---
title: 'The Twirling Tiles Puzzle'
source: 'https://youtube.com/watch?v=0W243LGSJFU'
video_id: '0W243LGSJFU'
date: 2026-08-08
duration_sec: 60
---

# The Twirling Tiles Puzzle

> Source: [The Twirling Tiles Puzzle](https://youtube.com/watch?v=0W243LGSJFU)

## Summary

This video presents a mathematical puzzle involving tilings of a hexagon with rhombus tiles. The core question is whether any tiling can be transformed into any other using a specific move: rotating a small hexagon formed by three rhombuses by 60 degrees. The video teases that the solution involves a clever visual insight.

### Key Points

- **Tiling Setup** [00:02] — A hexagon is tiled with rhombus tiles, each having internal angles of 60 and 120 degrees. The hexagon's side length is a whole number multiple of the tile's side length.
- **The Move** [00:16] — When three rhombuses form a small hexagon, you can rotate that hexagon by 60 degrees to create a different tiling. This may create new small hexagons that can also be rotated.
- **The Question** [00:29] — The central puzzle: using only these rotations, can you always transform any tiling of the hexagon into any other? The video hints that the answer involves a visual insight.
- **Video Context** [00:42] — The full video contains several puzzles with unexpected solutions. This particular puzzle is highlighted because the key insight is visually apparent when viewed correctly.

### Conclusion

The video teases a mathematical puzzle about tiling transformations, suggesting that the solution is revealed through a visual perspective. It encourages viewers to watch the full video for the complete answer.

## Transcript

you create a tiling pattern of a hexagon here each of those tiles is going to be a little rhombus whose internal angles are 60 and 120° and the side length of the hexagon will be some whole number multiple of the side length of the tile
whenever you see three of those little rhombuses make a little hexagon you could create a slightly different tiling by rotating that little hexagon 60° when you do this sometimes it creates a different little hexagon that wasn't
there before but which now can then be rotated to create yet another pattern the question is using only these moves can you necessarily get from any tiling of the hexagon to any other the full video that this comes from was really
fun to make it involves a number of very nice puzzles with unexpected Solutions and this puzzle in particular is fun because if you squint your eyes and see it in just the right way the key insight for answering kind of Pops right out at
click the link at the bottom of the screen