Problem 8 · 2010 Math Kangaroo
Medium
Algebra & Patterns
off-by-one
Herbert has cut firewood. After he has made 53 cuts, he realises that he has 72 pieces of wood. How many pieces of wood did he have to start with?
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Answer: C — 19
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Hint 1 of 2
Each single cut turns one stick into one more piece.
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Hint 2 of 2
So pieces = starting pieces + number of cuts.
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Approach: cuts add one piece each
- Every cut increases the number of pieces by exactly 1.
- After 53 cuts the count rose by 53, ending at 72, so he started with 72−53 = 19 pieces.
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