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Science Puzzle

Burning Crab Lines

Engineering Supernova ⚡⚡⚡
Two ropes. Each burns in 60 minutes but NOT uniformly. No ruler. Measure exactly 45 minutes. Rope A light light lit at both ends = burns in 30 min (not 60) Rope B light lit at one end = burns in 60 min Light both ends of A + one end of B simultaneously. When A is gone (30 min), light the other end of B. B burns out exactly 15 min later = 45 min total.
Fig. 1: Rope A burns from both ends simultaneously. When it is gone, light the second end of Rope B.

You have two ropes. Each takes exactly 60 minutes to burn from end to end, but they burn unevenly: some parts burn fast, some slow. You have no clock, no ruler, and no way to measure time except by burning the ropes.

How do you measure exactly 45 minutes?

The Answer

Light both ends of Rope A and one end of Rope B at the same moment. Rope A, burning from both ends, uses up its 60-minute burn in 30 minutes, regardless of where it burns fast or slow.

The instant Rope A goes out, 30 minutes have passed, and Rope B has 30 minutes of burn time remaining (from its one lit end). At that moment, light the other end of Rope B. Now Rope B is burning from both ends and its remaining 30 minutes of material burns in 15 minutes.

Total time: 30 minutes (A burns out) + 15 minutes (B burns out) = 45 minutes exactly. The key insight is that burning from both ends always halves the remaining time, even if the rope burns unevenly.

The principle: Algorithmic timing. Burning from both ends always halves the remaining burn time, regardless of the unevenness of the rope. Chaining two such operations produces any target that is a sum of halves.