Problem 9 · 2015 Math Kangaroo
Easy
Algebra & Patterns
work-backwarddivision
Herr Waxi buys 100 candles. Each day he burns down one candle. From the left overs of seven burned down candles, he can always make a new candle. After how many days does he have to buy new candles?
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Answer: D — 116
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Hint 1 of 2
Every candle burned leaves a stub, and 7 stubs become a fresh candle — keep recycling.
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Hint 2 of 2
Count how many candles in total he can burn, recycling stubs, then that many days pass before he needs more.
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Approach: recycle stubs until none remain
- 100 candles burn to 100 stubs → 14 new candles (2 stubs left).
- Those 14 burn → 14 + 2 = 16 stubs → 2 new candles (2 left).
- Those 2 burn → 2 + 2 = 4 stubs (not enough for another).
- Total burned = 100 + 14 + 2 = 116, so he must buy new candles after 116 days.
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