Thread: Thinking Cap Time Again.

You are given 2 lengths of rope and a lighter. You are told that each rope when lit will burn up in one hour. The ropes do not burn at a constant rate and they are of different lengths. Your task is to measure 45 minutes of elapsed time using nothing but the ropes and the lighter. Good luck!

I'd time the 45 minutes on my watch and burn the ropes for fun at my leisure.

Hmmm. The ropes both will burn for 1 hr each at difference rates so the length is not the concern, the % of rope burned is the issue.

I would fold and cut them into 1/2 and then again to get quarters out of each rope then burn 3/4's of them to get the 45 min burn time.

Correct??

Will N.

Light one of the ropes at each end so it burns toward the middle. At the same time light only one end of the other rope. Since the first rope is burning twice as fast as it would if only one end was burned it will take 30 minutes. When the 30 minutes are up the half rope remaining will have 30 minutes of burn time left. Now light the other end of the second rope so it is now burning at both ends. This will give another 15 minutes of burning. Total time = 45 minutes.

Originally Posted by Ogershok

Light one of the ropes at each end so it burns toward the middle. At the same time light only one end of the other rope. Since the first rope is burning twice as fast as it would if only one end was burned it will take 30 minutes. When the 30 minutes are up the half rope remaining will have 30 minutes of burn time left. Now light the other end of the second rope so it is now burning at both ends. This will give another 15 minutes of burning. Total time = 45 minutes.

A winner I think.

Burning one of the one hour ropes does get you 30
min.

Now how to burn the second one hour rope in 15 min?
Since you have had it burning from only one end for 30
min already then doubling it back to burn from both ends (twice
as fast) results in 15 min to finish.

ding ding ding...

Me I would use a watch and use the saved rope to
tie up a package for the give away.

What kind of a rope does not burn at a contstant speed?

The official answer is:


Take rope 1. Lighting it at both ends means that it would take 30 minutes for it to completely burn away. So light rope 1 at both ends and rope 2 at 1 end.

After 30 minutes have elapsed, rope 1 is completely burned through. Rope 2 has 30 minutes of burning remaining, since you know it takes an hour to fully burn.

Light the other end of rope 2 now, and it will take 15 minutes to finish burning since now it's burning from both ends.

Originally Posted by thebigspendur

The ropes do not burn at a constant rate

This means they burn at a variable rate. The solutions above, if I understand them correctly, rely on each rope burning at a constant but different rate. I'm puzzled so far...

Even if they burn at a variable rate the entire ropes are consumed for my solution making the variability no longer a factor. Hey big spender - whatcha think?

Originally Posted by Ogershok

Even if they burn at a variable rate the entire ropes are consumed for my solution making the variability no longer a factor. Hey big spender - whatcha think?

Yeah, but when you account for the time spent lighting each end, you're up to 46 minutes.