Disentangling Wire-and-String Puzzles in 3D

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Here are the solutions to several 3D wire-and-string puzzles. Drag the time slider to see how the string comes off the wire.

Contributed by: Karl Scherer (May 2012)
Open content licensed under CC BY-NC-SA



How Is It Done?

When you move the time slider you see the string being disentangled from the wire.

This smooth movement is based on several intermediate stages, with the computer calculating the smooth transitions between the fixed 3D images of the string.

These intermediate stages have been created with the help of the Demonstration "3D Curve Constructor".

The wires and strings are both displayed using Mathematica's built-in Tube and BsplineCurve commands.


The examples provided are wire-and-string puzzles invented by the author in 1993. The task in these puzzles is to remove the closed string from the closed wire loop without cutting the string.

In this Demonstration an elastic string is used for convenience, but this has no influence on the validity of the solutions.

The Demonstration "3D Curve Constructor" by the same author shows several wire-and-string puzzles (in their entangled state) as examples.

The Demonstration "Wire-and-String Puzzles" by the same author lets you play with and solve these puzzles, but the presentation of the puzzles is two-dimensional and very simplified.

The real wire-and-string puzzles are manually created from copper or steel wire. Silver plated and produced in small sizes, some puzzle types are flat enough to be worn as pendants around your neck as puzzle jewelry.

In this case a narrow black ribbon is used instead of a string.

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