Folklore

A rope was folded in half, then again in half, and once more in half, and then all layers of the rope were cut in one place.

What could have been the length of the rope, if it is known that some two of the resulting pieces had lengths of 9 meters and 4 meters?
![](https://cdn.mathpix.com/cropped/2024_05_06_f36000480089c1ccffcbg-32.jpg?height=241&width=801&top_left_y=1363&top_left_x=640)

When cutting, three different types of pieces could be formed (see fig.), and the length of one type of piece is exactly twice that of another. Let's denote these lengths as \( x, 2x \), and \( y \) respectively, and the total length of the rope as \( L \). By counting the number of pieces of each type, we get \( L = 8x + 4y = 4(2x + y) \). All possible lengths of the pieces, based on the condition, are presented in the table:

| \( x \) | 4 | 2 | 9 | 4.5 |
| :---: | :---: | :---: | :---: | :---: |
| \( y \) | 9 | 9 | 4 | 4 |
| \( L \) | 68 | 52 | 88 | 52 |

## Answer

52 m, 68 m, or 88 m.