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Vandaag is het 10 December 2019

# Light a candle - math puzzle

Difficulty:

Rating: 3.1/5.0

 In a group of 200 people, everybody has a non burning candle. On person has a match at lights at some moment his candle. With this candle he walks to somebody else and lights a new candle. Then everybody with a burning candle will look for somebody without a burning candle, and if found they will light it. This will continue until all candles are lit. Suppose that from the moment a candle is lit it takes exactly 30 seconds to find a person with a non burning candle and light that candle. From the moment the first candle is lit, how long does it take before all candles are lit?

# Explanation

After 30 seconds 2 candles are lit.
After 60 seconds 4 candles are lit.
After 90 seconds 8 candles are lit.

So every 30 seconds, the number of lighted candles doubles. So after 7*30 seconds 2^7 = 128 candles are lit. And after 8*30 seconds 2^8 = 256 could be lit. But were only 200 candles to start with. So in the last step some people will not find a candle to light. It will hence take 4 minutes to light all candles.