燃烧绳子
Burning Cords
题目详情
有两根绳子，每根从任意一端点燃都会在恰好 1 小时内烧完，但燃烧速度不一定均匀。
问：应如何点燃这两根绳子，精确计时 15 分钟？
提示：由于燃速不均，不能简单对半折断来“半小时”。但如果同时点燃一根绳子的两端，它仍会在 30 分钟内烧完。
You are given two cords that both burn in exactly one hour, not necessarily at a uniform rate. How should you light the cords to determine a time interval of exactly 15 minutes?
Hint
Because this lacks uniformity, we cannot break the cord in half, and expect it to burn in half the time. But we can burn both ends of a cord to finish it in half the time it would have taken otherwise!
解析
做法：
- 第一根绳子只点燃一端。
- 第二根绳子两端同时点燃。
- 当第二根绳子烧完时，恰好过去 30 分钟；此时第一根绳子还剩恰好 30 分钟的“燃烧时间”。
- 立即把第一根绳子的另一端也点燃，两端同时燃烧，则剩余部分会在 15 分钟内烧完。
因此可以精确计时 15 分钟。
Original Explanation
Solution
First, let's try to measure thirty minutes. To do that, we can burn both ends of a cord. Even if it burns non-uniformly, it will still finish in exactly 30 minutes.
To measure 15 minutes, burn the first cord at one end and the second cord at both ends. Half an hour later, when the second cord finishes burning, the first cord has exactly 30 minutes of length left. Now we can burn the other end of the first cord, and it shall finish in exactly 15 minutes.
Follow-up Question
Instead of having two cords, what if you only had one cord, how would you measure 15 minutes?
Follow-up Answer
Break the cord into approximately half, and burn these two cords from both of their ends. If both these cords finish burning together, that means exactly 15 minutes have passed. If any one of these cords finishes first, break the other cords from approximately the middle, and further burn all ends of these little cords. Continuing this way theoretically leads to exactly 15 minutes!