Problem 2 · 2017 Math Kangaroo
Easy
Geometry & Measurement
careful-counting
Into how many pieces will the string be cut?
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Answer: E — 9
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Hint 1 of 2
Put your finger on the cut line and touch every spot where it crosses the string.
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Hint 2 of 2
A cut always makes one more piece than the number of times it crosses the string.
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Approach: count crossings along the cut
- The string is one long curve, and the dashed line is one straight cut across it.
- Walk along the dashed line and count the dots where it crosses the string: there are 8 crossings.
- Each crossing makes one extra piece, so 8 crossings give 8 + 1 = 9 pieces.
- So the string is cut into 9 pieces.
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