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Have you ever measured time without using stopwatches? When you move in the sun and sky, can you measure the time carefully by watching the wobble of the sun? I know this is not the most unforgettable statement in the world, but it is absolutely true. The puzzle is a dream exercise for your brain. Therefore, you will be wise to try to solve at least several different types of puzzles at least once a week. And the best part is that this mental exercise is very interesting.

To help you start to get more confused, today we have to see a great intellectual challenge I met recently. The problem is all about time, and how to measure time intervals in a very unusual way: instead of using stopwatch, it is to measure the time by burning a special string. How does it work? What is a brain Trailer?

How do you measure 45 minutes without stopwatch?

Imagine that you have given several strings of different length and thickness. Not only is the length and width of a single piece different, but also the width of each piece is uneven along its length. In other words, when you go from one end to the other, they become thicker and thicker, in different places and different places.Although all works are different, they have one thing in common: if you light one end, it usually takes an hour to burn to the other end. However, as each piece becomes thicker and thinner, a given string does not necessarily burn at an average speed. I mean, if you want stopwatch to record a rope in 30 minutes, it doesn't necessarily burn half the length - we can say that it burns the whole length in an entire hour.

This is the setting. The following question is: can you use these strings (as many as possible) to measure the interval of 45 minutes? And, if possible, what would you do? Just like every puzzle, if you try before finding the answer, it will become more interesting. So I encourage you to suspend for a few minutes and let it go forever. Then, when you are ready, keep looking for answers.

This is a simple problem. Before we solve today's problems, let's imagine a slightly simpler jigsaw where all the strings we give are burning at a uniform rate. In this case, you can simply fold the single string into one half to solve the problem, and then fold it in half to make the chord creases the entire length of 1/4, 1/2 and 3/4. Because the string is burning at a consistent speed, the 45 minute time to measure is only to ignite one end of the flame string, and then wait until the mark on the other end of the 3/4; is it simple enough, if it can do so, do not need stopwatch?

But, sadly, the performance of string pieces we gave in this puzzle is not so good, because they do not burn at uniform speed. This means that we can not simply break a chord into 1/4 to calculate the time. But that does not mean that we are not lucky... Because we can be smarter.

Here's what we need to do: we are not just lighting one end of the line, but lighting both ends. What does this have to do with us? Then, the uneven thickness of a string means that we can't say how fast the fire can burn from one end to the other at any given time. Nevertheless, we do know that after two or three minutes, the two flames that we have to burn together must get together and meet each other.

This means that we now have a way to use stopwatch to measure the interval of 30 minutes every 1 hours. Of course, what we really want is to measure the time interval of 45 minutes. So we haven't finished it yet. What are we doing now? Before answering this question, if you haven't figuring out this question, I encourage you to stop and wait for a while, then go on.

OK, so what can we do to measure the time interval between 45 minutes instead of 30 or 60 minutes? The trick is that when we light the first string from both ends, we need to light another string from one end. Then, when the two flames of the first string are gathered together, we need to ignite the second ends of the half burnt side according to time. At this point, the second flame of the string will start to burn to the other, and after the other 15 minutes, they will meet in the middle, and you can also use stopwatch to calculate.

So let's put all this together, and we can see that after we start the whole process of setting up the string, the second strings need a total of 30 + 15 or 45 minutes for the end of the burning. Therefore, by using some clever ideas, we managed to measure the interval of 45 minutes. It's cool, right? So we can measure time without the use of stopwatch, but these techniques are not good, and we have to use stopwatch to measure time, and the stopwatch is irreplaceable.