Two String Puzzler


#1

Congrats to Tom and Ray and the Car Talk staff for the Two-String Puzzler. I couldn’t solve it. I did figure out how to get the string to burn for 1/2 hour, but couldn’t figure out how to get 15 minutes. When Tom and Ray gave the answer, I said to myself “You stupid!” for not seeing how to do it. … lol … I must say it was a pretty good solution to a pretty good puzzler.

I tried both waking and sleeping. Waking produced the method to get 30 minutes. But not 15 minutes. I put my brain on the 15 minute problem in the background, during sleep. This almost always works; but the most my apparently inferior brain could come up with after 8 hours of sleeping on it was this: Make a pendulum with one of the strings, tying the lighter on the end of the string for the weight. Then burning the other string to calibrate the pendulum. Close, but definitely no cigar :wink:

Anyway, thanks to everybody there at Car Talk for some great Puzzler amusement.


#2

George, you’ll be very interested in their next in their series of string puzzlers.


#3

The thing I like about that puzzler is that while I found it difficult to solve, I later realized it should have been easy for me to solve. It tricked my brain into making it seem more difficult than it was. That’s the sign of a good puzzler. In my opinion anyway.

Like this puzzler: Jennie takes 3 year old Sally to the park every afternoon, placing a blanket on the grass for Sally to sit and play and enjoy the sunshine. One day Jennie notices a large Rottweiler approaching Sally at a rapid pace. Yet Jennie is not bothered by this. Why?


#4

Because Sally is an even larger Rottweiler?


#5

Very good! Sally is indeed a Rottweiller and the other dog’s sister. The owners know each other and bring them to the park every afternoon so they can play together.


#6

Small historical note concerning the pendulum/fuse solution: Galileo famously first observed the equal periods of a pendulum’s swing while watching the motion of a cathedral chandelier in a breeze. Sitting in a pew, without access to a timing device, he measured the intervals against his own pulse. In solving the 6-minute puzzler, why not eliminate the pendulum altogether, count the number of heartbeats in a 15-minute burndown and multiply by 2/5?


#7

Where else can you get nuggets like this? Thanks!


#8

Convinced there would be a solution to this puzzler, I delayed learning the answer for two weeks while I worked on the problem. I have come up with a solution which I believe also works, although somewhat involved.

Divide one length of fuse into five segments, preferably with one or two longer than the others, and divide the other into six segments, also with one or two preferably longer than the others. If all 11 segments are ignited at the same time, The total burn time for the five segment group will be 12 minutes, and the total burntime for the six segment group will be 10 minutes. Once the 10 minute burn time is reached, the total time remaining of the fuse lengths in the five segment group, If burned separately, will be a total of 12 minutes.

The trick is to have all of the fuse segments burn simultaneously, even though they are of different lengths. To do this, within each group, whenever a segment is exhausted, the second end of the longest remaining fuse in that group must be ignited, and so on so that there are always five, or six burning ends in the respective group. Then, when all of the fuse in the six segment group is exhausted, all of the fuses in the five segment group must be extinguished and all of the fuse segments connected together. Then, this remaining fuse segment, having a 12 minute duration, can be ignited from both ends, and when it is extinguished, six minutes will have elapsed.


#9

What if, in the 5 segment group, 3 of the segments burn rather quickly. How do you maintain 5 burning ends in the two remaining segments?


#10

Insightful, you point out the limitations in this approach. You would have to cut one or more of the remaining segments and light the appropriate number of unlit ends to keep the same number (five) of ends burning at all times. Admittedly, this approach produces only an approximation of the desired time interval. It likely has the same degree of precision as the pendulum approach.


#11

Another technicality: the statement of the Puzzler doesn’t say you have any knife or scissors, just the two fuses and a Zippo lighter.

I’m still confused by your answer, though. When the 6 segment group is burned up, the 5 segment group (if maintained with 5 burning ends) would have 2 minutes left, but you quench the flames. Then when you connect the pieces together, wouldn’t you have a fuse that would last 5X2=10 minutes if one end were lit or 5 minutes if both ends were lit?