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|
Any story about interlocking puzzles has to start with the traditional six-piece burr puzzle.
Like other well-known puzzles, it has acquired a probably-fanciful backstory,
and is known by several names, including the "puzzle knot," the "Devil's Knot"
(Teufelsknoten in German), "Chinese Cross,"
the "Lock of Luban" (Luban Suo)
or the "Lock of Kongming" (Kongming Suo).
Stewart Coffin's
The Puzzling World of Polyhedral Dissections
hosted on John Rausch's site
is a great introduction to this type of puzzle.
Martin Gardner discusses burrs briefly (as an introduction to the puzzle sculptures of Miguel Berrocal)
in his 1989 book Penrose Tiles to Trapdoor Ciphers, and most of the key puzzle authors mention the puzzle.
There have been sporadic fits of research into the six-piece burr, including an extensive analysis by hand by the Dutch
mathematician J. H. de Boer, and work by Tom O'Beirne and Arthur Cross,
but
Bill Cutler has performed the definitive computer
analysis,
and the statistics cited below are based on his analysis.
The earliest relevant U.S. Patent seems to be
1225760 - Brown 1917.
However, a traditional six-piece burr appears in Hoffmann's 1893 classic "Puzzles Old and New"
in Chapter III as No. XXXVI "The Nut (or Six-piece) Puzzle."
Jerry Slocum and Dieter Gebhardt put together a compendium of puzzle advertisements found in the
1785 catalogue of the merchant Peter Friedrich Catel, who established a retail store in Berlin in 1780.
The 1785 catalogue contains an ad for a traditional six-piece burr puzzle called "The Small Devil's Hoof"
(in addition to an ad for the Large Devil's Hoof which is a 24-piece cage burr).
In Stewart Coffin's Geometric Puzzle Design,
Stewart discusses the six-piece burr in chapter 7, and reports that Jerry Slocum's New Findings on the History of the Six Piece Burr
traces the six-piece burr back to Germany in 1698.
There is a distinction made between burr puzzles that contain no
internal "holes" or voids - termed "solid" burrs,
and those that do contain one or more - termed "holey" burrs.
Also, there is a distinction made among the pieces which can be produced without
hard-to-manufacture blind (or internal) corners
versus those that cannot.
The 59 "easy" pieces are called "notchable" and there are only 25 of them that can be used to build
solid burrs.
Those 25 pieces can be put together in 314 ways.
There are 369 general pieces that can be used to produce 119,979 solid burrs.
Of those 369, 112 can be used in duplicate and 2 in triplicate, making a useful set of 485 pieces.
The 59 notchable pieces can be used to make 13,354,991 assemblies, most of which are holey.
Overall, there are 837 pieces that can be used to produce an estimated 5.95 billion constructible puzzles.
So, to make a traditional six-piece burr, six pieces, usually but not always distinct, are selected from the
overall set of 837 possible such pieces, and interlocked in a characteristic 2x2x2
pattern along 3 orthogonal axes - see the photo at upper left.
The burr shape is tricky to envision without an example in front of one, but it gets easier with practice.
Bill Cutler has done extensive analysis on both the
"holey" six-piece burr
and
all six-piece burrs in general,
and Bill
offers several burrs for sale.
Jurg von Kanel created the wonderful
Burr Puzzles Site hosted at IBM Research.
Jurg's site offers a
solution analyzer applet
and
historical info about burrs.
Bruno Curfs' site
offers additional analysis.
Ed Pegg wrote a
good survey article about burrs.
Peter Roesler's site also discusses burr puzzles, and has
an interesting history of Willem van der Poel's Grandfather 6x6x6 burr.
You can see some burrs at
John Rausch's Puzzleworld
and at
Wayne Daniel's site.
You can use
Andreas Roever's
Burr Tools
and
Andre van Kammen's
Puzzlesolver 3D
to model, solve, and design burr puzzles.
If you're interested in collecting 6-piece burrs, I suggest you first check out the
"Puzzle Will Be Played" site
to get some idea of the variety available.
Look under "Interlocking (6 piece burr: traditional)."
Though they may be sold under different names and by different vendors,
burr puzzles that use the same set of six pieces are isomorphic and have identical solutions
(although using pieces longer than six units might eliminate some solutions).
That site also provides a comprehensive
catalogue of burr pieces.
The "level" of a burr puzzle is the number of distinct moves
(a shift of one or more pieces as a unit, usually by one unit in one direction)
that must be performed to remove the first piece or pieces - there can be a concatenation of figures usually separated by dots -
these are the numbers of steps to remove successive pieces.
All solid burrs are level 1 - they come apart without any preliminary shifting.
Burrs with internal holes, of which there can be from 1 to 20, can achieve higher levels, and one goal of research has been
to delimit what is possible in terms of level complexity.
I admit that, early on, I didn't like burr puzzles. But as I read more about them, and tried various designs,
my appreciation for them grew.
I put together the diagram below to try to summarize and organize some of the facts
I learned about this category of puzzle.
1 A A A [p] 1
+----+----+----+----+----+----+
/ /|
+ + |
/ / +
+----+----+----+----+----+----+ |
| | |
| | +
+ + /
| | +
| |/
+----+----+----+----+----+----+
The Key |
|||||
18 B B L [p] 2
+----+ +----+----+----+----+
/ /| / /|
+ + | + + |
/ / +-/ / +
+----+ / +----+----+----+----+ |
| | + | | |
| |/ | | +
+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
35 C E 1
+----+----+ +----+----+----+
/ /| / /|
+ + | + + |
/ / +-/ / +
+----+----+ / +----+----+----+ |
| | + | | |
| |/ | | +
+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
52 D P J [p] 2
+----+ +----+----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+ / +----+----+----+ |
| | + | | |
| |/ | | +
+ +----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
The Side Tray |
103 F S H 1
+----+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +---+--/ / +
+----+----+ / +----+----+ |
| | + | | |
| |/ | | +
+ +----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
The Half-Tray |
120 G U 1
+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+---+--/ / +
+----+ / +----+----+ |
| | + | | |
| |/ | | +
+ +----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
The Three-Quarters Tray |
256 J X B [p2] 3
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + | | |
| |/ | | +
+ +----+----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
The Tray |
86 E H 1
+----+ +----+ +----+----+
/ /| / /| / /|
+ + | + + | + + |
/ / +-/ / +-/ / +
+----+ / +----+ / +----+----+ |
| | + | | + | | |
| |/ | |/ | | +
+ +----+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
154 H K I [p] 1
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +-/ / +-/ / +
+----+ / +----+----+ / +----+ |
| | + | | + | | |
| |/ | |/ | | +
+ +----+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
The Toaster |
188 I M M [p] 2
+----+ +----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +----+-/ / +-/ / +
+----+ / +----+ / +----+ |
| | + | | + | | |
| |/ | |/ | | +
+ +----+----+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
The (Bottle) Opener |
871 M T K 2
+----+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+----+ / +----+----+ |
| | +----+--| | |
| | | | | +
+ + | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The Barbells |
928 V L D 2
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | +----+----+ | + + |
/ / +--| | +-/ / +
+----+ / | |/ +----+ |
| | + + + | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The Tongue |
1024 Y Y F [p2] 3
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The Y |
792 R D 2
+----+ +----+----+----+----+
/ /| / /|
+ + | +----+----+ + |
/ / +--| / / +
+----+ / | +----+----+ |
| | + + | | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
911 N C G 2
+----+----+----+----+ +----+
/ /| / /|
+ +----+----+ | + + |
/ /| | +-/ / +
+----+----+ | |/ +----+ |
| | + + | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
824 T R C [p] 2
+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +----+--| / / +
+----+ / | +----+----+ |
| | + +----+ | | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
975 O Q E [p] 2
+----+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +----+-/ / +
+----+----+ | |/ +----+ |
| | + +----+ | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
888 U W 2
+----+ +----+----+
/ /| / /|
+ + | + + |
/ / +----+----+-/ / +
+----+ / +----+----+ |
| | + +----+--| | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
1007 Q V 2
+----+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+-/ / +
+----+----+ / +----+ |
| | +----+----+ | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
| The Walls | The Offsets | The Clubs | |||
960 X N 2
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +-------| | +-/ / +
+----+ / | |/ +----+ |
| | + +----+ + | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
992 W O [p] 2
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +----+-/ / +
+----+ / | |/ +----+ |
| | + + +----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
359 L F 1
+----+----+----+ +----+----+
/ /| / /|
+ +----+ | + + |
/ /| | +-/ / +
+----+----+ | |/ +----+----+ |
| | + +--| | |
| | | | | +
+ + | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
615 K G 1
+----+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +--| / / +
+----+----+ / | +----+----+ |
| | +----+ | | |
| | | | | +
+ + | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
856 S J 1
+----+ +----+ +----+----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +-/ / +
+----+ / | |/ +----+----+ |
| | + + +--| | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
943 P I 1
+----+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +-/ / +
+----+----+ / | |/ +----+ |
| | +----+ + | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
| The Fingers | The Notched Half-Trays | The Fingered Clubs | |||
56
+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +----+--| / / +
+----+ / | +----+----+ |
| | + +--| | |
| |/ | | +
+ +----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
Triple Slide |
72
+----+----+----+ +----+----+
/ /| / /|
+ +----+----+ | + + |
/ /| | +-/ / +
+----+ | |/ +----+----+ |
| | +----+----+ | | |
| |/ | | +
+ +----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
Interrupted Slide |
88
+----+ +----+ +----+----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +-/ / +
+----+ / | |/ +----+----+ |
| | + +----+ | | |
| |/ | | +
+ +----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
Piston, Hordern,Dozen, BB31-10-40 |
94
+----+ +----+ +----+----+
/ /| / /| / /|
+ + | + + | +----+ + |
/ / +-/ / +--| / / +
+----+ / +----+ / | +----+ |
| | + | | + +--| | |
| |/ | |/ | | +
+ +----+ +----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
Triple Slide |
109
+----+----+ +----+----+
/ /| / /|
+ +----+ +----+ + |
/ /|----| / / +
+----+----+----+ | | +----+ |
| | + +--| | |
| |/ | | +
+ +----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
BCL6000 |
112
+----+----+ +----+----+
/ /| / /|
+ +----+ | +----+ + |
/ /| | +-------| / / +
+----+ | |/ | +----+ |
| | +----+ +--| | |
| |/ | | +
+ +----+----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
Interrupted Slide |
126
+----+ +----+----+
/ /| / /|
+ + | +----+ +----+ + |
/ / +-/ /|----| / / +
+----+ / +----+ | | +----+ |
| | + | | + +--| | |
| |/ | |/ | | +
+ +----+ +----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
STC#36 |
128
+----+ +----+----+
/ /| / /|
+ + | +----+ + |
/ / +------------| / / +
+----+ / | +----+ |
| | + +--| | |
| |/ | | +
+ +----+----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
Hedgehog, Kaldeway |
156
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | +----+ + | + + |
/ / +--| / / +-/ / +
+----+ / | +----+ / +----+ |
| | + +--| | + | | |
| |/ | |/ | | +
+ +----+----+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
Triple Slide |
160
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | +----+----+ | + + |
/ / +--| | +-/ / +
+----+ / | |/ +----+ |
| | + +----+----+ | | |
| |/ | | +
+ +----+----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
(many) |
192
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +----+--| | +-/ / +
+----+ / | |/ +----+ |
| | + +----+ | | |
| |/ | | +
+ +----+----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
#G |
224
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +----+-/ / +
+----+ / | |/ +----+ |
| | + +----+ | | |
| |/ | | +
+ +----+----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
JVK, Millable 5.4 |
412
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | +----+ + | + + |
/ / +--| / / +-/ / +
+----+ / | +----+ / +----+ |
| | + + | | + | | |
| |/ /| | |/ | | +
+ +----+ | + +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
(many) |
448
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +----+--| | +-/ / +
+----+ / | |/ +----+ |
| | + +----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
Interrupted Slide |
736
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +----+-/ / +
+----+ / | |/ +----+ |
| | + +----+----+ | | |
| |/ /| / | | +
+ +----+----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
BCL6000, #G |
464
+----+----+----+ +----+
/ /| / /|
+ +----+----+ | + + |
/ /| | +----+-/ / +
+----+ | |/ +----+ |
| | +----+ + | | |
| |/ /| / | | +
+ +----+ | +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
Brown's |
576
+----+ +----+----+----+
/ /| / /|
+ + | +----+----+ + |
/ / +----+--| / / +
+----+ / | +----+ |
| | + + +--| | |
| |/ /| / | | +
+ +----+----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
D. Kriz II |
511
+----+ +----+
/ /| / /|
+ +----+ + + |
/ /|-+----+----+-/ / +
+----+----+ | +----+ |
| | +----+ | | |
| | | / | | +
+ + | +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
Interrupted Slide, #D, F#73 |
476
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+----+ + + |
/ / +--| / /|-+-/ / +
+----+ / | +----+ | +----+ |
| | + + | | + | | |
| |/ /| | |/ | | +
+ +----+ | + +----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
Prog. Nightmare |
702
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+----+ | + + |
/ / +-/ /| | +-/ / +
+----+ / +----+ | |/ +----+ |
| | + | | + + | | |
| |/ | | | / | | +
+ +----+ + | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
BC-CCU10, Mega-6 |
512
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+ | | |
| |/ /| / | | +
+ +----+ | +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
(many) |
768
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+ | | |
| |/ /| / | | +
+ +----+----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
(many) |
551
+----+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +--| / / +
+----+----+ / | +----+----+ |
| | + + | | |
| |/ /| | | +
+ +----+ | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
BC-L5N |
624
+----+----+ +----+----+
/ /| / /|
+ +----+ | +----+ + |
/ /| | +----+--| / / +
+----+ | |/ | +----+ |
| | +----+ +----+--| | |
| |/ /| / | | +
+ +----+----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
BC-CCU10 |
704
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +----+--| | +-/ / +
+----+ / | |/ +----+ |
| | + + + | | |
| |/ /| / | | +
+ +----+----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
(many) |
499
+----+ +----+
/ /| / /|
+ +----+ +----+----+ + |
/ /|-+-/ / +
+----+----+ | +----+----+----+ |
| | +--| | |
| | | | | +
+ + | + + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
BC-CC5H |
757
+----+ +----+
/ /| / /|
+ +----+----+ +----+ + |
/ /|-+-/ / +
+----+----+----+ | +----+----+ |
| | +--| | |
| | | | | +
+ + | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
Prog. Nightmare |
760
+----+ +----+
/ /| / /|
+ + | +----+ + |
/ / +----+----+-/ / +
+----+ / +----+----+ |
| | + +--| | |
| |/ /| | | +
+ +----+----+ | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
Baffling, Brother |
800
+----+ +----+----+----+----+
/ /| / /|
+ + | +----+----+----+ + |
/ / +--| / / +
+----+ / | +----+ |
| | + + +--| | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Brown's |
820
+----+ +----+----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+ / +----+----+----+ |
| | + +--| | |
| |/ /| | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
STC#36 |
832
+----+ +----+----+----+
/ /| / /|
+ + | +----+----+ + |
/ / +----+--| / / +
+----+ / | +----+ |
| | + +----+ +--| | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Brown's, G4 |
976
+----+----+----+ +----+
/ /| / /|
+ +----+----+ | + + |
/ /| | +----+-/ / +
+----+ | |/ +----+ |
| | +----+ +----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
D. Kriz II, Enigma, #G |
880
+----+----+ +----+----+
/ /| / /|
+ +----+ | +----+ + |
/ /| | +----+--| / / +
+----+ | |/ | +----+ |
| | +----+----+----+--| | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Dubois/Gaby |
883
+----+ +----+----+
/ /| / /|
+ +----+ +----+ + |
/ /|-+-/ / +
+----+----+ | +----+----+----+ |
| | +--| | |
| | | | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
BC-CCU10 |
922
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +-/ / +-/ / +
+----+ / +----+----+ / +----+ |
| | + | | + | | |
| |/ | |/ | | +
+ +----+----+----+----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Piston |
926
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | + +----+ | + + |
/ / +-/ /| | +-/ / +
+----+ / +----+ | |/ +----+ |
| | + | | + + | | |
| |/ | |/ / | | +
+ +----+----+ +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
BC-CC5H |
956
+----+ +----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +----+-/ / +-/ / +
+----+ / +----+ / +----+ |
| | + +--| | + | | |
| |/ /| | |/ | | +
+ +----+ | +----+----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Prog. Nightmare, BC-CC4H |
990
+----+ +----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +-/ / +----+-/ / +
+----+ / +----+ / +----+ |
| | + | | +----+ | | |
| |/ | |/ / | | +
+ +----+----+ +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Interrupted Slide |
996
+----+----+ +----+
/ /| / /|
+ +----+ | +----+----+ + |
/ /| | +-/ / +
+----+ | |/ +----+----+----+ |
| | +----+--| | |
| |/ /| | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Baffling |
1008
+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +----+----+-/ / +
+----+ | |/ +----+ |
| | +----+----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
(many) |
1015
+----+ +----+
/ /| / /|
+ +----+ +----+ + |
/ /|-+----+-/ / +
+----+----+ | +----+----+ |
| | +----+--| | |
| | | | | +
+ + | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
(many) |
1021
+----+ +----+
/ /| / /|
+ +----+----+ + + |
/ /|-+----+-/ / +
+----+----+----+ | +----+ |
| | +----+ | | |
| |/ / | | +
+ +----+ +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Prog. Nightmare |
1 A A [p]
+----+----+----+----+----+----+
/ /|
+ + |
/ / +
+----+----+----+----+----+----+ |
| | |
| | +
+ + /
| | +
| |/
+----+----+----+----+----+----+
The Key |
256 J X [p2]
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + | | |
| |/ | | +
+ +----+----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
The Tray |
256 J X [p2]
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + | | |
| |/ | | +
+ +----+----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
The Tray |
256 J X [p2]
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + | | |
| |/ | | +
+ +----+----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
The Tray |
928 V L
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | +----+----+ | + + |
/ / +--| | +-/ / +
+----+ / | |/ +----+ |
| | + + + | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The Tongue |
928 V L
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | +----+----+ | + + |
/ / +--| | +-/ / +
+----+ / | |/ +----+ |
| | + + + | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The Tongue |
1 A A [p]
+----+----+----+----+----+----+
/ /|
+ + |
/ / +
+----+----+----+----+----+----+ |
| | |
| | +
+ + /
| | +
| |/
+----+----+----+----+----+----+
The Key |
256 J X [p2]
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + | | |
| |/ | | +
+ +----+----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
The Tray |
824 T R [p]
+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +----+--| / / +
+----+ / | +----+----+ |
| | + +----+ | | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The |
975 O Q [p]
+----+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +----+-/ / +
+----+----+ | |/ +----+ |
| | + +----+ | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Offsets |
928 V L
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | +----+----+ | + + |
/ / +--| | +-/ / +
+----+ / | |/ +----+ |
| | + + + | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The Tongue |
1024 Y Y [p2]
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The Y |
 This small plastic red burr is one of my older puzzles - I don't recall where I got it. It uses the following pieces: 1, 256, 824/975, 928, 1024. This set of pieces has been used often, and has appeared in ivory. Jurg von Kaenel refers to this as "the well-known one." |
Reiss 1974 Licorice Stix |
This is a small plastic burr pendant, made in China. |
 This set also appeared as "Dohikus." (I don't have this.) |
52 D P [p]
+----+ +----+----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+ / +----+----+----+ |
| | + | | |
| |/ | | +
+ +----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
The Side Tray |
792 R D
+----+ +----+----+----+----+
/ /| / /|
+ + | +----+----+ + |
/ / +--| / / +
+----+ / | +----+----+ |
| | + + | | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The |
911 N C
+----+----+----+----+ +----+
/ /| / /|
+ +----+----+ | + + |
/ /| | +-/ / +
+----+----+ | |/ +----+ |
| | + + | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Walls |
824 T R [p]
+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +----+--| / / +
+----+ / | +----+----+ |
| | + +----+ | | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The |
975 O Q [p]
+----+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +----+-/ / +
+----+----+ | |/ +----+ |
| | + +----+ | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Offsets |
1024 Y Y [p2]
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The Y |
I got this aluminum burr called "Rainbow" from Bits and Pieces - it came in a nice black drawstring pouch. It was designed by Paul Eibe. It uses the following pieces: 52, 792/911, 824/975, 1024. This is the only notchable, voidless set that can be put together six different ways. |
This is DNORTY from Pentangle. The name derives from the bold piece letters given in my table above. It uses the same set of pieces as the Rainbow: 52 (D), 911 (N), 975 (O), 792 (R), 824 (T), 1024 (Y). |
This is a Toyo Glass puzzle called "Tongari Kun and Roppongi." Not only is there a burr, but it must be assembled inside the glass container. The mouth is too small to pass the burr in fully assembled form. Remember, there are 6 different ways to construct this burr - you must find one that permits construction within the container! |
This set was sold some time ago as "The Zoozzler." (I don't have it.) |
1 A A [p]
+----+----+----+----+----+----+
/ /|
+ + |
/ / +
+----+----+----+----+----+----+ |
| | |
| | +
+ + /
| | +
| |/
+----+----+----+----+----+----+
The Key |
188 I M [p]
+----+ +----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +----+-/ / +-/ / +
+----+ / +----+ / +----+ |
| | + | | + | | |
| |/ | |/ | | +
+ +----+----+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
The (Bottle) Opener |
824 T R [p]
+----+ +----+----+----+
/ /| / /|
+ + | +----+ + |
/ / +----+--| / / +
+----+ / | +----+----+ |
| | + +----+ | | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The |
975 O Q [p]
+----+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +----+-/ / +
+----+----+ | |/ +----+ |
| | + +----+ | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Offsets |
1024 Y Y [p2]
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The Y |
1024 Y Y [p2]
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The Y |
This is the Yamato Block puzzle. This burr uses pieces nos. 1, 188, 824/975, and 2x 1024. |
This is "No. P19 Joe's Puzzle" from Wm. F. Drueke & Sons of Grand Rapids Michigan. There is no date on the box but it seems fairly old. |
This is a small brass burr, called the "Ultimate Puzzle," made for Chadwick Miller and dated 1969. It came with a small black case with a question mark on the front. |
In this aluminum burr, piece 824 is fixed to the base. |
This set of twelve burrs is called "6+6=Cube."
It was designed by Kozy Kitajima.
The pieces include: 1, 52, 103, 120, 188, 256, 911, 928, 992, 960, and 2x 1024.
There is only one way to build two burrs at once. The twelve pieces can also be combined to form a cube.
88
+----+ +----+ +----+----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +-/ / +
+----+ / | |/ +----+----+ |
| | + +----+ | | |
| |/ | | +
+ +----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
512
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+ | | |
| |/ /| / | | +
+ +----+ | +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
704
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +----+--| | +-/ / +
+----+ / | |/ +----+ |
| | + + + | | |
| |/ /| / | | +
+ +----+----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
960
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +-------| | +-/ / +
+----+ / | |/ +----+ |
| | + +----+ + | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
992
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +----+-/ / +
+----+ / | |/ +----+ |
| | + + +----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
1008
+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +----+----+-/ / +
+----+ | |/ +----+ |
| | +----+----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
88
+----+ +----+ +----+----+
/ /| / /| / /|
+ + | +----+ | + + |
/ / +--| | +-/ / +
+----+ / | |/ +----+----+ |
| | + +----+ | | |
| |/ | | +
+ +----+----+----+ + /
| | +
| |/
+----+----+----+----+----+----+
|
512
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+ | | |
| |/ /| / | | +
+ +----+ | +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
768
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+ | | |
| |/ /| / | | +
+ +----+----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
922
+----+ +----+----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +-/ / +-/ / +
+----+ / +----+----+ / +----+ |
| | + | | + | | |
| |/ | |/ | | +
+ +----+----+----+----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
1008
+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +----+----+-/ / +
+----+ | |/ +----+ |
| | +----+----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
1008
+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +----+----+-/ / +
+----+ | |/ +----+ |
| | +----+----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
624
+----+----+ +----+----+
/ /| / /|
+ +----+ | +----+ + |
/ /| | +----+--| / / +
+----+ | |/ | +----+ |
| | +----+ +----+--| | |
| |/ /| / | | +
+ +----+----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
702
+----+ +----+ +----+
/ /| / /| / /|
+ + | +----+----+ | + + |
/ / +-/ /| | +-/ / +
+----+ / +----+ | |/ +----+ |
| | + | | + + | | |
| |/ | | | / | | +
+ +----+ + | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
768
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+ | | |
| |/ /| / | | +
+ +----+----+ | +----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
883
+----+ +----+----+
/ /| / /|
+ +----+ +----+ + |
/ /|-+-/ / +
+----+----+ | +----+----+----+ |
| | +--| | |
| | | | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
1015
+----+ +----+
/ /| / /|
+ +----+ +----+ + |
/ /|-+----+-/ / +
+----+----+ | +----+----+ |
| | +----+--| | |
| | | | | +
+ + | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
1024 Y Y [p2]
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The Y |
463
+----+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +----+-/ / +
+----+----+ | |/ +----+ |
| | + + | | |
| | | / | | +
+ + | +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
564
+----+ +----+----+----+
/ /| / /|
+ + | + + |
/ / +----+-/ / +
+----+ / +----+----+----+ |
| | + | | |
| |/ | | +
+ +----+----+----+ + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
760
+----+ +----+
/ /| / /|
+ + | +----+ + |
/ / +----+----+-/ / +
+----+ / +----+----+ |
| | + +--| | |
| |/ /| | | +
+ +----+----+ | + + /
| | +--| | +
| |/ | |/
+----+----+----+ +----+----+
|
909
+----+----+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +-/ / +
+----+----+----+ | |/ +----+ |
| | + + | | |
| |/ / | | +
+ +----+ +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
927
+----+ +----+----+ +----+
/ /| / /| / /|
+ +----+----+----+ | + + |
/ /| | +-/ / +
+----+----+ | |/ +----+ |
| | + + | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
1016
+----+ +----+
/ /| / /|
+ + | +----+ + |
/ / +----+----+-/ / +
+----+ / +----+----+ |
| | + +----+--| | |
| |/ /| | | +
+ +----+ | + + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
I bought this plastic burr in Japan. I believe it was made by Tenyo.
It is number 4 in a "Family" of burrs - this one is called "Brother."
This burr uses six general pieces: 463, 564, 760, 909, 927, 1016.
It has no holes, and comes apart in one move into two 3-piece halves.
1 A A [p]
+----+----+----+----+----+----+
/ /|
+ + |
/ / +
+----+----+----+----+----+----+ |
| | |
| | +
+ + /
| | +
| |/
+----+----+----+----+----+----+
The Key |
188 I M [p]
+----+ +----+ +----+
/ /| / /| / /|
+ + | + + | + + |
/ / +----+-/ / +-/ / +
+----+ / +----+ / +----+ |
| | + | | + | | |
| |/ | |/ | | +
+ +----+----+ +----+ + /
| | +
| |/
+----+----+----+----+----+----+
The (Bottle) Opener |
512
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+ | | |
| |/ /| / | | +
+ +----+ | +----+----+ + /
| | +--| | +
| |/ | |/
+----+----+ +----+----+----+
|
832
+----+ +----+----+----+
/ /| / /|
+ + | +----+----+ + |
/ / +----+--| / / +
+----+ / | +----+ |
| | + +----+ +--| | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
|
975 O Q [p]
+----+----+----+ +----+
/ /| / /|
+ +----+ | + + |
/ /| | +----+-/ / +
+----+----+ | |/ +----+ |
| | + +----+ | | |
| | | / | | +
+ + | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
Offsets |
1024 Y Y [p2]
+----+ +----+
/ /| / /|
+ + | + + |
/ / +----+----+----+-/ / +
+----+ / +----+ |
| | + +----+----+ | | |
| |/ /| / | | +
+ +----+ | +----+ + /
| | +----+--| | +
| |/ | |/
+----+----+ +----+----+
The Y |
This burr's wooden length-12 pieces are stained a dark color. The burr comes in a box with a fitted slip-out cover.
At some point I saw it referred to as "G4."
The pieces used are: 1, 188, 512, 832, 975, 1024.
Here is a group of miscellaneous wooden burrs I've accumulated.
Their pieces are shown below.
The light brown burr is perhaps the more difficult of this group, but we've seen it already -
its pieces are the familiar "Rainbow" set:
Another classic puzzle book, 100 Puzzles - How to Make and Solve Them, written by Anthony S. Filipiak,
was published in 1942 by A. S. Barnes and Company.
In his book, Filipiak includes a section on the "Six Piece Burr Puzzle," beginning on page 79.
He says that though he has over a thousand mechanical and manipulative puzzles in his collection, his favorite puzzle is the
six piece burr.
He gives diagrams for 38 burr pieces, and lists his "prize collection" of 73 burr puzzles using those pieces,
"collected the world over by correspondence, travel, and research into ancient books of magic, tricks, games, and puzzles."
He admits "no doubt there are a few more to be added."
I have not reproduced all 73 designs here, but I highlight Filipiak designs like this.
Filipiak's notes seem to contain several errors: pieces #2 and #32 appear to be duplicates of what I call #18;
#10 as drawn equals #463, but that interpretation results in several of Filipiak's designs having no solution - from its
position in his list it might be a mistaken drawing of my #911, the complement to its neighbor #11 which is #792.
Filipiak missed pieces #35 and #86, but there are only 3 uses of #35 among the 314 solid burrs, and only 2 of #86.
He also missed the pair 856/943, but neither of those are used often, either.
Several of the designs in his list of 73 puzzles, when I checked using Jurg's applet, have no solution - maybe
the wrong pieces were listed,
or as previously noted, the actual configuration of the pieces themselves are open to interpretation.
Or, perhaps Filipiak himself hadn't bothered to actually construct all of the designs -
but that seems unlikely given his enthusiasm.
I cannot imagine that his editor could have checked the work!