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@quintic@engineers_feed I would argue that because I have control over the orientation (as I am the one trying to time something) that there is no need for an extra property. I can simply control for that by laying the rope flat. Additionally, that would be an experimental property, not a rope property
@quintic@engineers_feed The strands cannot add energy. If their tip is close enough to the rope to carry flame to it, then in the opposite direction the rope would similarly ignite the tip, giving equal burn time.
I'm not placing ropes vertically, everything is on the ground.
@quintic@engineers_feed Your example relys on the assumption that the rope can burn at different rates in different directions. I am convinced that is not possible. The strand example does not work because if the strands are close enough to make the fire faster that would happen in both directions.
@quintic@engineers_feed By that logic, the rope would burn at different rates from end to end depending on which side was lit first, which would violate the stated properties of the rope.
@quintic@engineers_feed If it was a thin to thick rope, the thin part would burn faster than the thick, but that would occur in both directions. Either way you would get the same time. The directionality of strands does not matter as they begin to burn from their base, which is the rope.
@quintic@engineers_feed For the purposes of this brain teaser, I am confident that the same section of rope will burn at the same rate from either direction. Irregular construction or not, you still have the exact same mass that needs to be burnt.
@quintic@engineers_feed However, if X is in a different location for each scenario then it would take 15 minutes to burn the rope and the flames would meet somewhere in the 20 minute section.
@quintic@engineers_feed If X is the same place on the rope in both scenarios then what you have described is not possible. If X to B takes 10 minutes for a given rope then B to X must also take 10 minutes, otherwise you have a different rope with different properties.
@quintic@engineers_feed What property? The only property needed is that the rope burns end to end in 30 mins. Regardless of "how" that rope gets to 30 mins, if you light both ends it will burn in 15 minutes. The flames may not meet in the center if it burns unevenly, but it will burn for 15 minutes.
@quintic@engineers_feed Since it burns end to end in 30 minutes (only lighting one end), regardless of how quick each portion burns, when you light both ends, the flames will meet (and the rope will be done burning) in half that time.
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