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| [[File:Burr Puzzles.jpg|thumb|400px|Burr puzzles]]
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| A '''burr puzzle''' is an [[interlocking puzzle]] consisting of notched sticks, combined to make one [[Three-dimensional space|three-dimensional]], usually [[Symmetry|symmetrical]] unit.
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| These puzzles are traditionally made of wood, but versions made of plastic or metal can also be found. Quality burr puzzles are usually precision-made for easy sliding and accurate fitting of the pieces.
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| In recent years the definition of "burr" is expanding, as puzzle designers use this name for puzzles not necessarily of stick-based pieces.
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| The term "Burr" is first mentioned in a 1928 book by Edwin Wyatt,<ref name="Wyatt28">{{ cite book | title = Puzzles in Wood | first = E. M. | last = Wyatt | publisher = Bruce Publishing Co | location = Milwaukee, Wisc | year = 1928 | isbn = 0-918036-09-7 }}</ref> but the text implies that it was commonly used before. The term is attributed to the finished shape of many of these puzzles, resembling a seed [[burr (fruit)|burr]].
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| The origin of burr puzzles is unknown. The first known record<ref>{{ citation | title = New Findings on the History of the Six Piece Burr | first = Jerry | last = Slocum | publisher = Slocum Puzzle Foundation }}</ref> appears in a 1698 [[engraving]] used as a [[title page]] of [[Chambers's Cyclopaedia]].<ref>[[:commons:File:Cyclopaedia, Chambers - Volume 1 - 0008.jpg|The title page of Chambers's Cyclopaedia]] on [[Wikimedia Commons]]</ref> Later records can be found in [[Germany|German]] catalogs from the late 18th century and early 19th century.<ref>{{ citation | title = Puzzles from Catel's Cabinet and Bestelmeier's Magazine, 1785 to 1823 | first = Jerry | last = Slocum | first2 = Dieter | last2 = Gebbardt | publisher = Slocum Puzzle Foundation | year = 1997 }}</ref> There are claims of the burr being a [[China|Chinese]] invention, like other classic puzzles such as the [[Tangram]].<ref>{{ citation | title = Chinese Puzzles: Games for the Hands and Mind | first = Wei | last = Zhang | first2 = Peter | last2 = Rasmussen | publisher = Art Media Resources | year = 2008 | isbn = 1588861015 }} ([http://chinesepuzzles.org/burr-puzzles/ A page about burr puzzles in the book's website])</ref>
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| ==Six-Piece Burr==
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| [[File:SixPartWoodKnot.jpg|right|thumb|250px|An assembled six-piece burr]]
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| The six-piece burr, also called "Puzzle Knot" or "Chinese Cross", is the most well-known and presumably the oldest of the burr puzzles. This is actually a family of puzzles, all sharing the same finished shape and basic shape of the pieces. The earliest US [[patent]] for a puzzle of this kind dates back to 1917.<ref>{{Citation | inventor1-last = Brown | inventor1-first = Oscar | title = Puzzle | issue-date = 1917 | patent-number = 1225760 | country-code = US }}</ref> | |
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| For many years, the six-piece burr was very common and popular, but was considered trite and uninteresting by enthusiasts. Most of the puzzles made and sold were very similar to one another and most of them included a "key" piece, an unnotched stick that slides easily out. On the late 1970s, however, the six-piece burr regained the attention of inventors and collectors, thanks largely to a computer [[analysis]] conducted by the [[mathematician]] [[Bill Cutler]] and its publication in [[Martin Gardner]]'s column on ''[[Scientific American]]''.<ref>{{Citation | last = Gardner | first = Martin | title = Mathematical Games | journal = Scientific American |date=January 1978 | pages = 14–26 |url=http://www.nature.com.ezaccess.libraries.psu.edu/scientificamerican/journal/v238/n1/pdf/scientificamerican0178-14.pdf}}</ref>
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| ===Structure=== | |
| All six pieces of the puzzle are square sticks of equal length (at least 3 times their width). When solved, the pieces are arranged in three perpendicular, mutually intersecting pairs. The notches of all stick are located within the region of intersection, so when the puzzle is assembled they are unseen. All notches can be described as being made by removing [[cube|cubic]] units (with an edge length of half the sticks' width), as shown in the figure:
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| [[File:Six-Piece Burr - Cubic Units.svg|150px|none|]]
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| There are 12 removable cubic units, and different puzzles of this family are made of sticks with different units removed. 4,096 [[permutation]]s exist for removing the cubic units. Of those, we ignore the ones that cut the stick in two and the ones creating identical pieces, and are left with 837 usable pieces.<ref name="Cutler78">{{Citation | last1 = Cutler | first1 = William H. | title = The Six-Piece Burr | journal = Journal of Recreational Mathematics | volume = 10 | issue = 4 | year = 1978 | pages = 241–250 }}</ref> Theoretically, these pieces can be combined to create over 35 [[1,000,000,000 (number)|billion]] possible assemblies, however it is estimated that less than 6 billion of them are actual puzzles, capable of being assembled or taken apart.<ref name="Cutler94">{{Citation | last1 = Cutler | first1 = Bill | url = http://home.comcast.net/~billcutler/docs/CA6PB/index.html | title = A Computer Analysis of All 6-Piece Burrs | year = 1994 | accessdate = February 17, 2013 }}</ref>
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| [[File:Six-Piece Burr - Nut Puzzle.svg|right|thumb|250px|The "Nut" puzzle from Hoffmann's 1893 book,<ref>{{Citation | last1 = Hoffmann | first1 = Professor | title = Puzzles old and new | place = London | publisher = Frederick Warne and Co. | year = 1893 | chapter = Chapter III, No. XXXVI }} ([http://archive.org/details/puzzlesoldnew00hoff Available for download] at the [[Internet Archive]])</ref> an example of a solid burr.]]
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| ===Solid Burr===
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| A burr puzzle with no internal voids when assembled is called a '''solid burr'''. These burrs can be taken apart directly by removing a piece or some pieces in one move. Up until the late 1970s, solid burrs received the most attention and publications referred only to this type.<ref name="Coffin92">{{Citation | last1 = Coffin | first1 = Stewart | title = Puzzle Craft | year = 1992 | url = http://www.puzzleworld.org/PuzzleCraft/pc92.pdf | format = PDF }}</ref> 119,979 solid burrs are possible, using 369 of the usable pieces. To assemble all these puzzles, one would need a set of 485 pieces, as some of the puzzles include identical pieces.<ref name="Cutler78" />
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| [[File:Six-Piece Burr - Burr 305.svg|right|thumb|250px|"Burr no. 305", named after its location in Culter's analysis tables. It was found to be the most "interesting" of the 314 solid burrs of notchable pieces, because it is the only one containing no duplicate or symmetric pieces, and also having one unique solution that does not employ a common 2-piece key.]]
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| ===Pieces Types===
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| For [[aesthetics|aesthetic]], but mostly practical reasons, the burr pieces can be divided into two types:
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| * '''Notchable''' pieces - with full notches that can be made with a [[saw]] or a [[milling machine]].
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| * '''Non-notchable''' pieces - with internal corners that have to be made with a [[chisel]] or by gluing parts together.
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| [[File:Six-Piece Burr - Piece Types.svg|none|thumb|450px|Right to left: a notchable piece, a non-notchable piece and a piece that is technically notchable, but cannot be used with other notchable pieces to create solid burrs]]
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| 59 of the usable pieces are notchable, including the unnotched stick. Of those, only 25 can be used to create solid burrs. This set, often referred to as "The 25 notchable pieces", with the addition of 7 duplicates, can be assembled to create 314 different solid burr puzzles. These pieces are very popular, and full sets are manufactured and sold by many companies.
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| [[File:Six-Piece Burr - Bill's Buffling Burr.svg|right|thumb|250px|"Bill's Buffling Burr" of level 5, by Bill Cutler]]
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| [[File:Six-Piece Burr - Philippe Dubois.svg|right|thumb|250px|A level-7 burr by the Israeli designer and maker Philippe Dubois who sold his puzzles under the name Gaby Games"]]
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| ===Holey Burr===
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| For all solid burrs, one movement is required to remove the first piece or pieces. However, a '''holey burr''', which has internal voids when assembled, can require more than one move. The number of moves required for removing the first piece is referred to as the ''level'' of the burr. All solid burrs are therefore of level 1. The higher the level is, the more difficult the puzzle.
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| During the 1970s and 1980s, attempts were made by experts to find burrs of an ever-higher level. On 1979, the American designer and craftsman [[Stewart Coffin]] found a level-3 puzzle. In 1985, Bill Cutler found a level-5 burr<ref>{{Citation | last = Dewdney | first = A. K. | title = Computer Recreations | journal = Scientific American | volume = 253 | issue = 4 |date=October 1985 | pages = 16–27 }}</ref> and shortly afterwards a level-7 burr was found by the [[Israel]]i Philippe Dubois.<ref name="Coffin92" /> In 1990, Cutler completed the final part of his analysis and found that the highest possible level using notchable pieces is 5, and 139 of those puzzles exist. The highest level possible for a six-piece burr with more than one solution is 12, meaning 12 moves are required to remove the first piece.<ref name="Cutler94" />
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| ==Three-Piece Burr==
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| A three-piece burr made from sticks with "regular" [[Right angle|right-angled]] notches (as the six-piece burr), cannot be assembled or taken apart.<ref>{{Citation | url = http://www.research.ibm.com/BurrPuzzles/Burr3.html | title = Three-piece burrs | accessdate = February 19, 2013 | publisher = [[IBM]] | year = 1997 | author = Jürg von Känel | archiveurl = http://web.archive.org/web/20120111151627/http://www.research.ibm.com/BurrPuzzles/Burr3.html | archivedate = January 11, 2012 }}</ref> There are, however, some three-piece burrs with different kinds of notches, the best known of them being the one mentioned by Wyatt in his 1928 book, consisting of a rounded piece that is meant to be rotated.<ref name="Wyatt28" />
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| <gallery>File:Three Piece Burr Small.jpg|Three piece burr</gallery>
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| ==Known Burr Families==
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| [[File:PuzzleByAltekruse.jpg|right|thumb|200px|An Altekruse puzzle]]
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| ===Altekruse===
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| The Altekruse puzzle is named after the grantee of its 1890 patent, though the puzzle is of earlier origin.<ref>{{Citation | inventor1-last = Altekruse | inventor1-first = William | title = Block Puzzle | issue-date = 1890 | patent-number = 430502 | country-code = US }}</ref> The name "Altekruse" is of [[Austria]]n-[[Germany|German]] origin and means "old-cross" in [[German language|German]], which led to the presumption that it was a [[pseudonym]], but a man by that name immigrated to America in 1844 with his three brothers to avoid being drafted to the [[Prussian Army]] and is presumed to be the one who filed this patent.<ref>{{Citation | last1 = Coffin | first1 = Stewart | url = http://www.johnrausch.com/PuzzlingWorld/ | title = The Puzzling World of Polyhedral Dissections | chapter = The Altekruse Puzzle | chapter-url = http://www.johnrausch.com/PuzzlingWorld/chap06.htm#p4 | accessdate = February 19, 2013 | year = 1998 }}</ref>
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| A classic Altekruse consists of 12 identical pieces. In order to disassemble it, two halves of the puzzle have to be moved in opposite directions. Using two more of these pieces, the puzzle can be assembled in a different way. By the same principle, other puzzles of this family can be created, with 6, 24, 36 and so forth. Despite their size, those bigger puzzles are not considered very difficult, yet they require [[patience]] and [[dexterity]] to assemble.
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| [[File:Chuck Burr Puzzle.jpg|right|thumb|200px|A Chuck puzzle]]
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| ===Chuck===
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| The Chuck puzzle was invented and patented by Edward Nelson in 1897.<ref>{{Citation | inventor1-last = Nelson | inventor1-first = Edward | title = Puzzle | issue-date = 1897 | patent-number = 588705 | country-code = US }}</ref> His design was improved and developed by Ron Cook of the [[United Kingdom|British]] company ''Pentangle Puzzles'' who designed other puzzles of the family.<ref>{{Citation | url = http://www.pentangle-puzzles.co.uk/acatalog/WoodChuck_Puzzles.html | title = WoodChuck Puzzles | publisher = Pentangle Puzzles | accessdate = February 19, 2013 }}</ref>
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| The Chuck consists mostly of U-shaped stick pieces of various lengths, and some with an extra notch that are used as key pieces. For creating bigger Chuck puzzles (named Papa-chuck, Grandpapachuck and Great Grandpapachuck, by Cook) one would need to add longer pieces. The Chuck can also be regarded as an extension of a six-piece burr of very simple pieces called Baby-chuck, which is very easy to solve. Chuck pieces of different lengths can also be used to create asymmetryic shapes, assembled according to the same principle as the original puzzle.
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| [[File:Chuck Burr Puzzle - Typical Pieces.svg|none|thumb|250px|Typical Chuck pieces: a U-shaped piece and a key piece]]
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| [[File:Pagoda Burr Puzzle.jpg|right|thumb|200px|Pagoda of size 5, with 51 pieces (crafted by Philippe Dubois)]] | |
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| ===Pagoda===
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| The origin of the Pagoda, also called "Japanese Crystal" is unknown. It is mentioned in Wyatt's 1928 book.<ref name="Wyatt28" /> Puzzles of this family can be regarded as an extension of the "three-piece burr" (Pagoda of size 1), however they do not require special notches to be assembled or taken apart. Pagoda of size 2 consists of 9 pieces, and bigger versions consist of 19, 33, 51 and so forth. Pagoda of size <math> n </math> consists of <math> 2n^2+1 </math> pieces.
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| ==Diagonal Burr==
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| [[File:Giant Star Burr Puzzle.jpg|right|thumb|200px|A diagonal burr - Giant Star puzzle (manufactured by Gaya Games)]]
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| Though most burr puzzle pieces are made with square notches, some are made with [[diagonal]] notches. Diagonal burr pieces are square sticks with V-shaped notches, cut at an [[angle]] of 45° off the stick's [[Face (geometry)|Face]]. These puzzles are often called "Stars", as it is customary to also cut the sticks' edges at an angle of 45°, for aesthetic reasons, giving the assembled puzzle a [[Star (polygon)|Star]]-like shape.
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| ==See also==
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| * [[Disentanglement puzzle]]
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| ==References==
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| {{Reflist}}
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| ==Further reading==
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| * {{ cite book | title = Geometric Puzzle Design | first = Stewart T. | last = Coffin | publisher = Wellsley, K. Peters | year = 2007 | isbn = 1568813120 }}
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| * {{ cite book | title = Puzzles in Wood | first = Edwin Mather | last = Wyatt | publisher = Fox Chapel Publishing | year = 2007 | edition = 3rd | isbn = 1565233484 }}
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| ==External links==
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| {{Commons category-inline|Burr puzzles}}
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| * {{Citation | last1 = Coffin | first1 = Stewart | url = http://www.johnrausch.com/PuzzlingWorld/ | title = The Puzzling World of Polyhedral Dissections | edition = Online Edition | accessdate = February 19, 2013 | year = 1998 }} - Previous edition of his book ''Geometric Puzzle Design''.
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| * {{Citation | last1 = Keiichiro | first1 = Ishino | url = http://puzzlewillbeplayed.com/ | title = Puzzle will be played... | accessdate = February 19, 2013 }} - With hundreds of burr puzzles described.
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| * {{Citation | url = http://www.robspuzzlepage.com/ | title = Rob's Puzzle Page | chapter = Interlocking Puzzles | chapter-url = http://www.robspuzzlepage.com/interlocking.htm | accessdate = February 19, 2013 }}
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| * {{Citation | url = http://www.research.ibm.com/BurrPuzzles/ | title = IBM Research: The burr puzzles site | accessdate = February 19, 2013 | publisher = [[IBM]] | year = 1997 | author = Jürg von Känel | archiveurl = http://web.archive.org/web/20121013222922/http://www.research.ibm.com/BurrPuzzles/ | archivedate = October 13, 2012 }}
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| {{DEFAULTSORT:Burr Puzzle}}
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| [[Category:Mechanical puzzles]]
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