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Disentanglement Puzzles

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The aim is to remove the rope with the two balls from the figure in steel wire.
In this kind of puzzle, the goal is to untangle the noose of rope or metal from an object. Topology plays an important role in these puzzles. 

The image on th eright shows a version of the Derringer Puzzle. Although it looks simple, it is quite sophisticated: most puzzle websites point to it as one of the most complicated.
Vexiers is another different group of disentanglement puzzles, where two or more twisted metal wires must be untangled. This typology had a great diffusion in the world at the end of the XIX century as well. Many modern games of this kind come from this period.

rompicapo_dell_anelloThe so-called "Ring Teasers" among which the most famous is "The Chinese Rings" or "The Lord of the Rings" are a different type of Vexier. In these puzzles, a circle of steel wire must be untangled by a weaving of rings and wires. The number of steps required for the solution often has an exponential relationship with the number of circles in the puzzle.

A considerable puzzle, known as "Chinese Rings", Cardano's Rings, Baguenaudier or Renaissance puzzles, was recorded for the first time around 1500 as "problem number 107" in "De Viribus Quantitatis" manuscript by Luca Pacioli. This puzzle is mentioned again in 1550 by Girolamo Cardano in the edition of his book "De subtililate". Although it is a kind of disentanglement puzzle, at the same time it has mechanical puzzles attributes and, therefore, the solution may derive from binary mathematics.

NB: The Chinese Rings are associated with a story set in the Middle Ages, where knights used to give these puzzles to their wives to pass the time during their long absences. Tavern Puzzles, made of durable metals, were a good practice for blacksmith apprentices.

Danish physicist Niels Bohr used disentanglement puzzles called "Tangloids" in order to demonstrate the properties of rotation to his students.

Some examples are:

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