Burning Ropes
37 Answers 
Challenge Your Friends
Tweet this
You have a large selection of ropes of varying lengths. The ropes burn at different rates, even one part of a rope may burn differently than another part, but there’s no way to tell just by looking at them. What you do know is that every single rope will take exactly 1 hour to burn from one end to the other. You also have access to matches, but nothing else (obviously no clocks, etc).
How can you time exactly 30 minutes using the ropes?
Get Puzzles Delivered:
Burn one rope at both ends. When the rope is all burned up you should have one half hour completed.
Light any or all ropes on fire at both ends. After 30 minutes the fires will converge and the rope(s) will be completely obliterated.
Take one rope and start burning at both ends. When there is no more rope, 30min has past.
How about another one: You have two 4min fuses and a bomb. You want to be able to time the detonation of the bomb for 1min. Like the ropes above, neither fuse burns at a uniform rate throughout. How do you time your act of senseless destruction?
Fold a rope in half and light the rope at the fold. The entirety of the rope will have been consumed after 30 minutes. This will work for any of the ropes.
@NickScott : Your solution won’t work. The ropes burn at inconsistent rates. Lighting it in the middle may produce a 15 minute burn on one half and 45 on the other, leaving no indicator of a 30 minute mark.
@theo Ahhh, yes, you are correct. Thanks for pointing that out! Maybe next time
@NickScott I suppose if you somehow joined the two ends together it wouldn’t matter where you lit it.
I wonder if a better answer than “Light both ends at the same instant” might be “1) join the ends so you have a perfect loop; 2) Light the loop on fire at any point”
We then encounter the engineering problem of how to bend the ends of the rope together without actually using a bending knot. I suspect you could use one of the other lengths of rope to do a whipping or bend the two ends together…
hmmm…
Set afire another end of the rope. The rope will completely burn in 30 min.
The other interesting question is how do you time other increments of time, say 45 minutes (popular), or 10 minutes (not-so popular)
I take an infinite number of ropes, set them on fire and when most of the ropes have burnt one half most certainly 30 minutes have passed.
I don’t see how the first correct solution is a solution at all.
The problem statement states clearly that “one part of a rope may burn differently than another part.” Okay. So suppose — because we don’t know differently, so all possibilities are fair game — the ropes all burn the same and that one half of any given rope takes 45 minutes to burn and the other half takes only 15 minutes to burn.
Now light that rope at both ends.
At the end of 30 minutes, one half of the rope will have been long consumed and the other half will still be burning.
The problem becomes more complicated with varying burn rates at different points along any rope, such as if the ropes are, say, poorly made and have wildly varying thicknesses. I could be wrong — and I respectfully and readily admit that — but I don’t see any obvious and universally correct answer to this problem.
Oh, wait. Good grief. I just saw the error in my reasoning. Yikes!
The solution only works until someone constructs a pathological rope that burns with different speeds depending on the direction it burns
I think Rafa? Dowgird (cool name) is right. The definition is inaccurate, because it allows ropes burning *only* from one end to the other in exactly 1 hour (saying nothing about the time for the reverse direction). Hairsplitting? Or is my English not good enough?!
Agh, I can’t solve the 10 minute problem…45 minutes I figured out!
That’s not a puzzle, it’s a trick question. I hate trick questions
.
Well, let’s try this.
We have here a rope:
‘0′: |000—–0|
Dashes represent easily burnt rope, while 0s are harder to burn. Note that the number in single quotes is the tick number Let’s say that a dash takes 1 tick to burn, while an 0 takes 2. Lets try lighting both ends. During the first tick nothing happens, as both ends are 0s. However, at the second tick, we get this:
‘2′: |*00—–*|
As you can see, *s represent burnt areas.
‘3′: |*00—-**|
Next tick, a dash burns, and the next 0 partially burns. At this point, I can see that this model is imperfect (as we have no way of representing a partially burned 0) but I think we can keep all the information in our heads.
‘4′: |**0—***|
‘5′: |**0–****|
‘6′: |***-*****|
Which leaves a single dash, which takes a half tick to burn.
‘7′: |*********|
^
Ending point is marked. Now, the total time it would take for the rope to burn (in 1 direction) is 13. This diagram (and example) is imperfect again because we have no mechanism for representing half ticks, plus we have an example rope that is odd, so we end up with half a tick. This means that it took 6.5 ticks to for the burns to meet, which is half of 13. While this is just a single case for which this works, it proves that at least in some cases, lighting both ends would work.
Here is a general proof:
Light both ends A and B, wait until the flames meet at point x after time t. The time to burn the whole rope is the time to burn from A to x (which is t) plus the time to burn from x to B (which is t). So the time to burn the whole rope is 2*t, so t is half an hour.
The trick here is that this relies on the time to burn from x to B being the same as from B to x.
Tie both ends of a rope in a know and light the knot… when the (now loop) burns up, 30 min will have passed (sorry… just had to find a variation, albeit slight)
excuse the typo :S
I thought this was going to be actual programming puzzles… like write a program that will solve an 8×8 maze made of ASCII chars. I wasn’t always the fastest at solving the puzzles but I usually could come up with the right algorithm. I, like most CS majors, enjoy solving problems with programs.
I tought about this:
time how much water will pour in a recipient when one rope burns completely then mark half of it in the recipent then empty it and start burning a rope while the recipient fills. when water reaches the mark it’s 30 mn.
Like the solutions before me, I suggest lighting both ends or forming a loop and lighting anywhere (the same solution really). When the fire meets, the rope is exhausted, and exactly 30 minutes has passed. This is assuming a perfect environment with no external factors, such as the point Burki brought up. A hanging rope could burn faster upward than downward, for instance.
@urtard: This could work on a large set of uniform or normally distributed ropes. However, given the problem statement, we could be dealing with a set of identical ropes for which the first 90% of the rope burns in the first 10% of the time allotted. I do love the probabilistic approach, though.
You can’t time half an hour. You have rope,matches AND NOTHING ELSE. Without oxygen there is no way to make the rope burn.
Light one end of any rope and at the same time like one new match. Once that match is out light another and keep repeating lighting new matches until all the rope is burnt through. You now have the number of matches that are burnt through in 1hour and are able to calculate how much time is required to burn through each match. You can now determine any time you wish to calculate from burning any number of matches.
Hop on a spaceship along with whatever things that you need to keep doing something for 30 minutes. Leave the burning rope on the ground.
Travel at sqrt(3)/2 times the speed of light, passing very near the rope at the frequency at which you require for the resolution of your timer.
When the rope is fully burnt, 30 minutes have passed from your frame of reference.
For 45 min one, light one rope on both the ends. And second rope at only one end. While the first rope burns completely second one still has thirty min to go to completely burn. Now light the other end of the second rope. It would take 15 more min to burn completely, cumulatively 45 min for the second rope to burn.
weigh all the ropes. Light 1 end of all the ropes at the same time. When the weight is half of the start weight, 30 mins has passed. (works better if you know the weight of all the burnt ropes beforehand)
Main problem: light a one-hour fuse at both ends; when the burning ends meet, half an hour has passed.
Bonus problem (posed by Andy): light four-minute fuse A at both ends, and four-minute fuse B at one end. When A is completely burned, 2 minutes have passed; light the other end of B. You now have a one-minute fuse (time to leave!).
Post very nicely written, and it contains useful facts. I am happy to find your distinguished way of writing the post. Now you make it easy for me to understand and implement. Thanks for sharing with us.
comment2, 3, %-DD, 2, kya, 1, lmkroh, 1, 2808, 3, vlc, 1, =-DD, 2, wibep, 2, =-D, 1, 195, 3, 322629, 1, 1880, 2, =-[, 1, kjlzwe, 2, 1643, 2, =-), 2, 8[[, 1, jhdf, 2, >:[, 3, 93861, 2, =), 1, >:-]], 1, 8-]]], 3,
)), 3, 511625, 1, 7548, 3, rts, 3, 0096, 1, =OO, 2, qrrjha, 2, 210969, 3, %-(((, 3, 5282, 1, 192298, 1, 
), 1, lkwspv, 1, =PPP, 1, 153, 2, 4814, 1, 8OO, 1, 8(((, 2, nbhms, 3, xydc, 2, :]], 2, wmx, 1, ajngj, 2, 284, 1, >:-D, 1, %]]], 3, 59028, 3, 93362,
I am often blogging and i really appreciate your content. The article has really peaked my interest. I am going to bookmark your site and keep checking for new information.
Seem great. It is also my personal favorite subject.That is excellent andthanks for your great sharring.
can anyone tell how can we do it if we want a to time 75 mins exactly with same conditions ??
selena gomez desnuda