燃烧的绳子
Burning Ropes
题目详情
你有两根绳子。每根绳子完全烧完需要整整 1 个小时。每根绳子的密度以未知的速率变化，导致某些部分燃烧得快，而另一些部分则燃烧得慢。
仅使用打火机和两根绳子，如何精确测量 45 分钟？
You have two ropes. Each rope will take exactly 1 hour to burn all the way through. The densities of each rope vary throughout at unknown rates which cause some portions to burn fast and others to burn slow.
Using nothing but a lighter and the two ropes, how can you measure exactly 45 minutes?
解析
回答这个问题的关键是将1小时的绳子转换成其他计时器。例如，如果将1小时的绳子两面都烧掉，就可以将其变成30分钟的绳子。
假设一开始，你烧毁了第一根绳子的一侧，以及第二根绳子的两侧。当第二根绳子完全燃烧时，你知道 30 分钟已经过去，你的第一根绳子现在是 30 分钟的绳子。你点燃第一根绳子未点亮的一侧，将其变成一根 15 分钟的绳子。一旦燃烧完毕，45 分钟就过去了。
Original Explanation
The key to answering this question is converting the 1-hour ropes into other timers. For example, if you burn both sides of 1-hour rope, you can turn it into a 30-minute rope.
Suppose at the start, you burn one side of the first rope, and both sides of the second rope. The instant the second rope fully burns, you know 30 minutes has past and your first rope is now a 30-minute rope. You light the unlit side of the first rope turning into a 15-minute rope. Once that has finished burning, 45 minutes has passed.