Fold both ropes to find 5/12ths of each length of rope. Cut off those lengths and burn both of the 5/12 portions? Sounds like it'd work.
this post was submitted on 04 Jul 2023
10 points (100.0% liked)
Math Riddles
84 readers
1 users here now
Guidelines
-
Riddles, not homework. This community is for people to share math problems that they think others would enjoy solving. It is not intended for helping students with homework problems or explaining mathematical concepts. Posting riddles which you do not know the answer to is permitted.
-
Harder than trivial. While math riddles of any difficulty are welcomed, please avoid posing problems whose solution is formulaic and/or trivial.
-
Spoiler your answers. The intent here is to let others engage in discussion without giving the answer away. It's fun to think about it, and choose when you need a hint!
-
Text & image focus. The purpose of this community is for its members to try and solve it themselves. Video links are only accepted when they present the question but no solution. If they include a solution, feel free to post the riddle as text and to include a link to your source.
Code of Conduct
For now, code of conduct shall simply follow the official CoC from the Lemmy organization: Link
Some highlights:
- Remarks that violate the Lemmy standards of conduct, including hateful, hurtful, oppressive, or exclusionary remarks, are not allowed. (Cursing is allowed, but never targeting another user, and never in a hateful manner.)
- Remarks that moderators find inappropriate, whether listed in the code of conduct or not, are also not allowed.
founded 2 years ago
MODERATORS
Burn the four portions cut this way from the ropes, starting to burn them simultaneously. The 5/12 should be taken starting from the end of the ropes. When the second of these four pieces has burnt fully, say it's approx 25 min.
Good suggestion! That would work well if the ropes burned consistently, but it's possible that those 5/12 portions are more/less volatile than the remainders, meaning they could burn for 25 minutes, but also they could burn for 10 minutes, or 50.
Ah, very tricky. I'm not very good at math, so my next idea is to brute force it by unraveling both ropes into their individual threads, counting up 5/12ths of each ropes' threads and re-tying and burning those threads. Each thread would be the same length as the original rope and would have the same inconsistencies, you'd just be left with a skinnier rope that hopefully has 25min of material left to burn between the two.
Hopefully somebody figures out the real answer and can chime in, ::: I'm curious how lighting multiple fires helps :::
Waited 24 hours in case anyone could figure it out. I've posted the solution as it's own top comment.
Answer context: if you light both ends of one rope, the two flames will always meet each other and fizzle out in exactly 30 minutes.
Key takeaway:
- 1 flame on a rope = 1 hour
- 2 flames on a rope = ½ hour
So you may (correctly) think that 3 flames = ⅓ hour. But there's trick to it. Those 3 flames should always be; 2 on the end, and 1 arbitrarily in the middle.
Doing this will actually cause 1 rope segment with 3 flames to turn into 2 rope segments with 4 flames. Since that middle flame was placed arbitrarily, we can expect one of the segments to burn up before the other. When this happens, we just place a new flame arbitrarily in the middle of the remaining segment, splitting it back into 2.
As long as we keep adding flames so that we always have 2 segments, the total rope will ultimately burn in 20 minutes (⅓ hour).
This is generalizable; to achieve any fraction of 1/x hours, we need to always maintain x-1 segments (min 1). So for ½ hour, we need to maintain 1 segment. For ⅐ hour, we need to maintain 6 segments, etc.
Final answer: 25 minutes can be expressed as ⅙+¼ hours. Therefore we need to burn the first rope such that we always maintain 5 segments. Then once that's fully burnt, we just burn the second rope such that we always maintain 3 segments.
I feel like I've entered a Google interview