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Rui - Your problem is actually just like the 7.5 minute soltion discussed above. See Mapraputa's post which begins with "To elaborate on the rope problem:". Take your mouse and try to select the big empty area immediately after this sentence. When you highlight the area with your mouse, you will see that it actually contains text. We sometimes hide solutions this way to avoid spoiling the answer for everyone. Anyway, the 7.5-minute solution uses only the 30-minute rope. A 15-minute solution can use the same technique on a 60-minute rope. As discussed, it may require an infinite number of steps to be exact.

Ah! Thank you, I found it. Really, in a quick view I had not get it because of that hidden technique This is really a good solution but there's a practical problem: no one has infinite time to do such job. Now I have a mathematical solution but easy to accomplish (although in an infinite time), and a physical solution but yet very sci-fi. I know there is a easy solution! Just want to find it I'm now trying a solution using mirrors, but I could not find it yet. Im' really addicted to this problem... eheh Rui

Originally posted by Pranav Jaidka: There are 2 ropes . When one is lighted it burns out in 1 hour. when the other is ligthed it burns out in half hour. Measure 45 minutes using these ropes . Ropes are uneven in density and do not burn out evenly.

[This message has been edited by Pranav Jaidka (edited May 30, 2001).]

Kindly ignore, if the correct answer is already posted ... !! Start by lighting up both the ends of the 1 hr rope .... it will take 30 min. to burn it out completely .. and the moment it is completed ... burn both ends of the 30 min. rope ... it will be burnt completely in 15 min., Hence 30 + 15 = 45 ....

- Varun

Varun Khanna
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Originally posted by Jim Yingst: Folding in half doesn't work if the ropes are uneven in density - you don't know that the midpoint of the rope necessarily represents the point where half the time has elapsed. But there is a way... As a variation, try to measure a length of 37.5 minutes.

60 min. = Rope A 30 min. = Rope B Light up both the ends of rope B, and one end of Rope A simultaneously !!! moment B is burnt out (15 min.), light up the second end of Rope A, it will take (60-15)/2 min. to burn ... i.e. 22.5. Hence total time 22.5+15 = 37.5

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VK - correct both times. Now, see if you can do 7.5 minutes. Rui - hey, the solution doesn't take infinite time; it takes an infinite number of steps. Not the same thing. The time required is still 7.5 minutes - that's the point. All right, an infinite number of steps is kind of hard to do, but as long as each step becomes less and less significant, for practical purpposes we can get as close an approximation as we desire by executing enough of the steps. If we get tired, we can just let the remaining fires burn out, and when they're all done we know that just over 7.5 minutes have elapsed. I'll be interested to hear if you come up with any other good variants. Mirrors? I can't imagine what you'd do with them, but let us know if you find a good use. Cheers...

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Originally posted by Jim Yingst: VK - correct both times. Now, see if you can do 7.5 minutes.

Okey here is my attempt for the "solution", and I will only use the rope, which burns in 30 min. : Lets assume, "A" to be the cross sectional area of the rope and "L" to be its length. Now since the rope is not uniform, its safe to assume that "A" may vary along the length of the rope. Lets cut the rope in "n" number of pieces of "l" length, {(l+l+l+ ... n times) = L (where n tends to infinity)} such that every piece of rope with the length "l" and Area "A" will have a constant and even density along its length and also the difference between its properties (like density,etc.) and that of the next piece of "l" length will tend to zero: Now we need to cut all the "n" pieces with area "A" into half and light up the upper half of the first piece along its "l" length (from both the ends) and moment is finishes, light up the upper half of the second piece ...do this till nth piece .. the total time taken will be exact 7.5 minutes(ideally). The solution is a bit unrealistic, but under "ideal conditions" (reminding me of those good old PV=nRT equations) it will measure 7.5 min. [ September 24, 2003: Message edited by: varun Khanna ]

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I'm afraid I didn't follow that, VK. You're going to light n fires at the very beginning, and each time one burns out, immediately light another in its place? And n will tend to infinity? Then it sounds to me as though the time required for evereything to burn will tend to 0, not 7.5 min. It sounds like you've divided the whole rope into a lot of little pieces that will all burn up simultaneoursly in a fraction of a second. What am I misunderstanding?

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I'm afraid I didn't follow that, VK. You're going to light n fires at the very beginning, and each time one burns out, immediately light another in its place? And n will tend to infinity? Then it sounds to me as though the time required for evereything to burn will tend to 0, not 7.5 min. It sounds like you've divided the whole rope into a lot of little pieces that will all burn up simultaneously in a fraction of a second. What am I misunderstanding?

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Come think of it, this should really be in Programming Diversions now, so I'm moving it there...

1. Dip thread A in gasoline and calculate how much time does it take to burn 2. Dip the other thread in Old Monk burn it and calculate time 3. Or Thread A soak in gasoline and Hang Osama Binladen on it and burn it and calculate the time 4. Hang Saddam on thread B and soak it with old Monk burn it and calculate the time taken to burn 5. Thread A burn it and let a man blow Air while it is burning and calculate the time 6. Thread B burn it and let a woman blow ( ) Air while it is burning and calculate time Goddamn unlimited possibilities

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Originally posted by Jim Yingst: I'm afraid I didn't follow that, VK. You're going to light n fires at the very beginning, and each time one burns out, immediately light another in its place? And n will tend to infinity? Then it sounds to me as though the time required for evereything to burn will tend to 0, not 7.5 min. It sounds like you've divided the whole rope into a lot of little pieces that will all burn up simultaneously in a fraction of a second. What am I misunderstanding?

Oopps .. I edited my message now !!! My intension was to burn them one by one ... so that the total time to burn all of them adds up to 7.5 minutes. Actually, I knew the whole rope will burn in 30 min. and if I burn it from both the ends it will take 15 min., so the aim was to divide the rope into two "EQUAL" parts, along its length, so that if I light up one part from both the ends, it sud take 15/2 = 7.5 min. But since the rope is not uniform, I use differential approach to eliminate this issue of non uniformity, but still its not perfect, as I didn't considered the 3 dimensional scenario, & I cut the rope along one dimension only. [ September 24, 2003: Message edited by: varun Khanna ]