---
title: 'Tie Random Ends: How Many Loops?'
source: 'https://youtube.com/watch?v=ZHXt0-_gSj4'
video_id: 'ZHXt0-_gSj4'
date: 2026-08-10
duration_sec: 82
---

# Tie Random Ends: How Many Loops?

> Source: [Tie Random Ends: How Many Loops?](https://youtube.com/watch?v=ZHXt0-_gSj4)

## Summary

This video presents a probability puzzle involving tying random ends of strings together and asks how many loops will form when starting with 50 strings. The puzzle is part of a monthly series, with solutions to be released in longer-form videos.

### Key Points

- **The Puzzle Setup** [00:02] — You have a box of strings. You randomly grab two ends, tie them together, and repeat until no ends remain. The process ends when all strings form loops.
- **Example with 10 Strings** [00:28] — Starting with 10 strings, the process results in 3 loops. This serves as an illustrative example of the puzzle.
- **The Question** [00:43] — If you start with 50 strings and repeat the tying process 50 times, how many loops will you end up with?
- **Solution Format** [00:55] — Solutions to monthly puzzles are packaged into longer videos that group puzzles by theme or problem-solving tactics. Previews are available on Patreon.

### Conclusion

The video poses a classic probability puzzle and explains the format for future solution releases, encouraging viewers to engage with the puzzle before the solution is published.

## Transcript

string and you drop them into a box. You reach in and blindly grab two random ends and then you tie those ends together and then you do it again. You choose two more ends of the strings at random, tie them together, and put the
result back in. Choose another two, tie those together, and so on and so forth. >> Every now and then you grab two ends of the same string, meaning when you tie them together you form a loop. In fact, [music] the end condition here, when
there are no more endpoints left, is one where all you have are loops inside that box. In this example that started with 10 total strings, we end up with three total loops. Here's your puzzle. If instead we started with 50 total strings
and you go through this whole process tying random ends together 50 times, how with? >> [music] >> By the way, for solutions to these monthly puzzles, rather than making
individual videos for each one, what I've decided to do is make longer form videos that package together ones that have similar themes or problem-solving tactics in their solutions. For the last two puzzles, I have previews of those
solutions up on Patreon and in general Patreon is probably your best bet for made. This isn't like a gimmick just to get more support, it's just genuinely a little bit of feedback before their final form.