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 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.

This makes my head hurt...

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

It's true the variability factor is taken care of in your solution, but you're assuming the rope will burn in 30 minutes when lit from both ends. However the problem states that you are told the rope will take an hour to burn "when lit." If you were told that the rope when lit "at one end" will burn in an hour, then your solution works. Or am I reading the problem too narrowly? Maybe it is supposed to be a given that if I light the entire rope at once, it will not take an hour to burn ie. maybe it is possible to trick the rope

I think thebigspendur has been smoking his rope, discovered he'd been drifting and can't find the fifteen minutes he lost.