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Riddle of the Burning Ropes

Here’s a gorgeous logic problem I heard recently:

You’re given two ropes and a lighter. These are your only tools.

Each of the two ropes, when lit on one end, will take exactly one hour to burn all the way through to the other end. However, neither of the ropes burn at a constant rate. For instance, it may take 59 minutes to burn through the first half of a rope, and then burn through the second half in the final minute. (Imagine that the ropes vary in thickness in density.) Also, the ropes are not identical, so Rope A does not necessarily burn at the same rate of Rope B.

Your mission, should you choose to accept it:

Measure a period of 45 minutes.


3 comments… add one
  • matt November 30, 2006, 11:56 am

    a watch is not a tool, it is jewelry, I would click the stop watch on my timex, light both ropes and put them out at 45 minute mark.

  • Triggerhappy January 12, 2007, 7:43 pm

    Here’s a hint:
    If you both ends of a rope, the flames with meet at exactly 30 minutes.

  • Jessica May 15, 2008, 8:50 pm

    you burn one rope on both ends
    while at the same time burning the 2nd rope as well.

    when the first rope is all burned you will know that 30 min have passed.
    when that happens you light the 2nd rope at the other end as well (since it will have 30 min remaining) and measure the last 15 min left (:

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