系随机线头：能形成多少个环？

YouTube Transcript

Language: English (auto-generated) (en)

[0:00] It's time for a new puzzle of the month.

[0:02] Imagine you have a lot of pieces of

[0:03] string and you drop them into a box. You

[0:05] reach in and blindly grab two random

[0:08] ends and then you tie those ends

[0:10] together and then you do it again. You

[0:12] choose two more ends of the strings at

[0:14] random, tie them together, and put the

[0:16] result back in. Choose another two, tie

[0:18] those together, and so on and so forth.

[0:20] >> [music]

[0:21] >> Every now and then you grab two ends of

[0:23] the same string, meaning when you tie

[0:24] them together you form a loop. In fact,

[0:26] [music] the end condition here, when

[0:28] there are no more endpoints left, is one

[0:30] where all you have are loops inside that

[0:33] box. In this example that started with

[0:35] 10 total strings, we end up with three

[0:38] total loops. Here's your puzzle. If

[0:40] instead we started with 50 total strings

[0:43] and you go through this whole process

[0:44] tying random ends together 50 times, how

[0:47] many loops on average do you end up

[0:49] with?

[0:50] >> [music]

[0:51] >> By the way, for solutions to these

[0:53] monthly puzzles, rather than making

[0:55] individual videos for each one, what

[0:57] I've decided to do is make longer form

[0:59] videos that package together ones that

[1:01] have similar themes or problem-solving

[1:03] tactics in their solutions. For the last

[1:05] two puzzles, I have previews of those

[1:07] solutions up on Patreon and in general

[1:09] Patreon is probably your best bet for

[1:11] where to find these solutions as they're

[1:12] made. This isn't like a gimmick just to

[1:14] get more support, it's just genuinely a

[1:16] convenient place to start getting a

[1:17] little bit of feedback before their

[1:18] final form.

Translation:

YouTube Transcript

Language: English (auto-generated) (en)

[0:00] It's time for a new puzzle of the month.

[0:02] Imagine you have a lot of pieces of

[0:03] string and you drop them into a box. You

[0:05] reach in and blindly grab two random

[0:08] ends and then you tie those ends

[0:10] together and then you do it again. You

[0:12] choose two more ends of the strings at

[0:14] random, tie them together, and put the

[0:16] result back in. Choose another two, tie

[0:18] those together, and so on and so forth.

[0:20] >> [music]

[0:21] >> Every now and then you grab two ends of

[0:23] the same string, meaning when you tie

[0:24] them together you form a loop. In fact,

[0:26] [music] the end condition here, when

[0:28] there are no more endpoints left, is one

[0:30] where all you have are loops inside that

[0:33] box. In this example that started with

[0:35] 10 total strings, we end up with three

[0:38] total loops. Here's your puzzle. If

[0:40] instead we started with 50 total strings

[0:43] and you go through this whole process

[0:44] tying random ends together 50 times, how

[0:47] many loops on average do you end up

[0:49] with?

[0:50] >> [music]

[0:51] >> By the way, for solutions to these

[0:53] monthly puzzles, rather than making

[0:55] individual videos for each one, what

[0:57] I've decided to do is make longer form

[0:59] videos that package together ones that

[1:01] have similar themes or problem-solving

[1:03] tactics in their solutions. For the last

[1:05] two puzzles, I have previews of those

[1:07] solutions up on Patreon and in general

[1:09] Patreon is probably your best bet for

[1:11] where to find these solutions as they're

[1:12] made. This isn't like a gimmick just to

[1:14] get more support, it's just genuinely a

[1:16] convenient place to start getting a

[1:17] little bit of feedback before their

[1:18] final form.

中文翻译：

YouTube 录音

语言： 英语（自动生成）(en)

[0:00] 本月的新谜题时间到了。

[0:02] 想象一下，你有很多绳子碎片，把它们放进一个盒子里。你

[0:05] 伸手进去，盲目地抓取两个随机的

[0:08] 端点，然后把它们绑在一起，然后再做一次。你

[0:12] 再次随机选择两个绳子的端点，把它们绑在一起，然后把结果放回去。再选择两个，把它们绑在一起，依此类推。

[0:20] >> [音乐]

[0:21] >> 有时候，你会抓到同一根绳子的两个端点，这意味着当你把它们绑在一起时，会形成一个环。事实上，

[0:26] [音乐] 这里的结束条件是，当没有更多的端点剩下时，盒子里只剩下环。在这个从10根绳子开始的例子中，我们最终得到了三个环。这里是你的谜题。如果

[0:40] 我们从50根绳子开始，整个过程绑50次随机的端点，平均会得到多少个环？

[0:50] >> [音乐]

[0:51] >> 顺便说一下，关于这些月度谜题的解答，而不是为每个谜题制作单独的视频，我决定制作较长的视频，将具有相似主题或解题策略的谜题打包在一起。对于最后两个谜题，我已在 Patreon 上发布了解答的预览，一般来说，Patreon 可能是你找到这些解答的最佳地方，因为它们是在制作过程中发布的。这并不是为了获得更多支持的噱头，而只是一个方便的地方，在最终形式之前开始获得一些反馈。