Problem 6 · 2012 Math Kangaroo
Easy
Algebra & Patterns
arithmetic-sequence
A dragon has 5 heads. Each time someone chops off one head, 5 new heads grow back. If 6 heads are chopped off one after the other, how many heads does the dragon end up with?
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Answer: C — 29
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Hint 1 of 2
Each chop removes one head but adds five, so track the net change.
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Hint 2 of 2
What is the net change in the number of heads per chop?
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Approach: net change per step
- Each chop removes 1 head and grows 5, a net gain of 4 heads.
- After 6 chops the heads increase by 6 × 4 = 24.
- Starting from 5: 5 + 24 = 29 heads.
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