Problem 3 · 2011 Math Kangaroo
Easy
Geometry & Measurement
spatial-reasoning
A square piece of paper is cut in a straight line into two pieces. Which of the following shapes can not be created?
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Answer: A — A square
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Hint 1 of 2
One straight cut adds just a single new edge to each piece.
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Hint 2 of 2
Think about how many sides each listed shape needs and whether one cut can supply them.
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Approach: check which shape one straight cut cannot produce
- A single straight cut splits the square into two pieces, each bounded by part of the square plus the one cut line.
- A rectangle, a right-angled triangle, a pentagon, and an equilateral triangle can all appear as one of the two pieces for a suitable cut.
- But a smaller square cannot: a square needs four right angles, and one straight cut cannot create a second full square-shaped piece.
- So the impossible shape is a square.
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