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2015 Math Kangaroo

Problem 9

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
Show hints
Hint 1 of 2
Every candle burned leaves a stub, and 7 stubs become a fresh candle — keep recycling.
Still stuck? Show hint 2 →
Hint 2 of 2
Count how many candles in total he can burn, recycling stubs, then that many days pass before he needs more.
Show solution
Approach: recycle stubs until none remain
  1. 100 candles burn to 100 stubs → 14 new candles (2 stubs left).
  2. Those 14 burn → 14 + 2 = 16 stubs → 2 new candles (2 left).
  3. Those 2 burn → 2 + 2 = 4 stubs (not enough for another).
  4. Total burned = 100 + 14 + 2 = 116, so he must buy new candles after 116 days.
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