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| [[File:Staircasepuzzle-4ringspluspolewithcat.jpg|thumbnail|A baguenaudier]]
| | I would like to introduce myself to you, I am Andrew and my wife doesn't like it at all. Mississippi is exactly where her home is but her husband desires them to move. She is truly fond of caving but she doesn't have the time lately. My working day job is an invoicing officer but I've currently applied for another 1.<br><br>Feel free to surf to my weblog - real psychics [[http://www.skullrocker.com/blogs/post/10991 skullrocker.com]] |
| [[File:Baguenaudier.svg|thumbnail|right|Diagrammatic representation of a four-ring baguenaudier]]
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| [[File:Chinese_ring_full_brightened.jpg|thumbnail|right|A metal version of the puzzle]]
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| '''Baguenaudier''' (also known as the '''Chinese Rings''', '''Cardan's Suspension''', '''Cardano's Rings''', '''Devil's needle''' or '''five pillars''' puzzle) is a [[disentanglement puzzle]] featuring a loop which must be disentangled from a sequence of rings on interlinked pillars.<ref name=MW/> The loop can be either string or a rigid structure.
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| It is thought to have been [[invent]]ed originally in [[China]]. The origins are obscure, [[Stewart Culin]] attributes the puzzle to the second-century that it was invented by the 2nd/3rd century Chinese general [[Chu-ko Liang]].<ref name=DD/> The name "''Baguenaudier''" is [[French language|French]] for "time-waster".<ref name=MW/> It was used by French peasants as a locking mechanism.<ref name=MW>{{MathWorld | urlname=Baguenaudier | title=Baguenaudier}}</ref>
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| Variations of this include ''The Devil's Staircase'', ''Devil's Halo''<ref>[http://www.puzzlemuseum.com/month/picm05/200501d-halo.htm The Devil's Halo - The Puzzle Museum]</ref> and the ''Impossible Staircase''. Another similar puzzle is the ''Giant's Causeway'' which uses a separate pillar with an embedded ring.
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| ==Mathematical solution==
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| [[Édouard Lucas]], the inventor of the [[Tower of Hanoi]] puzzle, was known to have come up with an elegant solution which used [[Binary numeral system|binary]] and [[Gray codes]], in the same way that his puzzle can be solved.<ref name=DD>[http://www.daviddarling.info/encyclopedia/C/Chinese_rings.html David Darling – encyclopedia]</ref> The minimum number of moves to solve an ''n''-ringed problem has been found to be:
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| <math>a(n) = \begin{cases}
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| \frac{2^{n+1}-2}{3}, & \text{when }n\text{ is even,}\\
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| \frac{2^{n+1}-1}{3}, & \text{when }n\text{ is odd.}\end{cases}</math>
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| <ref name=MW/>
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| ==See also==
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| *[[Disentanglement puzzle]]
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| *[[Towers of Hanoi]]
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| ==References==
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| {{reflist}}
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| [[Category:Chinese ancient games]]
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| [[Category:Chinese games]]
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| [[Category:Chinese inventions]]
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| [[Category:Mechanical puzzles]]
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| [[Category:Educational toys]]
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I would like to introduce myself to you, I am Andrew and my wife doesn't like it at all. Mississippi is exactly where her home is but her husband desires them to move. She is truly fond of caving but she doesn't have the time lately. My working day job is an invoicing officer but I've currently applied for another 1.
Feel free to surf to my weblog - real psychics [skullrocker.com]