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Connected Loops

In this puzzle we challenge you to find a way to tie the three loops of string together so that untying any one of them causes the other two to be disconnected.

Can you tie three loops of string together in such a way that they are all connected, so that if you pick up one loop, the others will come with it? Here's one way.

Loops

If you now untie the blue string, the green and red loops are no longer connected.

Loops

But, if you untie the red string instead of the blue one, the other two loops remain attached.

Loops

Similarly, if you untie the green string, the red and blue loops remain connected to each other.

Loops

The Challenge

Can you find a way to tie the three loops together so that untying any one of them causes the other two to be disconnected?


This content has been re-published with permission from SEED. Copyright © 2025 Schlumberger Excellence in Education Development (SEED), Inc.

Course: 

  • Geometry [1]
Result/Solution(s)

Solution: Connected Loops Math Puzzle

 Loops

Here’s our way of tying three loops of string together so that untying any one of them leaves the other two disconnected.

 

  • Geometry puzzle [2]
  • Math Puzzle [3]
  • topology [4]
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[1] https://hootsgo.org/?q=taxonomy/term/62
[2] https://hootsgo.org/?q=tags/geometry-puzzle
[3] https://hootsgo.org/?q=tags/math-puzzle
[4] https://hootsgo.org/?q=tags/topology