Calculating 25 minutes by burning 2 inconsistently burning 1-hour ropes
You are given two ropes and are told that they burn at inconsistent rates, but will always take 1 hour to completely burn up. This means that cutting one of the ropes perfectly in half will not give you two smaller 30-minute ropes.
You are told that you need to approximately calculate 25 minutes by burning these ropes in some fashion.
How do you accomplish this?
Hint: ::: spoiler first ½ of hint I carefully chose approximately instead of precisely ::: ::: spoiler second ½ of hint because to calculate it precisely would require that you ignite an infinite number of flames :::
8 Comments
ascallion@lemmy.world · 2 pts · 3y
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.
pglpm@lemmy.world · 1 pts · 3y
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.
MrMusAddict@lemmy.world · 1 pts · 3y
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.
ascallion@lemmy.world · 1 pts · 3y
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 :::
MrMusAddict@lemmy.world · 2 pts · 3y
Waited 24 hours in case anyone could figure it out. I've posted the solution as it's own top comment.
MrMusAddict@lemmy.world · 2 pts · 3y
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:
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.
green_light_stop@kbin.social · 1 pts · 3y
I feel like I've entered a Google interview
owenfromcanada@lemmy.ca · 1 pts · 1y
I don't see any reasonable way to do this without either having something external to approximately gauge time, or making assumptions about the linearity of the burning of the ropes. I could time two hours, one hour, 30 minutes, or 15 minutes given the parameters.