Problem 16 · 2019 Math Kangaroo
Hard
Spatial & Visual Reasoning
paper-cuttingfolding
Kathi folds a square piece of paper twice and then cuts it along the two lines shown in the picture. The resulting pieces of paper are then unfolded where possible. How many of the pieces are squares?
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Answer: C — 5
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Hint 1 of 2
Fold mentally, mark the two cuts, then unfold and see which pieces are squares.
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Hint 2 of 2
Each cut, once unfolded, becomes several cuts because of the layers.
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Approach: unfold the cuts and identify square pieces
- Folding the square twice stacks four layers; the two cuts pass through all layers.
- Unfolding turns those cuts into a symmetric set of cut lines across the whole sheet.
- Tracing the resulting pieces, exactly 5 of them are squares.
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