6 minute measurement with string puzzler
How do you measure 6 minutes? I’m baffled.
Bad puzzlercsolution. A pendulum? With a fuse? An hour long fuse would be too long and too irregular to be used as a pendulum.
My solution was to have 10 flame fronts working on the fuse. The endpoints and 4 points in the middle. Whenever the flame fronts met and extinguished themselves then light another burning segment in the middle. 1 flame front burns the fuse in one hour. 10 would do it in six minutes.
But remember, the fuse can burn unevenly. It could burn up all but one inch in one second, and take 59 min, 59 sec to burn that last inch.
Yes that wouldn’t matter. As long as ten flame fronts are going constantly it would work. In reality that would be hard to do but it’s more realistic than a pendulum.
Ah, now I understand your method (I think). So, you could solve the “15 minute” version by using 4 flame fronts like this: On one fuse, light both ends and one point in the middle, thus producing 4 flame fronts. When one of the two pair of flames meet and extinguish each other, light the middle of the remaining burning segment. When another pair of flame fronts meet, again light the middle of the remaining burning segment. Repeat the last step until the two pair of flame fronts meet simultaneously and there’s your 15 minutes. Right?
I do believe the pendulum solution is easily doable. I took a 3 oz table knife and hung it on a 3 ft long string and measured the period with a stopwatch over 10 periods to get about 2 sec per period. It appears that it wouldn’t keep swinging for 30 min, so you’d have to give it a nudge every 10 min or so to keep it going.
@kenberthiaume … that’s a very clever idea. +1 for you. I think you are right, your method would time out 6 minutes as long as you could keep all 10 points burning simultaneously. Keeping all 10 points burning at the same time until the 6 minutes are up might be a practical problem, depending on how unevenly the string burns. But so would keeping the pendulum moving.
@kenberthiaume …The puzzle specifically says that the string can burn unevenly. If one of the short peices has most of the hour in it (as Insighful said), that piece would burn for longer than 6 minutes. The other pieces would have already finished burning. You can’t keep all ten ends burning the whole time because some would burn up early. This is another time when averaging doesn’t work.
I think the OP already addressed your point @David L . In their first May 3 posting. It was perhaps a little unclear maybe. Think of it this way. Cut the string into 5 equal length pieces first. Then light both ends of each segment. So you have 10 flame fronts burning at once. If all segments burn the same rate, they’ll all extinguish at the same time and you are done. 6 minutes. If one segment burns faster than another, it will burn itself out while another segment continues to burn. So OP would watch for this, then at that time light the middle of an existing segment, effectively creating another segment to replace the extinguished one. The idea is to always have 5 segments burning at all times.
Don’t see how that gets to 6 minutes. Five could burn in 1 minute, then what?
4 could burn in 1 minute. I think that is what you mean. If that happened, the 5th segment would still be burning at both ends. It would be re-cut into 5 segments, and both ends of each segment lit again. There’s some practical problems, but I think that is the idea.
yes, GeorgeSanJose, that’s my thinking exactly. It also has the benefit of measuring 6 minutes from the start, whereas the pendumlum has to go one full hour and then you divide your number of pendulum swings by 10. You also don’t have to light the exact middle of a segment, just anywhere will do. Although keeping 10 flame fronts going at once would be tricky, and you’d lose time lighting a new front, etc. But restarting a pendulum after it’s petered out would cause error too.
You don’t restart the pendulum, you nudge it every once and a while as it slows down (similar to a pendulum clock that nudges it every cycle). With any skill, very little error would result.
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.k