Burning ropes

On 12 Dec 2004 00:49:18 GMT, Pedro Graca

t = A + B

A = 10/a, where a = 1, 2, 3, 4, 5, ... B = 8/b, where b = 1, 2, 3, 4, 5, ...

That's if you burn the two ropes sequentially. If you burn them simultaneously, the interval from when the short burns out to when the long rope burns out is A-B.

How do you determine 'a' and 'b'? You cannot divide the ropes into equal length pieces because the burn rate is not constant. What you _can_ do is burn the rope from both ends. The two burning ends will meet in the middle. The middle of the total time, which is not necessarily the middle of the length.

) Mensanator wrote (re-formatted): )> start with one end lit )> 8 short rope *

You could light it at both ends and an arbitrary place in the middle; when one rope burns out, light at another place, and so on.

one rope burns out,

How do you know how many minutes have elapsed when this

If you keep four parts of the rope burning at all times, it will take exactly (normal length)/4 minutes to burn.

How to measure x/y minutes using the x minute rope?

1. Cut rope x into y pieces (of any length). 2. Light all pieces at one end. 3. When a piece is burnt cut one of remaining in half and light the new piece at one end. 4. Repeat step 3. until all pieces are burned.

(Be prepared to cut and light infinitesimal pieces infinitely fast.)

I am still not seeing how that works. It would work if the four pieces have uniform burn rates, but it is specifically stated in the problem that this is not the case.

Suppose you cut the 10 minute rope into four equal length pieces. Due to non-uniform burn rates, the four pieces could be 1, 2, 3 qnd 4 minutes. Keeping all four of them burning would only take 4 minutes (or 2 if each were burning from both ends). 4 is not 10/4 and furthermore, you would not even know that it was four minutes.

Mensanator schrieb:

1) You light up all 4 pieces at one end. 2) When 1 burns out, light up 4 at the other end. 3) When 2 burns out, light up 3 at the other end. 4) When all ropes have burned, 2.5 minutes have elapsed.

If you can't see which rope is the longest to burn in step 2, you could possibly do 2) When 1 burns out, light 3 at the other end. 3) When 2 burns out, light 4 at the other end. 4) When 3 burns out, light 4 in the non-burning middle. If you don't hit the middle exactly, whenever two flames meet, set fire to a remaining nonburning (and nonburnt) section of rope, so that you'll have 4 flames going at all times. This will nicely foursect your total burn time.

By keeping 3 flames going you can easily trisect the total burntime, etc.

Cheers

) I am still not seeing how that works. It would work if the four pieces have ) uniform burn rates, but it is specifically stated in the problem that this ) is not the case. ) ) Suppose you cut the 10 minute rope into four equal length pieces. Due to ) non-uniform burn rates, the four pieces could be 1, 2, 3 qnd 4 minutes. ) Keeping all four of them burning would only take 4 minutes (or 2 if each ) were burning from both ends). 4 is not 10/4 and furthermore, you would ) not even know that it was four minutes.

Then, after 1 minute, there are only 3 ends burning, so you need to light an extra end. Etcetera.

If you keep 4 ends burning AT ALL TIMES then the burning time will be N/4

SaSW, Willem

Ok, I grt it now. Looks like there are a lot more solutions.