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RobMiles  
Programming, gadgets and life as a lecturer in a UK university.

Advent Puzzle

Christmassy puzzle this week. The four weeks up to Christmas are called Advent. In the church there are four candles. On the first Sunday we light one candle in the service , on the second two are lit, and so on as the weeks go by. At the final service all four candles are lit. The candles are lit for the same amout of time in each service. What is the optimal strategy to ensure that all the candles get burnt down as equally as possible, and what is the shortest number of years would have to go by before the candles were all the same length again...

posted on Thursday, December 23, 2004 11:32 PM by RobMiles

# @ Friday, December 24, 2004 4:25 PM

On the second year, you light the candles in reverse, therefore the candle that burnt the least in year one, would burn the longest in year two. So, after two years, you would have all candles the same length again, you can do this numerically. All candles are say 10 inches long, and burn at one inch per service: In order to make sure that the candles are burnt as equally as possible, you would have to make sure that the air around them is constant (including any possible breeze, and air pressure - which is nearly impossible!!!), but assuming so, and assuming therefore that each candle burns an equal amount: Year 1: Candle 1 burns for 4 weeks - 6 inches left Candle 2 burns for 3 weeks - 7 inches left Candle 3 burns for 2 weeks - 8 inches left Candle 4 burns for 1 week - 9 inches left ....onto year 2! Candle 4 burns for 4 weeks - 5 inches left Candle 3 burns for 3 weeks - 5 inches left Candle 2 burns for 2 weeks - 5 inches left Candle 1 burns for 1 week - 5 inches left. *Cowers in the corner thinking that this is far too simple a solution* Merry Christmas.

Oliver_Drew


 
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