## Burning Rope Logic Puzzle, Difficult

This question has actually been asked at job interviews (Microsoft, for example) and on math final exams in college.

It’s fairly difficult.

There are two lengths of rope.

Each one can burn in exactly one hour.

They are not necessarily of the same length or width as each other.

They also are not of uniform width (may be wider in middle than on the end), thus burning half of the rope is not necessarily 1/2 hour.

By burning the ropes, how do you measure exactly 45 minutes worth of time?

Feel free to post your answer in the comments section. Don’t look, though, until you really give it a try!

Josh| Guest January 27th, 2007 - 11:04 pmI would light both ends of one rope and one end of the second rope. In 30 min, the first rope will be consumed entirely and 30 min worth of the second rope will be consumed. At the moment the first rope is completely burned, I would light the other (no burning) end of the second rope. 15 min later, the second rope would be consumed entirely in a total of 45 min.

Lee| Guest January 27th, 2007 - 11:15 pmLight rope A at both ends, and light rope B at one end.

When rope A burns out, it’s been half an hour, since it’s burning at both ends. When that happens, light the other end of rope B. It will take 15 minutes for the remainder of that rope to burn, totaling 45 minutes.

Vishvas Vasuki| Guest January 28th, 2007 - 12:22 amBurn rope 1 from both ends, and rope 2 from one end.

At the end of 1/2 hour, rope 1 is no more.

Immediately, start burning rope 2 from the other end as well.

When rope 2 has completely burnt, 45 minutes have elapsed.

-Vishvas Vasuki

tramminator| Guest January 29th, 2007 - 9:38 pmLight the first rope at both ends to create two flame fronts (burns at twice the consumption rate so it should be done in 30 minutes). At the end of the first rope burn light the second rope at both ends and in the middle. This second rope will now have 4 flame fronts and consume the second rope in half the time as the first rope (15 minutes) when the second rope is gone you should be at your 45 minute point.

Carlos Lopez Silva| Profile February 24th, 2007 - 11:38 pmCan I have a watch?

Antonio Bologna| Guest March 27th, 2007 - 9:50 amIs all about change, calculate the change of the rope by means of derivative.

Little Money| Guest April 4th, 2007 - 12:50 amthis one is very difficult….

luis| Guest April 5th, 2007 - 10:20 pmBring a stopwatch.

Jim Lutz| Guest September 25th, 2007 - 9:58 amUse a watch

padma| Profile September 14th, 2010 - 6:37 amArrange the ropes in the form of a ‘plus’ symbol (‘+’, so that the mid points of the ropes meet. Now the ‘+’ got 4 points,

1. Burn 3 points at a time

2. After 30 mins, all the 3 points gets burnt out and burns towards 4th point

3. Immediately burn the 4th point, it takes 15 mins.

So the entire time taken to burn 2 ropes comes to 45 mins.

padma| Profile September 15th, 2010 - 1:25 amEven better solution would be, arrange the ropes in the form of a ‘T’ symbol and burn the 3 ends. It takes 45 mins to burn

axiom| Profile June 7th, 2012 - 12:46 pmI doubt this question has ever been asked on a college math exam. Apart from anything else, the solution cannot be derived solely from the stated property (“Each one can burn in exactly one hour” of the ropes, but depends on an additional physical assumption.

jporter892| Profile October 10th, 2012 - 1:22 amI found a great answer to the problem here – love this puzzle by the way:

http://www.programmerinterview.....5-minutes/