Problem 18 · 2018 Math Kangaroo
Stretch
Logic & Word Problems
divisionwork-backward
To slay a dragon, Mathias has to cut off all of its heads. As soon as he has cut off 3 heads, one new head grows back right away. After Mathias has cut off 13 heads, the dragon is dead. How many heads did the dragon have at the start?
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Answer: B — 9
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Hint 1 of 2
A new head grows after every 3rd cut, so cuts at 3, 6, 9, 12 each add one back.
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Hint 2 of 2
Net heads removed = cuts minus regrowths.
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Approach: count regrowths during the 13 cuts and subtract
- Cutting 13 heads triggers a regrowth after cuts 3, 6, 9 and 12 — that is 4 new heads.
- For the dragon to end with no heads, start = 13 − 4.
- So it had 9 heads initially.
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