Burning ropes to measure time
Warm-up: You are given a box of matches and a piece of rope. The rope burns at the rate of one rope per hour, but it may not burn uniformly. For example, if you light the rope at one end, it will take exactly 60 minutes before the entire rope has burnt up, but it may be that the first 1/10 of the rope takes 50 minutes to burn and that the remaining 9/10 of the rope takes only 10 minutes to burn. How can you measure a period of exactly 30 minutes? You can choose the starting time. More precisely, given the matches and the rope, you are to say the words “start” and “done” exactly 30 minutes apart.
The actual problem: Given a box of matches and two such ropes, not necessarily identical, measure a period of 15 minutes.
1. Burn the rope 1 from one end and rope 2 from both ends
2. As soon as rope 2 burnt completely,
3. We have 30 minutes gone and 30 minute left in rope 1
4. Burn the other side of rope 2 and start counting (30 Minute left in rope 2)
5. Fire is from both end so, rope will be burnt in 15 minute and hence , we get 15 minutes
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Don’t you think rate of burning across the rope has to be uniform? Otherwise this burning from both sides won’t get you to the result.
Again in the second part if the ropes are not identical again rate of burning would be an issue.