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Puzzle crafting & workshops • Laboratorio di giochi d'ingegno • Atelier de puzzles
by Gianni A. Sarcone & Marie-Jo Waeber
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Torquato Puzzle

This game may have been given to Leonardo Pisano (Fibonacci) by Chandlahuri his Indian servant when he was living in Bougie (Algery) with his father. Leonardo renamed this puzzle afterwards: "lo joco enimmatico del brachiale torquato" (medieval italian, = the puzzle of the twisted bracelet). Torquato puzzle was inspired from the Chinese rings puzzle.

torquato bracelet 1 torquato bracelet 2
torquato bracelet 3 torquato bracelet 4

Let's Start

The puzzle consists in 3 parts: 1 paper braid and a string with 2 square cardboard pieces (one of them having a hole in the middle).
To make your own Torquato puzzle, download first the PDF file containing the 2 models shown below...

(To download, just click on the small PDF icon >>>torquato puzzle to download )

making 1

making 2

© Gianni A. Sarcone
Source: MateMagica, ISBN 88-89197-56-0



Separate the string from the puzzle without folding or tearing up the square cardboard pieces or the braided paper puzzle... Once you've freed the string, try to assemble the puzzle again!


Torquato, a topological puzzle

Topology is the study of geometric properties that are preserved under deformation. Sometimes topology is referred to as “rubber sheet geometry”, because it does not distinguish between a circle and a square (a circle made out of a rubber band can be stretched into a square) but does distinguish between a circle and a figure eight (you cannot stretch a figure eight into a circle without tearing).
Topology deals with the ways that surfaces can be twisted, bent, pulled, or otherwise deformed from one shape to another (without tearings!). A topologist is interested in the properties that remain unchanged after all these transformations have taken place. Topologically speaking there is no difference between a doughnut and a coffee cup (see drawing below), since either one can be deformed into the shape of the other. Many string and wire puzzles, like Torquato puzzle, are based on topological principles. Understanding a few basic principles will help you analyze and solve these puzzles.

topological transformation

Torquato is made of a ‘closed loop’ (the braid) interlaced with an ‘open loop’ (the string), having at one end a ‘locking loop’ (the cardboard piece with the hole) and at the other end an ‘end loop’ (the other cardboard piece). Since we can free the string from the braid bracelet we can consider the ‘closed’ and ‘open’ loops as two unlinked rings.

topology puzzle

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Archimedes journal ARCHIMEDES journal is an interactive review devoted to entertaining & involving the readers with puzzles, recreational mathematics and visual creativity. This journal is published for an audience without a specific math background. Each issue covers a broad range of mental and hands-on activities for the reader to enjoy! Workshop image "How to focus attention? Encourage creative exploration?" Multicultural interactive puzzle activities & workshops for museums and institutions.
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