Calculating 25 minutes by burning 2 inconsistently burning 1-hour ropes
Calculating 25 minutes by burning 2 inconsistently burning 1-hour ropes
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:
first ½ of hint
I carefully chose approximately instead of precisely
second ½ of hint
because to calculate it precisely would require that you ignite an infinite number of flames
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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.
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.
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.