Problem 10 · 2016 Math Kangaroo
Medium
Spatial & Visual Reasoning
composition
Robert has two equally big squares made of paper. He glues them together. Which of the following shapes can he not make?
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Answer: A — The house/pentagon shape (A).
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Hint 1 of 3
He may slide one square so the squares touch along an edge or just at a corner, but each square keeps its size and square shape.
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Hint 2 of 3
Try to draw two equal squares hidden inside each answer shape.
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Hint 3 of 3
The shape that cannot be cut back into two equal squares is the impossible one.
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Approach: try to split each outline back into two equal squares
- Gluing two equal squares (along a full edge, a partial edge, or at a corner) can make four of the shapes.
- But the house shape has slanted roof edges that no straight-sided square can produce, so it cannot be cut back into two equal squares.
- So the shape he cannot make is the house, choice (A).
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