 3 of 3
The figure you simply cannot split into the three parts is the one he canNOT make.
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Approach: try to split each figure into the three given parts (rotations and flips allowed)
- Each finished figure must be built from all three parts, so it always has the same total number of cubes.
- For each choice, try to break it into three pieces that match the three parts, allowing turning and flipping.
- Four of the figures can be split up neatly into the three parts.
- One figure cannot be split that way no matter how you turn the parts, so Kanga cannot make it: E.
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