Problem 4 · 2012 Math Kangaroo
Easy
Spatial & Visual Reasoning
paper-cutting
Eva has a pair of scissors and five letters made from cardboard. She cuts up each letter with a single straight cut so that as many pieces as possible are obtained. For which letter does she obtain the most pieces?
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Answer: E
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Hint 1 of 2
One straight cut makes more pieces when it crosses the letter's outline more times.
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Hint 2 of 2
Picture a single line drawn across each letter and count how many separate parts it leaves.
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Approach: count crossings of a single line
- A single straight cut splits a shape into one more piece for each time the cut crosses the shape.
- A wiggly outline like the letter S can be crossed by one straight line in the most places.
- Cutting M with one straight line through all four of its strokes leaves the most pieces of the five letters.
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