Problem 7 · 2023 Math Kangaroo
Medium
Spatial & Visual Reasoning
composition
Alice has four jigsaw pieces (see picture). Which two of them can be fitted together to form a hexagon?
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Answer: B — 1 and 3
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Hint 1 of 3
A finished hexagon has six straight sides and no bumps or dents, so any notch on one piece must be filled by a matching bump on the other.
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Hint 2 of 3
Pair up the pieces in your head and look for the bump that plugs a dent exactly, with no gap and no overlap.
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Hint 3 of 3
Slide the matching pair together along their jagged edges and check the outer outline really has six clean straight sides.
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Approach: match the notch of one piece to the bump of the other
- Each piece is a chunk of a hexagon with a notch cut out or a bump sticking in.
- To rebuild the full hexagon, one piece's bump must drop neatly into the other's notch with no overlap or gap.
- Pieces 1 and 3 fit together this way, and their outer edges line up to form the six straight sides of the hexagon.
- So the answer is B, 1 and 3.
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