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Burning ropes (Posted on 2002-03-28) Difficulty: 3 of 5
You have two ropes. You know that each rope takes one hour to burn from one end to the other, but that the burning does not take place at a constant rate (i.e. half the rope may burn in one minute, and the other half will take 59 more minutes to burn).

How would you go about measuring a 45 minute time interval with just these two ropes?

  Submitted by levik    
Rating: 3.7308 (26 votes)
Solution: (Hide)
The solution to this problem is fairly elegant.

Realize that if a rope takes an hour to burn from end to end, we can reduce that time to half an hour by lighting up both ends simultaneously. (This will work, even though the rope burns unevenly.)

So, we light up one rope from both ends, and the other rope from just one end. At the point that the first rope is completely consumed, we know that half an hour has elapsed. At this moment, the second rope still has half an hour to burn.

But we can reduce that to 15 minutes by lighting the second end of the second rope now, and when that rope is gone, we know that it's been 30 + 15 = 45 minutes.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionFirst puzzleMath Man2012-05-11 21:03:09
SolutionSolutionK Sengupta2007-05-16 06:17:05
Wowjbcf052007-03-07 16:26:16
Some Thoughtsa new curve on things.gabbo2004-09-15 21:46:54
re: a tryDacre2003-10-24 09:28:49
coolTalon50002003-07-31 11:04:58
SawJohn Tate2003-06-08 11:16:11
QuestionGive up.John Tate2003-06-08 11:14:28
Solutiontry thismark hartman2003-05-28 18:03:33
re: a tryEmon Hunte2003-02-02 16:49:24
Solutiona tryubergeek2002-12-26 00:23:16
re: Cooldex2002-12-18 13:29:51
CoolEric2002-05-07 06:38:30
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