How would you measure time, if you didnt have a stopwatch (or your smartphone)? Well, you could use the movement of the Sun across the sky, watch a pendulum swing, or even burn some special string.
Imagine you’ve been given several pieces of string with varying lengths and thicknesses. Not only do the lengths and widths of the pieces vary, each piece of string isn't even uniform in width along its own length. In other words, they get thicker and thinner (by different amounts and in different places) as you go from one end to the other. While all of the pieces are therefore different, they have one thing in common: if you light one end on fire, it will always take exactly 1 hour to burn through to the other side. But since each piece gets thicker and thinner as it goes, a given piece of string doesn’t necessarily burn at an even rate. By which I mean that a string doesn't necessarily burn half its length in 30 minutes—all we can say is that it burns its entire length in exactly 1 hour. So that's the setup.
Is it possible to use these pieces of string to measure a 45 minute time interval?
Now, here’s the question: Is it possible to use these pieces of string (as many as you want) to measure a 45 minute time interval? And, if it's possible, how would you do it? As with every puzzle, it’s a lot more fun if you give it a try before finding out the answer. So I encourage you to pause for a few minutes to give it a go. Then, when you’re ready, continue on for the answer.
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