You half to burn the rope6/14/2023 ![]() How do you use these two ropes to measure 45 minutes? There’s no guarantee of consistency in the time it takes different But either rope has different densities at different points, so Original question: There are two ropes, each rope takes 1 hour toīurn. So, for 4 ropes, we agree that there are 34 (23 11) different times that can be measured. The two numbers below the two sets are the lengths of the sets. The second set contains all of the intermediate start/stop pairs. For each number, the first set assumes the timer starts at time 0. I also wrote a Python program to solve this. The time elapsed between when we start and stop the timer is 5/8. Here are all the steps in the order in which they occur:ġ) simultaneously light A at both ends and light B at one end.Ģ) when A burns out: start the timer, light B at other end, light C at one end.ģ) when B burns out: light C at other end. Suppose the ropes are labeled A, B, and C. We can now assemble all these pieces of information to construct the solution. Now we have measured 1/4… and all we needed to do was be able to measure 1/2.ģ) 1/2 comes from S1 and is found by starting the timer, lighting the rope at both ends, and stopping the timer once the rope is burnt. Since there is 1/2 left of the rope and we just lit the second end, it will burn for 1/4. Assuming we are able to measure 1/2, we do the following: light the rope at one end, wait 1/2, light the other end, and start the timer. ![]() So we have measured 5/8… and all we needed to do was be able to measure 1/4.Ģ) 1/4 comes from (1-1/2)/2, where 1/2 belongs to S1. Since there is 3/4 left of the rope and we just lit the second end, it will burn for 3/8. Assuming we are able to measure 1/4, we do the following: start the timer, light the rope at one end, wait 1/4, then light the other end. As you’ll see, it should be possible to write a recursive computer program that spits out the recipes for each possible number. This may seem like a lot of work but it’s very formulaic. We can construct the 5/8 solution by working in reverse. ![]() I interpreted “measure” to mean that it’s possible to use a stopwatch that you start and top at specified events and the time indicated on the stopwatch would be the “measured” time. Note: my solution is incomplete (see comments below!) Author Laurent Posted on FebruFebruCategories The Riddler Tags recursion, Riddler This measures $|\tau-1|$ or $|\tau-\tfrac$ hours.
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