There are some puzzles that have been there for a long time and have their roots that far back in the past that their origin is not known exactly. The traditional six piece burrs are one such example, the Chinese Rings puzzle another. For some information about the history of the Chinese Rings (also known as "Nine Linked Rings") see [9].
In this compendium, we exhibit a collection of all puzzles known to us that are all related to this type of puzzles, why we will call them "ChineseRingslike puzzles", or more formally, "CR recursive puzzles". A common similarity for all these puzzles is that they have an astonishing high number of moves to solve and they have several rings or pieces working in a similar way in the solution.
Our Compendium features a large variety of different puzzles: Disentanglement puzzles, sliding pieces puzzles, puzzle boxes, burrs, sequential movement puzzles, ball maze puzzles, and even puzzle games with certain rules.
SpinOut 
Crazy Elephants Dance 
Kugellager 
The last example above, the "Kugellager", is the puzzle that started our research and lead to the first article about this puzzle and similar puzzles: [1]. In that article, the "Kugellager" puzzle with its 1250 moves is analyzed and later on short analyses of other puzzles like "Die Welle" were added and a table was created showing several puzzles that are now in this compendium. After collecting some of the related puzzles, a group page was set up and the term "nary puzzle" was termed for these puzzles: [2]. This term nary was also used in a nice article [11] about designing nary puzzles which appeared in CFF 15 in November 2014. The most recent exteded version of this article can be found in [12].
The list of puzzles is the main part of this compendium. It lists the puzzles with several details in entries ordered alphabetically by their names.
PuzzleID  Name  (example entry for explanation of fields)  

Image(s) of puzzle. Click on image or links for bigger image versions. 
Designer  Manufacturer  Year  
Name of creator of puzzle design  Name/Company name of manufacturer  Year of first release  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
# of Levels (n)  special pieces only  of special pieces (m)  exact or asymptotic (Θ) function of n and m  counted/calculated  
Remarks  Remarks about special features, similar puzzles.  
References  Links to patents, Extremely Puzzling page, other web pages on this puzzle  
Symbols:  ^{§}=counting moves of special pieces only; ^{‡}=counting moves until first piece comes out 
Hint: Even if the list cannot be ordered for other fields, you can easily search for a certain entry using your web browser's built in search function (usually invoked by keys CtrlF or F3).
Hint: For previews of secondary images or the variants (entries with IDs), please hover the mouse pointer over the corresponding link (without clicking). In the top right corner of the browser window, a preview will appear. Unfortunately, this does not work on all browsers; in particular some Internet Explorer versions do not show these previews.
Beside this introduction and the list of puzzles there are also a page with a formal definition of the structure of puzzles that belong into this compendium, including some properties and examples. The compendium is concluded by a page to contribute to this compendium by adding puzzles or new information. Please have a look at the navigation bar on top of all pages or the table of contents below.
PuzzleID  Name  (example entry for explanation of fields)  

Image(s) of puzzle. Click on image or links for bigger image versions. 
Designer  Manufacturer  Year  
Name of creator of puzzle design  Name/Company name of manufacturer  Year of first release  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
# of Levels (n)  special pieces only  of special pieces (m)  exact or asymptotic (Θ) function of n and m  counted/calculated  
Remarks  Remarks about special features, similar puzzles.  
References  Links to patents, Extremely Puzzling page, other web pages on this puzzle  
Symbols:  ^{§}=counting moves of special pieces only; ^{‡}=counting moves until first piece comes out  
CR091  Name  Algorithme 9  
Designer  Manufacturer  Year  
Patrick Farvacque  Patrick Farvacque  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  9  discs  
Remarks  The Algorithme series features different puzzles with different number of discs, different disc heights and post heights. They are all some variation of Tower of Hanoi, which can also be seen in the rules: move one disc at a time, which is on top of its pile; no bigger disc may be put on a smaller one (equal size is OK); piles may only go up to post end, not higher.  
References  CFF79 contains an article by Dick Hess about Algorithme 6  
CR174  Name  Alken/Kenal  
[1] [2] [3] 
Designer  Manufacturer  Year  
Alfons Eyckmans, Ken Johnson  Alfons Eyckmans  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  321  
Remarks  Variant of CR160, but not coming apart and only with 5 binary pieces, and one lid piece to be removed by the solution sequence. The lid piece has a different structure, and leads to four puzzles: Alken has lid piece which is binary (135 moves) in one orientation and 6ary (321 moves) in the other. Kenal has a binary (135 moves) and 4ary (257 moves) lid piece. The 135 move configurations also allow the solution sequence to run over the point branching into the last few moves before lid removal, and then leading to a dead end. These dead ends can also be reached when reinserting the lid and trying to close the box. Also at the beginning of the 135 move sequences (box closed) there are some dead ends possible. Second pictures shows the box open and details of the lid pieces, the third piece shows the lid to be slid open without removal, possible for the Kenal 135 configuration just before the end of the sequence.  
References  [1]  
CR127  Name  Alles Schiebung  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  slider  42  
Remarks  Additional locking mechanism; AKA: Sternary  
References  [1]  
CR172  Name  Aquarius Drawer (5 devices)  
Designer  Manufacturer  Year  
Hiroshi Iwahara  Hiroshi Iwahara  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  block  61  
Remarks  Five blocks form a ternary chain of pieces, with two small drawers at the ends. First drawer can be opened after 5 device moves, the other requires 61 moves.  
References  [1], [2]  
CR061  Name  A Slidely Tricky Tower  
[1] [2] [3] 
Designer  Manufacturer  Year  
Yee Dian Lee  Yee Dian Lee  1999  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  sliding piece  Θ( 3^{m} )  485  
Remarks  Different movement schemes by using additional blocking pieces. In the worst case (all blocking pieces), it has 2·3^{m—1}—1 moves. Other cases have just Θ(2^{m}) moves.  
References  [1]  
CR046  Name  Apricot  
Designer  Manufacturer  Year  
Akio Kamei  Akio Kamei  2002  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  panel  
Remarks  
References  [1]  
CR023  Name  Auf dem Holzweg  
Designer  Manufacturer  Year  
Juergen Reiche  Siebenstein  2011  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  slider  
Remarks  Two arity 3 puzzles in one  
References  [1]  
CR177  Name  Bald Eagle  
Designer  Manufacturer  Year  
DDK, Aaron (Yulong) Wang  Aaron (Yulong) Wang  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  ring+connector  Θ( m )  
Remarks  Goal is to remove the big foldable circle piece, which starts in the middle. It can traverse to the left or right end, both consisting of 5 ring+connector pairs. While there are two states for the big circle and each ring+connector pair (i.e. binary), the overall solution is linear. Each pair is traversed only once. The zigzag chain of rings on the main loop looks like the structures used in others of Aaaron's nary puzzles.  
References  [1]  
CR039  Name  Barcode Burr  
[1] [2] [3] 
Designer  Manufacturer  Year  
Lee Krasnow  Lee Krasnow  2004  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  burr piece  2^{m+1}—4  124  
Remarks  Variant: CR137; some shortcuts exist  
References  [1]  
CR137  Name  Barcode Burr (3D printed)  
Designer  Manufacturer  Year  
Lee Krasnow  Stephen Miller  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  burr piece  2^{m+1}—4  124  
Remarks  3D printed reproduction of CR039 in limited run; some shortcuts exist  
References  [1]  
CR160  Name  BBox  
[1] [2] 
Designer  Manufacturer  Year  
Goh Pit Khiam  Eric Fuller  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  135  
Remarks  This is a combination of puzzle box and burr. Not only the panels can be opened and removed, but also the frame can be taken apart completely. Inside the box is a second puzzle, the Reactor by Eric Fuller, a small puzzle box.  
References  [1]  
CR115  Name  Bicomplementary Formation b/b:1/2  
[1] [2] [3] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  11  bars, sticks  70^{‡}  
Remarks  V1, N01; Two interlocking binary sequences (one of bars, one a bit hidden of the sticks). Beside the binary moves, this puzzle also contains burr moves without an nary scheme and with halfnotches. The number of moves contains the binary sequences and some of the burr like moves.  
References  [1]  
CR134  Name  BiNary  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  sliderpair+ball  259  
Remarks  This puzzle combines the mechanisms of CR064 and CR087. The pictures shows second and first edition. The second is more stable and removes a solution issue of the first.  
References  [1], [2]  
CR006  Name  Bin Laden  
Designer  Manufacturer  Year  
Rik van Grol  Rik van Grol  2006  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  drawer  21  
Remarks  Partially ternary and modified sequence  
References  [1]  
CR150  Name  Bin Laden Too  
Designer  Manufacturer  Year  
Rik van Grol  Rik van Grol  2015  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  drawer  
Remarks  Additional mechanisms, modified sequence, combination of several binary sequences. The objective to remove the dice modifies the sequence even further, as a die can only be taken out when a drawer is fully extended and the drawer above in its starting position inside the box.  
References  [1]  
CR073  Name  Binary Bud  
[1] [2] [3] [4] [5] [6] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  leaf  Θ( 2^{m} )  
Remarks  The puzzle contains different challenges  
References  [1], [2]  
CR169  Name  Binary Ladder Disentanglement  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  ring  
Remarks  Name unknown; this version is of early 1990s or shortly before.  
References  [1]  
CR063  Name  Binary Key II  
Designer  Manufacturer  Year  
Goh Pit Khiam  Cubicdissection  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  switch  ^{1}⁄_{6} [—7·(—1)^{m}+2^{m+4}—9]  85  
Remarks  Variation of CR058  
References  [1]  
CR163  Name  BNary  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  slider  Θ( 3^{m} )  220  
Remarks  The mechanism is hidden and seems to consist of the four sliders, several ball bearings, and sliding pieces. There is also one additional ball bearing that has to travel from start to goal, from where it can be put into the start position via a reset feature. During this time, the ternary sequence is executed twice (forwards, then backwards) with 54 slider moves each. The total number of moves includes these slider moves (2·54), the corresponding tilting moves to move ball bearings/sliding pieces (2·54), tilting moves to move the extra ball bearing inside the puzzle and out (3+1). Once the extra ball bearing has reached the half way position, it can go inside the sliders and cause some lockups that have to be undone by reversed moves before the regular sequence can continue.  
References  [1]  
CR182  Name  Buggin  
Designer  Manufacturer  Year  
Stuart Gee  Stuart Gee  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  loop  
Remarks  Variant of: CR031 by linking two of these (with 3 loops) together at the end of the sequence. Sequences can mainly be traversed one after the other.  
References  [1]  
CR166  Name  Cast Infinity  
Designer  Manufacturer  Year  
Vesa Timonen  Hanayama  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
6  2  disc  
Remarks  Two interlocking discs which can rotate between six positions and can move up and down. Objective is to remove the discs.  
References  [1]  
CR059  Name  Chinese Rings 5  
[1] [2] [3] 
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  ring  [2^{m+1}/3]  21  
Remarks  Variant: CR042. The pictures 2 and 3 show other versions with 5 rings. Reference [14] shows a 7 ring variant including solution.  
References  [1], [2], [3], Reference Section [9] and [14] (pp. 100102)  
CR042  Name  Chinese Rings 9  
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  ring  [2^{m+1}/3]  341  
Remarks  Variant: CR059  
References  [1], Reference Section [9]  
CR123  Name  Complementary parity  
[1] [2] [3] [4] [5] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  14  bars, loops  102^{‡}  
Remarks  Complimentary combination of several different sequences: Top 5 bars run in a 3ary sequence, together with the 5 bottom bars, who run (slower) in a 2ary sequence. These interact with the 4 looppieces, which run accross in a 3ary sequence. First challenge of the puzzle is to understand these sequences, then the second is to disassemble and correctly reassemble the puzzle, with many other parts, alltogether 29 pieces.  
References  [1], [2]  
CR054  Name  Computer Loops  
Designer  Manufacturer  Year  
MagNif  1975  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  ring  [2^{m+1}/3]  170  
Remarks  
References  [1]  
CR031  Name  Computer Puzzler No 2  
[1] [2] 
Designer  Manufacturer  Year  
Tenyo  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  loop  Θ( 2^{m} )  
Remarks  
References  [1], [2] (US Patent 1091709), [3]  
CR034  Name  Computer Puzzler No 5  
[1] [2] 
Designer  Manufacturer  Year  
Tenyo  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  loop  
Remarks  was No 3 earlier; Variants: CR003, CR013, CR024, CR045, CR081, CR122  
References  [1], [2]  
CR010  Name  Crazy Elephant Dance  
[1] [2] [3] 
Designer  Manufacturer  Year  
Markus Goetz  Peter Knoppers  2005  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  elephant  3·(2^{m}—1)—2·m  83  
Remarks  The second and third pictures show the original prototype of the puzzle.  
References  [1]  
CR175  Name  Corn on the Cob I  
Designer  Manufacturer  Year  
Aaron (Yulong) Wang  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  ring pairs  
Remarks  Variants: CR178, CR188. This is mainly a (binary) Chinese Rings puzzle with single rings. The second ring of each pair is dropped from the main bar when the corresponding ring get's off the bar. It will then stay unhooked, while the primary ring follows the usual Chinese Rings sequence. For each pair there are four states (on/off loop for each ring), so this puzzle can also be considered quarternary. However, the main sequences and interactions are only binary, with touching every secondary ring only once, hence classified as binary here.  
References  [1]  
CR178  Name  Corn on the Cob II  
Designer  Manufacturer  Year  
Jianjiang Wu  Aaron (Yulong) Wang  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  ring pairs  
Remarks  Variants: CR175, CR188. This is mainly a (binary) Chinese Rings puzzle with single rings in a chinese rings chain (CRC) and then an additional chain, a zig zag chain (ZZC) through the connector piece ends. When the last ring from the CRC on the handle bar is dropped, a sequence through the ZZC follows. As this is a ZZC, half of the rings are wrongly oriented for the usual sequence, and at those points parts of the CRC are traversed to the beginning of the CRC, to allow access to the ZZC rings in the other orientation. These interruptions in the ZZC sequence by CRC sequences will then happen until the completion of the solution. The main scheme is that the rings of the CRC come off one after another like in a Chines Rings puzzle. Consequently, the reassemlby follows this scheme: Run through the CRC to put on the last free ring of the CRC, then put the lasts free ring of the ZZC on the handle bar. This automatically adds two rings of the ZZC, so one will need to be released to allow to put on the next CRC ring. For this some ZZC sequences are required, with some CRC sequences performed up to the correct entry point of the ZZC. The scheme can be learned with a few ring pairs (up to 4) initially, but only with 7 or 9 ring pairs, all required moves become apparent.  
References  [1]  
CR188  Name  Corn on the Cob III  
Designer  Manufacturer  Year  
Jianjiang Wu  Aaron (Yulong) Wang  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  ring pairs  
Remarks  Variants: CR175, CR178. Like the first two puzzles in the series, the CotC III is mainly a binary chinese rings puzzle. Each ring is part of a pair with a free ring (only one end caught in a connector) and a ring part of the main zigzag back bone. After analysis, the puzzle can be solved with some simple rules: Each ring has only one correct orientation on the handlebar piece. The free rings form a binary chinese rings puzzle that needs to be solved, and when the bar needs to go through one ring of a pair, it should always go through the free ring. The last rule is about reassembly (entanglement): When the handlebar is at the rightmost free/zigzag ring pair, it should break the rule before and go through the zigzag ring.  
References  [1]  
CR047  Name  Cross and Crown  
[1] [2] 
Designer  Manufacturer  Year  
Louis S. Burbank  1913  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  rivet  2·5^{m}  1250  
Remarks  Variants: CR120, CR121, CR158  
References  [1] (US Patent 1071874), [2]  
CR120  Name  Cross and Crown 2013  
Designer  Manufacturer  Year  
Louis S. Burbank  Robrecht Louage  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  rivet  2·5^{m}  1250  
Remarks  Reproduction based on the original patent; Variants: CR047, CR121, CR158  
References  [1], [2] (US Patent 1071874)  
CR121  Name  Cross and Crown 7  
Designer  Manufacturer  Year  
Louis S. Burbank, Michel van Ipenburg  Robrecht Louage  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  rivet  2·7^{m}  4802  
Remarks  Variants: CR047, CR120, CR158  
References  [1]  
CR140  Name  Crossing  
Designer  Manufacturer  Year  
Jack Krijnen  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  sliding piece  
Remarks  
References  reference section [12]  
CR056  Name  CUBI  
Designer  Manufacturer  Year  
Akio Kamei  Akio Kamei  1985  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  2^{m—1}  32  
Remarks  Variant: CR048, CR162  
References  
CR092  Name  Delirium  
[1] [2] [3] [4] 
Designer  Manufacturer  Year  
Stéphane Chomine  Claus Wenicker  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  28  burr pieces  (2^{m+2}—1 — (m mod 2))/3  357913941  
Remarks  Simplified version of: CR012, CR076, pictures show versions with 28, 5, 6, and 38 special pieces. Reference 1 shows form for arbitrary many special pieces. Variant: CR154  
References  [1]  
CR154  Name  Delirium 13  
Designer  Manufacturer  Year  
Stéphane Chomine  Johan Heyns  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  12  burr pieces  (2^{m+2}—1 — (m mod 2))/3  5461  
Remarks  Simplified version of: CR012, CR076. Reference 1 shows form for arbitrary many special pieces. Variant: CR092  
References  [1], [2]  
CR075  Name  Devil's Cradle  
Designer  Manufacturer  Year  
Rick Irby  2000  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  pair of loops  
Remarks  Variants: CR014, CR030, CR067, CR068, CR069, CR070  
References  
CR060  Name  Die Welle  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  3  ball  5^{m}—1  124  
Remarks  
References  [1]  
CR124  Name  Digi Fork Lock  
[1] [2] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  5  slider  
Remarks  Enhancement of CR093  
References  [1]  
CR159  Name  Digits' Compressor  
[1] [2] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  disc  49  
Remarks  Goal is to compress the digit stack to minimal height by rotating discs and moving them verticalle, and additionally to line up the red markings with the four red markings on top and bottom parts. There are several differentlength dead end sequences. The five gray discs move in a binary symmetric Gray code sequence, unlike the black ones. Each disc has an orange pin, which can interock with two different holes in the disc below, i.e. two differet positions for each disc.  
References  [1], [2]  
CR158  Name  Disc & Crown CFF 100 Jubilee Edition Puzzle  
[1] [2] 
Designer  Manufacturer  Year  
Robrecht Louage, Michel van Ipenburg  Robrecht Louage  1916  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  rivet  2·3^{m}  54  
Remarks  Limited edition of 500 that was a gift with CFF issue 100. Variants: CR047, CR120, CR121  
References  [1], Reference Section [15]  
CR192  Name  Disordered Chinese Rings  
Designer  Manufacturer  Year  
Yuandong Jiang, Aaron (Yulong) Wang  Aaron (Yulong) Wang  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  rings  
Remarks  While the rings in the classic Chinese Rings puzzle are linking their connector with the next connector each, in this one, the regular scheme is broken and some rings go over the next two or three connectors. Some of them lead to irregularly stacked rings on some connectors, while for others the rings over the next one and two connectors are aligned in parallel over one connector. When solving, one has to ensure to choose the right ring for the sequence and which ring to skip, while the overall solution sequence is aligned to the general Chinese Rings sequence.  
References  [1]  
CR074  Name  Dispersed GC Lock  
[1] [2] [3] [4] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  switch  184  
Remarks  Code corresponds to setting 1100 of CR020  
References  [1], [2]  
CR143  Name  DITWIBIN  
[1] [2] [3] [4] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  slider  Θ( 2^{m} )  
Remarks  One of the simplest designs of a whole puzzle family, with different number of sliders, disks, and arities. This design was devised fist for higher order variants in August 2014, about a month before this puzzle. One of the higher order variants is CR149.  
References  [1]  
CR170  Name  Double Helix  
Designer  Manufacturer  Year  
Goh Pit Khiam  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  pairs of burr sticks  73  
Remarks  This puzzle consists of 20 pieces, of which 8 are the special pieces (middle layers). A pair of pieces makes up one level, as outlined in the article referenced below.  
References  reference section [12]  
CR194  Name  Double Image  
Designer  Manufacturer  Year  
DDK  Aaron (Yulong) Wang  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  ring+connector  
Remarks  The main chain of this is a classic 9 ring Chinese Rings puzzle. Attached to rings 3, 5, 7, and 9 are a small ring and connected to that two regular sized rings. Those rings are linked with the previous and next connector. During the solution, only at most one ring of each additional ring pairs will be on the handle. The main solution sequence is still binary, but one has to determine when to pick up the forward / backward secondary ring. At some points in the solution, both the primary ring and the secondary ring are on the main bar, at other points in the solution, also only the secondary ring might be on the main bar (but this only holds for the forward rings, the secondary backwards rings are never on the handle alone). Therefore, the puzzle could also be classed as a ternary puzzle, or even quarternary, but the main structure is still binary.  
References  [1]  
CR135  Name  Double Loop  
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  2  loop pairs  
Remarks  Variant: CR067 (other variants see there)  
References  [1], [2]  
CR101  Name  Dragonfly  
[1] [2] 
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  rings  23  
Remarks  extra rings for symmetry; second picture shows Airplane puzzle  
References  [1]; Reference Section [7] and [8]  
CR146  Name  Drunter & Drueber  
Designer  Manufacturer  Year  
Juergen Reiche  Siebenstein  2015  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  loop  Θ( 2^{m} )  
Remarks  
References  [1]  
CR014  Name  Electro 1  
[1] [2] [3] 
Designer  Manufacturer  Year  
Tenyo  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  pair of loops  26  
Remarks  The second picture shows an unknown variant. Variants: CR030, CR067, CR068, CR069, CR070, CR075  
References  [1], [2]  
CR015  Name  Electro 2  
[1] [2] 
Designer  Manufacturer  Year  
Gabor Vizelyi  Tenyo  1981  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  loop  25  
Remarks  
References  [1] , [2] US Patent 4391445, [3]  
CR153  Name  Elephant Wire Puzzle  
Designer  Manufacturer  Year  
Beijing Oriental Top Science Trading Ltd  2003  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  loop  
Remarks  Variant of: CR031 with a more irregular shape. The instructions lists 11 different starting positions as challenges.  
References  [1]  
CR198  Name  Entwined Loop Lattice  
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
7  4  loop  Θ( 3^{m} )  80  
Remarks  This is actually a section of an infinite puzzle: The puzzle could be extended infinitely to the right or left. If this structure is closed as a loop, this will lead to something like CR197. Therefore, the arity is hard to determine. There are six loops and the configuration off the loop for each pole/sector, so 7ary might be a good description. However, the solution only makes use of 4 of the poles (and the rope off the puzzle), so it is more 5ary, and the actual solution length is 3ary. For the solution the two bends of the rope start in the compartments denoted by red triangles, and each bend will be maneuvered off the puzzle separately, with 40 moves each. In the IPP38 Design Competition it participated as part of "Loopy Lattice Puzzles"; other puzzles from the same series: CR196, CR197  
References  [1], [2]  
CR071  Name  Expansion V  
[1] [2] 
Designer  Manufacturer  Year  
Akio Kamei  Akio Kamei  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  2^{m—1}+3  35  
Remarks  Simpler variant of: CR094  
References  [1], [2]  
CR094  Name  Expansion VI  
[1] [2] [3] 
Designer  Manufacturer  Year  
Akio Kamei  Akio Kamei  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  Θ( 2^{m} )  83  
Remarks  More complicated variant of: CR071  
References  [1], [2]  
CR157  Name  Extended Chinese Rings  
Designer  Manufacturer  Year  
Ruan Liuqi  Bob Easter  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  rings  Θ( 2^{m} )  
Remarks  Various extended Chinese Rings, based on the designs from the book given in the references section. These designs are e.g.: CR108, CR110, CR111  
References  Reference Section [7] and [8]  
CR072  Name  Ferris Wheel  
Designer  Manufacturer  Year  
Jean Carle  Eureka 3D Puzzles  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  loop  
Remarks  Variant: CR144  
References  [1], [2]  
CR147  Name  Fibula Puzzle  
Designer  Manufacturer  Year  
Lord Minimal  Monkeys Cage  2015  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  loop  
Remarks  
References  [1], [2]  
CR052  Name  Fidgety Rabbits  
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2012  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  rabbit disc  Θ( 2^{m} )  170  
Remarks  Variant: CR018  
References  [1], [2]  
CR018  Name  Fidgety Rabbits ternary  
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2012  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  rabbit disc  Θ( 3^{m} )  230  
Remarks  Variant: CR052  
References  [1]  
CR129  Name  Find my Hole  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  discs  
Remarks  This puzzle contains three disks, but from a mathematical view, the top and bottom disc act as one and have to be moved simultaneously in different directions. Additional locking mechanism.  
References  [1]  
CR098  Name  Fish  
[1] [2] 
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  rings  27  
Remarks  The first picture shows the "Wicked Wire" version by Professorpuzzle.  
References  [1]; Reference Section [7], [8], and [14] (p.153)  
CR161  Name  Fishing Hook Chain 9Ring  
Designer  Manufacturer  Year  
DDK  Aaron (Yulong) Wang  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  9  rings+loops  
Remarks  The three states of each ring+loop pair are: main bar through the loop (or "fishing hook", initial configuration), through the ring, and off both. When reassembling the puzzle, an additional challenge arises: it may easily happen that some hooks end up on the main loop in wrong orientation. As this can only be seen after many (up to 1000s) of moves, careful planning is advised and analaysis of smallers problem of the first few hooks only. One feasible approach is to arrange the loops in an alternating pattern above and below the the backbone while running through the sequence.  
References  [1]  
CR114  Name  Football  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  21  
Remarks  
References  Reference Section [7] and [8]  
CR110  Name  Fortune  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  12  rings  993  
Remarks  
References  Reference Section [7] and [8]  
CR081  Name  Frame & Loop Octet  
[1] [2] 
Designer  Manufacturer  Year  
Abraham Jacob  Abraham Jacob  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  loop  
Remarks  Variants: CR003, CR013, CR024, CR034, CR045, CR122  
References  
CR024  Name  Frame & Loop Quartet  
Designer  Manufacturer  Year  
Abraham Jacob  Abraham Jacob  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  loop  
Remarks  Variant of Computer Puzzler No 5; Variants: CR003, CR013, CR034, CR045, CR081, CR122  
References  [1]  
CR003  Name  Frame & Loop Quintet  
Designer  Manufacturer  Year  
Abraham Jacob  Abraham Jacob  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  loop  
Remarks  Variants: CR013, CR024, CR034, CR045, CR081 , CR122  
References  [1]  
CR122  Name  Frame & Loop Septet  
Designer  Manufacturer  Year  
Abraham Jacob  Abraham Jacob  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  loop  
Remarks  Variants: CR003, CR013, CR024, CR034, CR045, CR081  
References  [1]  
CR045  Name  Frame & Loop Sextet  
Designer  Manufacturer  Year  
Abraham Jacob  Abraham Jacob  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  loop  
Remarks  Rereleased for IPP34 Exchange; Variants: CR003, CR013, CR024, CR034, CR081, CR122  
References  [1]  
CR013  Name  Frame & Loop Trio  
Designer  Manufacturer  Year  
Abraham Jacob  Abraham Jacob  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  loop  
Remarks  Variants: CR003, CR024, CR034, CR045, CR081, CR122  
References  [1]  
CR079  Name  Frequency Doubler 1  
[1] [2] 
Designer  Manufacturer  Year  
Oskar van Deventer  Tom Lensch  2012  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  slider  4·(m^{2}+2·m—1)  28  
Remarks  Variants: CR080, CR090 older design, but first made in this version in 2012  
References  [1]  
CR080  Name  Frequency Doubler 2  
[1] [2] 
Designer  Manufacturer  Year  
Oskar van Deventer  Tom Lensch  2012  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  6  slider  4·(m^{2}+2·m—1)  56  
Remarks  Variants: CR079, CR090 older design, but first made in this version in 2012  
References  [1]  
CR090  Name  Frequency Doubler 3  
[1] [2] 
Designer  Manufacturer  Year  
Oskar van Deventer  Tom Lensch  2012  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  8  slider  4·(m^{2}+2·m—1)  92  
Remarks  Variants: CR079, CR080, second picture shows solved state, older design, but first made in this version in 2012  
References  
CR089  Name  GC machine ternary  
[1] [2] [3] [4] [5] [6] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  switch  141  
Remarks  Goal is to move all switches to the "far out" position  
References  [1]  
CR065  Name  Generation Lock  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
15  8  slider  2·15^{m—1}  341718750  
Remarks  second picture shows comparison with CR037; Variant: CR037  
References  [1] [2]  
CR067  Name  Gordian Knot  
Designer  Manufacturer  Year  
Eureka 3D Puzzles  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  2  pair of loops  
Remarks  Variants: CR014, CR030, CR068, CR069, CR070, CR075, CR135; alternative version named "Gekkenwerk" was devised by Jack Botermans, see reference section [13] pp. 76 and 77, including a solution  
References  [1], [2], reference section [13]  
CR068  Name  Gordian Knot 2  
[1] [2] 
Designer  Manufacturer  Year  
Huso Taso  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  1  pair of loops  
Remarks  The second picture shows a variant built by Jan Sturm (new in 2014). Variants: CR014, CR030, CR067, CR069, CR070, CR075  
References  [1], [2]  
CR069  Name  Gordian Knot 4  
Designer  Manufacturer  Year  
Huso Taso  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  2  pair of loops  
Remarks  Variants: CR014, CR030, CR067, CR068, CR070, CR075  
References  [1]  
CR070  Name  Gordian Knot 6  
Designer  Manufacturer  Year  
Huso Taso  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  pair of loops  
Remarks  Variants: CR014, CR030, CR067, CR068, CR069, CR075  
References  [1]  
CR112  Name  Gourd  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  rings  5  
Remarks  
References  Reference Section [7] and [8]  
CR118  Name  Grydlock  
[1] [2] 
Designer  Manufacturer  Year  
Robert Hilchie  Robert Hilchie  1993  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  10  slider  3^{m/2}—1  242  
Remarks  The puzzle can be built with various slider shapes, leading to different mazes. Most of them are not nary, like the one shown in the pictures. Several puzzles have been implemented as online version (see reference [2]), an nary one has also has been implemented — please see reference [3], and for this the solution length and other details are provided here.  
References  [1] (US Patent 5470065), [2], [3]  
CR108  Name  Happiness  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  13  rings  364  
Remarks  
References  Reference Section [7] and [8]  
CR043  Name  Hanui  
Designer  Manufacturer  Year  
Yoshiyuki Kotani  1994  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  U piece  3^{m—1}·2^{i—1}  242  
Remarks  Piece i not allowed on middle position; 242 moves for i=biggest piece  
References  
CR020  Name  Hexadecimal Puzzle  
Designer  Manufacturer  Year  
William Keister  Binary Arts  1970  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  switch  Θ( 2^{m} )  170^{§}  
Remarks  Binary and 170 move sequence for setting 1110; Variants: CR040, CR066  
References  [1] (US Patent 3637216), [2], [3]  
CR040  Name  Hexadecimal Puzzle Reproduction  
Designer  Manufacturer  Year  
William Keister  Bill Wylie  2011  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  switch  Θ( 2^{m} )  170^{§}  
Remarks  Binary and 170 move sequence for setting 1110; Variants: CR020, CR066  
References  [1] (US Patent 3637216), [2], [3], [4]  
CR066  Name  Hexadecimal Puzzle 2013  
Designer  Manufacturer  Year  
William Keister  Creative Crafthouse  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  switch  Θ( 2^{m} )  170^{§}  
Remarks  Binary and 170 move sequence for setting 1110; Variants: CR020, CR040  
References  [1] (US Patent 3637216), [2], [3], [4]  
CR195  Name  JackintheBox  
Designer  Manufacturer  Year  
Jack Krijnen  Jack Krijnen  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  wheel  
Remarks  From the description: It's sequential discovery, it's riddle solving, it's ternary and in the end it's challenging.  
References  [1]  
CR164  Name  JUNC  
[1] [2] [3] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  slider pair  
Remarks  Goal is to move all light sliders down and all dark sliders left. By unlocking and removing the transparent lid, all little square pieces can be reoriented, allowing for 4^{25}≅10^{15} different challenges. Not all of these are possible as can be seen from the second picture, where a partial configuration is shown with the two topleft slider pairs blocking each other, unable to move. While the first picture shows the simple standard configuration of the puzzle, the third one shows one adapted from the N522 puzzle (CR087), with nontrivial solution and polynomial solution length. The letters of the name depict the various configurations of the small squares.  
References  [1]  
CR049  Name  Junk's Hanoi  
[1] [2] 
Designer  Manufacturer  Year  
Junk Kato  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  block  Θ( 3^{m} )  161  
Remarks  Variation: Israelogi by ThinkinGames / Ili Kaufmann. The image shows a different version created by Dirk Weber.  
References  [1], [2]  
CR053  Name  K323  
[1] [2] 
Designer  Manufacturer  Year  
Kim Klobucher  Kim Klobucher  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  block  323  
Remarks  Variants: CR016, CR038  
References  [1], [2]  
CR038  Name  K419  
Designer  Manufacturer  Year  
Kim Klobucher  Kim Klobucher  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  6  block  419  
Remarks  Variants: CR016, CR053  
References  [1], [2]  
CR017  Name  KingCUBI  
Designer  Manufacturer  Year  
Hiroshi Iwahara  Hiroshi Iwahara  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  6  panel  1536  
Remarks  
References  [1]  
CR051  Name  Kugellager  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  ball  2·5^{m}  1250  
Remarks  Variants: CR027, CR028  
References  [1]  
CR028  Name  Kugellager 7  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
7  4  rivet  2·7^{m}  4802  
Remarks  Variants: CR027, CR051  
References  [1]  
CR027  Name  Kugellager 8  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  ball  2·5^{m}  1250  
Remarks  Smaller Version and upsidedown to original Kugellager; AKA: Kugellager 2; Variants: CR028, CR051  
References  [1]  
CR088  Name  Labynary  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  slider pair+switches  
Remarks  Beside the 8 main sliders, the puzzle contains several other smaller sliders for the interaction between the 8 main sliders. Additionally, there is a small ball and a ball maze in this puzzle, and the goal is to get the ball out at one of the three maze exits. The maze is also part of the sliders (see second image) and therefore the binary character only holds for the basic puzzle, without the ball.  
References  [1]  
CR029  Name  LeftRight Chinese Rings  
Designer  Manufacturer  Year  
Jan Sturm  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  ring  
Remarks  
References  [1]  
CR078  Name  Lego Ternary Gray Code Puzzle  
[1] [2] 
Designer  Manufacturer  Year  
Adin Townsend  Adin Townsend  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  lever  3·(2^{m}—1)—2·m  177  
Remarks  Lego variant/implementation of CR010. Second picture shows the three different piece states, with one moved out to the right already. Second reference links to building instructions created by Jeremy Rayner; the puzzle can be built with the pieces of a Mindstorms NXT set, but slight modifications might be necessary depending on the actual piece set.  
References  [1], [2]  
CR100  Name  Lock  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  23  
Remarks  extra ring for symmetry  
References  Reference Section [7] and [8]  
CR130  Name  Lock 14  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  slider+ball  
Remarks  First shackle part has ternary sequence, second part additional trick. Mechanism is like in CR064; AKA: Alphalock  
References  [1]  
CR037  Name  Lock 250+  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
6  4  slider  Θ( 5^{m—1} )  310  
Remarks  Lowest (4th) ring piece has only 2 position and acts as slider, AKA: Big Sliding Lock, Schloss 250+; Variant: CR065  
References  [1]  
CR102  Name  Longevity  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  rings  37  
Remarks  extra rings for symmetry  
References  Reference Section [7] and [8]  
CR030  Name  Loony Loop  
Designer  Manufacturer  Year  
Trolbourne Ltd  1975  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  2  pair of loops  
Remarks  Variants: CR014, CR067, CR068, CR069, CR070, CR075  
References  [1] (US Patent 2091191), [2] (US Patent D0172310), [3], [4]  
CR196  Name  Loopary Branch  
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  loop  Θ( 2^{m} )  127  
Remarks  The linear structure is bent into U shape. In the IPP38 Design Competition it participated as part of "Loopy Lattice Puzzles"; other puzzles from the same series: CR197, CR198  
References  [1], [2]  
CR008  Name  Magnetic Tower of Hanoi  
Designer  Manufacturer  Year  
Uri Levy  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  disc  Θ( 3^{m} )  83  
Remarks  
References  [1], [2]  
CR111  Name  Mandarin Duck  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  15  rings  3287  
Remarks  
References  Reference Section [7] and [8]  
CR099  Name  Maze  
[1] [2] 
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  24  
Remarks  The first picture shows "Rat Race" by Puzzlemaster  
References  [1]; Reference Section [7] and [8]  
CR162  Name  Mechanic CUBI  
Designer  Manufacturer  Year  
Akio Kamei  Akio Kamei  2005  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  2^{m—1}  32  
Remarks  Variants: CR048, CR056. Mechanism is completely made out of wood, no metal (pins) used. Kamei also included a second alternate solution with a shortcut, which will only work at the beginning of the usual sequence, and is a couple of moves only.  
References  [1], [2]  
CR077  Name  Meiro Maze Variant  
Designer  Manufacturer  Year  
Fujita  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  pair of loops  
Remarks  First goal is to remove the coin, second the whole thread from the metal part. Both challenges are the same ternary puzzle repeated, but for releasing the coin additional restrictions exist. This seems to be a variant of the Meiro Maze shown in reference 2.  
References  [1], [2]  
CR167  Name  Merrygoround  
[1] [2] [3] [4] 
Designer  Manufacturer  Year  
Jack Krijnen, Goh Pit Khiam  Jack Krijnen  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
6  6  burr sticks  13432  
Remarks  Variants: CR126, CR136; This puzzle is a further developed variant of the original Power Tower, and as such it also comes as a whole set of pieces. With these pieces coming as 2ary, 3ary, 4ary, 5ary, and 6ary (in the version shown in the pictures), different configurations can be created. There is a special binary piece as a key piece that is part of all configurations as top piece. Therefore, there are 6 slots and 5 of each piece arity (only 2 for 6ary). Reducing the massive block to a slim tower allows pieces of different length and theoretically in arbitary arity without changing the central tower or other pieces. In the pictures, different examples are shown: 3 binary pieces (solved), 6 binary pieces (solved), one of each kind (midsolution). While the Power Tower has pairs of mirrorsymmetric pieces, here all pieces of same arity are the same and have to be entered in a helical pattern. While the sequences for even and odd arity pieces differ especially at the beginning, they are the same in this puzzle. Goal is to choose a configuration, enter the pieces into the tower, and slide them until they are all flush with the tower side on one end. The maximum number of moves for the puzzle in the picture is 13432, with pieces: (2*, 5, 5, 5, 6, 6).  
References  [1]  
CR139  Name  Mini Num Lock (binary)  
[1] [2] 
Designer  Manufacturer  Year  
Goh Pit Khiam  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  slider  
Remarks  Variants: CR125 and CR176; the second picture shows three different even and odd base variants: bases 2, 3, and 4. The ternary one is the cross referenced Num Lock in this puzzle list.  
References  reference section [12]  
CR180  Name  MiSenary Puzzle Box  
[1] [2] 
Designer  Manufacturer  Year  
Michel van Ipenburg  Michel van Ipenburg  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
7  2  slider  Θ( 7^{m} )  
Remarks  The object is to open the box, by tilting it to the left and right, while pulling/pushing the lid. The puzzle was entered into the 2017 IPP Nob Yoshigahara Puzzle Design Competition.  
References  [1], [2]  
CR149  Name  MixTerMaxTer  
[1] [2] [3] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2015  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  8  slider  Θ( 3^{m} )  342  
Remarks  One of a whole puzzle family, with different number of sliders, disks, and arities. CR143 is a simpler variant. The goal of MinTerMaxTer is to move the sliders from the outer discs with two slots to the outer disc with 8 slots and collect them there.  
References  [1], [2]  
CR016  Name  MMMDXLVI  
Designer  Manufacturer  Year  
Kim Klobucher  Kim Klobucher  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  9  block  3546  
Remarks  Variants: CR038, CR053  
References  [1], [2]  
CR171  Name  Mountain Trail  
Designer  Manufacturer  Year  
DDK, Aaron (Yulong) Wang  Aaron (Yulong) Wang  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  rings+connectors  
Remarks  Main binary chinese rings chain, with three additional binary chains of 2 rings each, attached to rings 5, 7, and 9. These are interwoven with the main chain, leading to ternay subsequences, with some quaternary positions, where two subchains meet. Of each of those additional sequences, there is always only one of the two rings on the main loop. This is one of six puzzles in the Chinese 99ring series.  
References  [1]  
CR193  Name  Mountain Trail II  
Designer  Manufacturer  Year  
DDK, Aaron (Yulong) Wang  Aaron (Yulong) Wang  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  rings+connectors  
Remarks  This one is based on a main binary chinese rings chain, with an additional chain of 3 rings starting under the 5th and 8th ring. Unlike CR171, these additional chains are not rings linked directly with each other, but each ring is connected to one of the vertical bars via a smaller ring. In the starting position, these look like linked chains, during the solve, the chains act like secondary chinese rings chains, and therefore also multiple rings of the same secondary chain will be on the main bar at the same time, especially when one of them is put on/off the main bar. While the overall structure of the chains is binary, each of the four possibilities for each ring pair of ring on/off the handle (on/on, on/off, off/on, off/off) occurs and this puzzle could also partially be classified as a quarternary puzzle. For each pair of primary and secondary ring, putting on/off each of the rings of the pair requires a traversal of the lower rings sequence, making it a quite long solution sequence, adding up all these binary sequences. From the solution standpoint it might therefore also be classified as being partially ternary, and probably this is the main influence on the solution length. This is a later puzzle of the Chinese 99ring series.  
References  [1]  
CR033  Name  Mysterians  
Designer  Manufacturer  Year  
Oskar van Deventer  George Miller  2002  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  3  plate  5^{m}—1  124  
Remarks  
References  [1], [2], [3]  
CR131  Name  N5  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  2  sliderpair  20  
Remarks  Variants: CR087, CR132,CR133; Beside ternary sliders in two orientations, there is a simple ball maze built into the left end of the sliders and the ball is to move from bottom to top as goal, while the moving sliders obstruct and open some of the maze parts. The second picture shows the position in which the maze is usable; only the first slider has to be moved up and down while the ball traverses the maze. The number of moves is for putting all sliders up/to the right (calculcated with BurrTools, see second reference), with one additional move of the left slider to remove the ball, totalling 21.  
References  [1], [2]  
CR132  Name  N52  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  sliderpair  68  
Remarks  Variants: CR087, CR131,CR133; Beside ternary sliders in two orientations, there is a simple ball maze built into the left end of the sliders and the ball is to move from bottom to top as goal, while the moving sliders obstruct and open some of the maze parts. The second picture shows the position in which the maze is usable; only the first slider has to be moved up and down while the ball traverses the maze. The number of moves is for putting all sliders up/to the right (calculcated with BurrTools, see second reference), with three additional moves of the left slider to remove the ball, totalling 71.  
References  [1], [2]  
CR087  Name  N522  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  sliderpair  212  
Remarks  AKA: "522"; Variants: CR131, CR132,CR133; Beside ternary sliders in two orientations, there is a simple ball maze built into the left end of the sliders and the ball is to move from bottom to top as goal, while the moving sliders obstruct and open some of the maze parts. The second picture shows the position in which the maze is usable; only the first slider has to be moved up and down while the ball traverses the maze. The number of moves is for putting all sliders up/to the right (calculcated with BurrTools, see second reference), with five additional moves of the left slider to remove the ball, totalling 217. This is the first model of the series. Physically built have been all versions from 2+2 to 10+10 sliders, and some are presented on this page.  
References  [1], [2]  
CR133  Name  N522222222  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  10  sliderpair  
Remarks  Variants: CR087, CR131,CR133; Beside ternary sliders in two orientations, there is a simple ball maze built into the left end of the sliders and the ball is to move from bottom to top as goal, while the moving sliders obstruct and open some of the maze parts. The second picture shows the position in which the maze is usable; only the first slider has to be moved up and down while the ball traverses the maze. Number of moves yet to be determined. This is the biggest of the series actually built.  
References  [1]  
CR116  Name  New Puzzle Rings 3  
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  ring  
Remarks  Variant: CR117  
References  [1]  
CR117  Name  New Puzzle Rings 5  
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  ring  
Remarks  Variant: CR116  
References  [1]  
CR187  Name  New Secret Box IV  
Designer  Manufacturer  Year  
Akio Kamei  Karakuri Creation Group  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  2^{m—1}  32  
Remarks  Variants: CR048, CR056, CR162. Mechanism is completely made out of wood, no metal (pins) used.  
References  [1], [2]  
CR106  Name  Nine Twists  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  
Remarks  
References  Reference Section [7] and [8]  
CR179  Name  No Full Pirouette!  
[1] [2] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  6  module  61  
Remarks  Starting position is with all green arrows pointing to the green rectangle (right). Goal is to turn all the elements on the modules with the blue arrows pointing right. There are dead ends and it is not always immediately obvious which move should be the next one. The modules have arities (left to right): 4,3,3,2,3,2. The puzzle won a Jury First Prize in the 2017 IPP Nob Yoshigahara Puzzle Design Competition. The name is based on the following little anecdote relating to the movement of the pieces: The teacherchoreographer of ballet school gathered the students of various classes near the bar and tried to arrange a new divertissement with pirouette as the main element of group dance in a limited area. He ordered to make pirouette one by one to avoid collisions. But it was impossible in limited space to do that. The lesson failed. Somebody suggested asking the math teacher to help. Luckily the mathematics was passing near and was interested in assigned task. After some measuring, he proposed a scenario and exclaimed: One by one spin back and forth and no full pirouette!  
References  [1], [2]  
CR125  Name  Num Lock  
[1] [2] 
Designer  Manufacturer  Year  
Goh Pit Khiam  Tom Lensch  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  sliders  16 (3^{m—2}) —1 ^{‡}  143^{‡}  
Remarks  Variants: CR139 and CR176  
References  [1], [2], reference section [12]  
CR176  Name  Num Lock (mixed bases)  
[1] [2] [3] 
Designer  Manufacturer  Year  
Goh Pit Khiam  Johan Heyns  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
9  9  sliders  4 n_{0}··· n_{m—1}(n_{m}+1) —1 ^{‡}  50009399^{‡}  
Remarks  Variants: CR125 and CR139. The first piece shows the puzzle on the stand with 9 sliders entered and one of each arity 3, 5, 7, and 9 coming with the set, and some sheets listing number of moves for certain configurations. Those sheets are based on above formula involving the base/arity n_{m} of the leftmost piece and the product n_{0}··· n_{m—1} of the arities of the other pieces, regardless of their order. The second picture shows the puzzle with 9 sliders and all 16 knobs in two rows. The third picture shows all pieces of the set, including the leftmost pieces (called "starting block") for each arity, and the common piece. There are following piece counts: 3ary: 7+1 (1 block attached), 5ary: 4+1 (2 blocks), 7ary: 3+1 (3 blocks), 9ary: 3+1 (1 blocks), 1 common piece, 16 knobs. The reset and piece number selection mechanism has not been shown in the pictures, as finding this is an extra puzzle posed by Johan.  
References  [1], reference section [12]  
CR151  Name  Oh Sh*t! Puzzle  
Designer  Manufacturer  Year  
Woodenworks  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  loop  Θ( 2^{m} )  
Remarks  Variants: CR032, CR145  
References  
CR107  Name  Pagoda  
[1] [2] [3] 
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  rings  397  
Remarks  The third picture shows the simpler variant "Tree Puzzle" by Puzzlemaster  
References  [1]; Reference Section [7] and [8]  
CR009  Name  Panex Gold  
Designer  Manufacturer  Year  
Toshio Akanuma  TRICKS  1983  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  20  slider  31537  
Remarks  Variant: CR035. Goal is to slide the pieces (without turning) to exchange the left and right stacks.  
References  [1], [2], [3]  
CR035  Name  Panex Silver  
Designer  Manufacturer  Year  
Toshio Akanuma  TRICKS  1983  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  20  slider  31537  
Remarks  Variant: CR009. Goal is to slide the pieces (without turning) to exchange the left and right stacks.  
References  [1], [2]  
CR128  Name  Panex Squared  
Designer  Manufacturer  Year  
John Haché  John Haché  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  12  slider  68  
Remarks  Variant of CR035 which includes overlapping and interacting Panex instances. As the original design was not solvable (as discovered by Bob Hearn), this puzzle has to be modified by removing the blocking mechanism in the center. Goals are: 1) to swap pieces horizontally (e.g. A and B), and 2) swap pieces vertically (e.g. A and C), obeying the Panex rules, i.e.: in the vertical grooves, no smaller piece can be below (i.e. closer to the center) than a larger piece, same for the horizontal grooves (no larger piece closer to the center, but for both sides of the groove). This modification was proposed by Diniar Namdarian in 2015. The solutions provided have 46 moves for swapping A and B, and 68 moves for swapping A and C.  
References  [1]  
CR113  Name  Pear  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  rings  62  
Remarks  
References  Reference Section [7] and [8]  
CR036  Name  Pharaoh's Dilemma  
Designer  Manufacturer  Year  
Mag Nif  1970  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  disc  
Remarks  Tower of Hanoi variant  
References  [1]  
CR109  Name  Phoenix  
[1] [2] 
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  16  rings  502  
Remarks  
References  Reference Section [7] and [8]  
CR119  Name  Pin Burr 2  
[1] [2] [3] [4] 
Designer  Manufacturer  Year  
Jerry McFarland  Jerry McFarland  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  burr pieces  Θ( 2^{m} )  38^{§}^{‡}  
Remarks  Binary sequence, which is nonGC based and uses a pinmazemechanism, a little trick was added corrupting the sequence and making it more interesting for the solver. The third picture shows the prototype, which has a simpler frame but same sequence, the last picture shows both puzzles.  
References  [1]  
CR186  Name  Planex  
Designer  Manufacturer  Year  
Goh Pit Khiam  JL Puzzles (Jerry Loo)  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  sliding block  42  
Remarks  Variant: CR035, CR009. This puzzle is basically a Panex puzzle with only 3 levels (6 pieces) instead of the 10 levels (20 pieces) of the Panex puzzles. Goal is to slide the pieces (without turning) to exchange the yellow and blue stacks.  
References  [1]  
CR126  Name  Power Tower  
[1] [2] [3] 
Designer  Manufacturer  Year  
Jack Krijnen, Goh Pit Khiam  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  burr sticks  3^{m}—m—1 ^{‡}  76^{‡}  
Remarks  Variants: CR136, CR167  
References  [1], reference section [12]  
CR136  Name  Power Tower (mixed base — variable stage)  
[1] [2] 
Designer  Manufacturer  Year  
Jack Krijnen, Goh Pit Khiam  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  6  burr sticks  2·(n^{m}—1)/(n—1)—m  7806  
Remarks  Variants: CR126, CR167; This Power Tower is a whole set with a block hosting up to 6 stages, a blocker piece to set the number of stages (between 3 and 5, 6 stages without blocker), and a set of pieces for each of the two orientations (two different woods). The pieces come in binary, ternary, and quaternary shape and can be combined arbitrarily, leading to mixed (or uniform) base sequences, which can be quite confusing. There are 1080 different possibilities, with the level varying from 11 to 2724. The solution length is for a uniform nary configuration with m pieces. Addition: This now includes an extension set of quinary pieces. The overall entry now contains these pieces and there are now solutions possible up to level 7806.The second picture shows this extension set.  
References  [1], reference section [12]  
CR141  Name  Power Box  
[1] [2] 
Designer  Manufacturer  Year  
Goh Pit Khiam  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panels  
Remarks  
References  reference section [12]  
CR032  Name  Puzzle H  
Designer  Manufacturer  Year  
Eureka 3D Puzzles  1997  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  loop  Θ( 2^{m} )  
Remarks  Variant: CR145  
References  [1]  
CR004  Name  PyraCircle  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2008  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  10  block  116  
Remarks  Variation of Panex, a nondisjoint union of several such puzzles; 116 is minimum number of moves  
References  [1]  
CR197  Name  Quadrupled Quadlooplet  
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  loop  3^{m}  81  
Remarks  This puzzle contains multople challenges, i.e. starting configurations of the loop: adjacent compartments or opposite compartments. The whole puzzle consists of four modules/sectors with four loops each. During the solution sequence, the loop bend will traverse through multiple sectors/modules. The solution works in several stages: First, remove one of the bends from the puzzle (steps 1 to 41), and then only one bend will be caught in the puzzle center. Then in the second stage, remove the other bend, which may be accomplished in several ways. Move the free bend into the puzzle via a different path so that both bends meet at the end and the rope can be pulled out, or remove the second bend like the first one before. The configuration vector will denote the position of the rope (bend) in the compartments defined by the layers of loops, counting them from innermost to outermost.During the solution, the rope will go through at most one of them at each time, leading to configurations of 0 to 4 (number of sectors/modules). The solution does not make use of all combinations, leading to a ternary solution path length. Other puzzles from the same series: CR196, CR198  
References  [1], [2]  
CR082  Name  Quatro  
Designer  Manufacturer  Year  
Eric Johansson  Eureka 3D Puzzles  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  loop  Θ( 2^{m} )  7  
Remarks  One of the solutions (reference 2) acts like Chinese Rings, please see reference 3. There are also other solutions.  
References  [1], [2], [3], [4]  
CR148  Name  Racktangle  
Designer  Manufacturer  Year  
Goh Pit Khiam  Tom Lensch  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  plate  
Remarks  Variable number of stages (1 to 4, box is built modular) and plates of base 2 and 3 included, which together with the solid plate for the lowest position, can be used to create all mixed base 2 and 3 puzzles for up to 4 stages.  
References  [1], [2], reference section [12]  
CR093  Name  Railing with Draining ternary  
[1] [2] [3] [4] [5] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  slider  
Remarks  
References  [1]  
CR173  Name  Reflection  
Designer  Manufacturer  Year  
DDK  Aaron (Yulong) Wang  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  9  pairs of rings  
Remarks  Variation directly created from Chinese Rings by attaching a small connector ring and a second bigger ring to each ring, below the first and around the same vertical rod. There are four states for each ring pair: main bar through lower ring (initial position), through upper ring, through both rings ("double ring"), and off the rings. All those appear in the solution, and the double ring configuration is used to mimic the classic binary chinese rings. The configurations with one ring on the loop appear exactly once in the solution sequence, and their transitions interrupt the binary sequence in a regular pattern and increase the number of moves considerably. This is one of six puzzles in the Chinese 99ring series.  
References  [1]  
CR155  Name  ReTern Key  
Designer  Manufacturer  Year  
Goh Pit Khiam  Charlie Rayner  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  slider  8 · 3^{m—1}—8·m+1  185  
Remarks  The full name is "The Return of Tern Key" and demonstrates a variant of CR125 without a long synchronizing slider piece. Variant: CR168  
References  reference section [12], [1]  
CR168  Name  ReTern Key with circular pieces  
Designer  Manufacturer  Year  
Fredrik Stridsman  Fredrik Stridsman  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  slider  
Remarks  Variant: CR155. The ReTern Key was the base for this puzzle, and the designer replaced the groups of small pieces running on the sides of the puzzle for synchronization by circular pieces.  
References  
CR189  Name  Reverse Chinese Rings  
Designer  Manufacturer  Year  
Aaron (Yulong) Wang  Aaron (Yulong) Wang  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  ring pair+connector  Θ(m·2^{m})  
Remarks  This puzzle looks like a chinese rings with all the rings put on the main handle backwards. At a closer look, each ring has a second ring attached at the bottom. To solve this puzzle, the bottom chain has to be solved like a standard chinese rings puzzle, and at the end of each run, one more ring from the reversed top chain comes off. While there are more than two states for each ring pair (4 states, each ring can be on or off the handle), the main sequence is binary, which is why it is classed binary here, and considered as chinese rings puzzle with some extensions.  
References  [1]  
CR021  Name  Rings Bottle  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2012  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  ring  
Remarks  
References  [1], [2]  
CR041  Name  Row to Row  
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  8  disc  Θ( 2^{m} )  
Remarks  
References  [1]  
CR007  Name  Rudenko Clips  
Designer  Manufacturer  Year  
Valery Rudenko  Roscreative  2011  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  7  clip  ( 3^{m}—1 )/2  1093  
Remarks  Tower of Hanoi with move restriction  
References  [1], [2], [3]  
CR019  Name  Rudenko Disc  
Designer  Manufacturer  Year  
Valery Rudenko  Roscreative  2011  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  7  disc  Θ( 2^{m} )  
Remarks  Tower of Hanoi with simplification  
References  [1], [2], [3]  
CR044  Name  Rudenko Matryoshka  
Designer  Manufacturer  Year  
Valery Rudenko  Roscreative  2011  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  7  slider  Θ( 2^{m} )  
Remarks  Tower of Hanoi equivalent  
References  [1], [2], [3]  
CR086  Name  Seestern  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
11  3  Layers  11^{m}—1  1330  
Remarks  
References  [1]  
CR190  Name  Second Order Chinese Rings  
Designer  Manufacturer  Year  
Aaron (Yulong) Wang  Aaron (Yulong) Wang  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  11  rings  
Remarks  While the rings in the classic Chinese Rings puzzle are linking their connector with the next connector each, in this one, each ring links its connector with the next two adjacent connectors. The solution is based on the Chinese Rings solution, and is in fact the same sequence like for the Dispersed GC lock CR074  
References  [1]  
CR001  Name  Short Big Sliding Lock  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  3  slider  2·5^{m}  250  
Remarks  AKA: Kleines dickes Schloss, Voidlock  
References  [1]  
CR064  Name  Six Bottles  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  slider+ball  4·(2^{m}—1)  252  
Remarks  Each metal ball can be in a topleft, bottomleft, or a bottomright position, and there are corresponding slider positions middle and top. The bottom slider position occurs only during transition of ball between left and right. A newer circular version replacing balls by switches is: CR083  
References  [1]  
CR011  Name  SlidingBlock Chinese Ringsstyle Puzzle  
[1] [2] [3] 
Designer  Manufacturer  Year  
Bob Hearn  2008  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  pair of yellow blocks  
Remarks  The second picture shows the different position of the special pieces, the pairs of yellow blocks in positions 0, 1, and 2. There are other positions not part of the solution. Recently, we found a shorter, nonternary solution that was not intended, with goal configuration in third picture; under investigation.  
References  [1], [2]  
CR142  Name  Slots and Pins (mixed base)  
Designer  Manufacturer  Year  
Goh Pit Khiam  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  slider  
Remarks  This version has mixed bases, i.e. binary and ternary pieces/piece parts.  
References  reference section [12]  
CR048  Name  Small CUBI  
Designer  Manufacturer  Year  
Akio Kamei  Akio Kamei  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  2^{m—1}  32  
Remarks  Variants: CR056, CR162. Mechanism is completely made out of wood, no metal (pins) used.  
References  [1], [2]  
CR022  Name  SpinOut  
Designer  Manufacturer  Year  
William Keister  Binary Arts  1970 / 2006  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  disc  [2^{m+1}/3] ^{§}  85 ^{§}  
Remarks  Version with elephants and reset shortcut, green/red/orange. There exists an unintended shortcut solution with 49 moves (see Jaaps's page below). Variants: CR026, CR050  
References  Variation on [1] (US Patent 3637215), [2], [3], [4], [5]  
CR050  Name  SpinOut  
Designer  Manufacturer  Year  
William Keister  Binary Arts  1970 / 1987  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  disc  [2^{m+1}/3] ^{§}  85 ^{§}  
Remarks  There exists an unintended shortcut solution with 49 moves (see Jaaps's page below); Variants: CR022, CR026  
References  [1] (US Patent 3637215), [2], [3], [4]  
CR026  Name  SpinOut  
Designer  Manufacturer  Year  
William Keister  ThinkFun  1970 / 2001  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  disc  [2^{m+1}/3] ^{§}  85 ^{§}  
Remarks  reset shortcut. There exists an unintended shortcut solution with 49 moves (see Jaaps's page below); Variants: CR022, CR050  
References  [1] (US Patent 3637215), [2], [3], [4]  
CR084  Name  Spiralschloss  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  shacklelayer  2·(n^{m}—1)  160  
Remarks  Mechanism similar to CR085. Goal: Open all shacklelayers completely.  
References  [1]  
CR083  Name  Steuerrad  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  8  slider+switch  3·2^{m}  768  
Remarks  Round variant of CR064. Goal: Move all handles to the outer position and reveal hidden message "Nicht durchdrehen", German for "do not get mad" and also referring to turning the steering wheel (German: Steuerrad)  
References  [1]  
CR025  Name  SuperCUBI  
[1] [2] [3] 
Designer  Manufacturer  Year  
Hiroshi Iwahara  Hiroshi Iwahara  2000  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  panel  324  
Remarks  First image shows newer version (opposite panels following in solution), second and third the older version (panels following in 90° turn order); Variant: CR165  
References  [1]  
CR165  Name  SuperCUBI (small)  
[1] [2] 
Designer  Manufacturer  Year  
Hiroshi Iwahara  Hiroshi Iwahara  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  panel  324  
Remarks  Smaller version of original SuperCUBI with adjacent panels moving on opposite sites. Comes with a solution leaflet showing all 324 moves, and additionally some instructions on how to calculate and identify the current configuration. Varaiant: CR025  
References  [1], [2]  
CR104  Name  Teapot  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  22  
Remarks  
References  Reference Section [7] and [8]  
CR002  Name  Tern Key  
Designer  Manufacturer  Year  
Goh Pit Khiam  Cubicdissection  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  switch  12·(2^{m})—12·m—10  134  
Remarks  
References  [1], [2], [3]  
CR005  Name  Ternary Burr  
Designer  Manufacturer  Year  
Goh Pit Khiam  Jack Krijnen  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  burr pieces  6·2^{m}—4·m—5 ^{§}^{‡}  75^{§}^{‡}  
Remarks  Move count includes control bar; Variant with only two frame pieces; Variants: CR055, CR095  
References  [1]  
CR055  Name  Ternary Burr  
Designer  Manufacturer  Year  
Goh Pit Khiam  Mr. Puzzle  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  burr pieces  6·2^{m}—4·m—5 ^{§}^{‡}  75^{§}^{‡}  
Remarks  Move count includes control bar; 95 moves for complete disassembly; Variants: CR005, CR095  
References  [1], [2], [3], [4], [5]  
CR095  Name  Ternary Burr  
Designer  Manufacturer  Year  
Goh Pit Khiam  Eric Fuller  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  burr pieces  6·2^{m}—4·m—5 ^{§}^{‡}  75^{§}^{‡}  
Remarks  Move count includes control bar; 95 moves for complete disassembly; Variants: CR005, CR055  
References  [1], [2]  
CR181  Name  The Bell  
Designer  Manufacturer  Year  
Juergen Reiche  Siebenstein  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  12  slider  881  
Remarks  Variant: CR035, CR009. This puzzle is basically a Panex puzzle with only 6 levels (12 pieces) instead of the 10 levels (20 pieces) of the Panex puzzles.  
References  [1]  
CR012  Name  The Binary Burr  
[1] [2] 
Designer  Manufacturer  Year  
Bill Cutler  Jerry McFarland  2003  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  burr pieces  ( (1)^{m+1} + 2^{m+2} ) / 3 ^{§}^{‡}  85^{§}^{‡}  
Remarks  Move count includes control bar; There is also a very rare 10 ring piece version, which is shown in the pictures; Variants: CR076, CR156  
References  [1]  
CR076  Name  The Binary Burr  
Designer  Manufacturer  Year  
Bill Cutler  Eric Fuller  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  burr pieces  ( (1)^{m+1} + 2^{m+2} ) / 3 ^{§}^{‡}  85^{§}^{‡}  
Remarks  Move count includes control bar; Variants: CR012, CR156  
References  [1], [2]  
CR156  Name  The Binary Burr (small)  
[1] [2] [3] [4] [5] [6] [7] [8] [9] 
Designer  Manufacturer  Year  
Bill Cutler  Maurice Vigouroux  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  10  burr pieces  ( (1)^{m+1} + 2^{m+2} ) / 3 ^{§}^{‡}  1385^{§}^{‡}  
Remarks  Move count includes control bar; the first picture shows the whole group of the Binary Burrs (small) with 3 to 10 special pieces, all with solid cage, the other pictures show the individual puzzles; Variants: CR076, CR012  
References  [1], [2], [3], [4], [5], [6], [7], [8]  
CR057  Name  The Brain  
[1] [2] [3] [4] 
Designer  Manufacturer  Year  
Marvin H. Allison, Jr.  MagNif  1973  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  switch  [2^{m+1}/3]  170  
Remarks  Pictures 2, 3, and 4, and reference 2 show the newer version  
References  [1], [2], [3], [4]  
CR096  Name  The Cat  
Designer  Manufacturer  Year  
William Keister  Binary Arts  1985  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  2  rings  
Remarks  
References  [1]  
CR097  Name  The Horse  
Designer  Manufacturer  Year  
William Keister  Binary Arts  1985  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  rings  
Remarks  
References  [1]  
CR058  Name  The Key  
[1] [2] [3] 
Designer  Manufacturer  Year  
Goh Pit Khiam  Walt Hoppe  2004  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  switch  40  
Remarks  Variant: CR063  
References  [1], [2]  
CR191  Name  Third Order Chinese Rings  
Designer  Manufacturer  Year  
Aaron (Yulong) Wang  Aaron (Yulong) Wang  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  13  rings  
Remarks  While the rings in the classic Chinese Rings puzzle are linking their connector with the next connector each, in this one, each ring links its connector with the next three adjacent connectors. This is a logical extension of CR190.  
References  [1]  
CR062  Name  Tower of Hanoi  
Designer  Manufacturer  Year  
Edouard Lucas  Philos (and others)  1883  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  disc  Θ( 2^{m} )  
Remarks  
References  [1], [2]  
CR105  Name  Trapeze  
[1] [2] [3] 
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  61  
Remarks  extra rings for symmetry; third picture shows puzzle Dingo Trap, a variant with the rings separated and held by smaller loops; reference [14] shows this variant including building instructions and solution  
References  [1], [2]; [3] (US Patent 4497489) Reference Section [7], [8], and [14] (p.109)  
CR144  Name  Tricky Frame  
Designer  Manufacturer  Year  
Philos  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  loop  Θ( 2^{m} )  
Remarks  Variant: CR072  
References  [1]  
CR145  Name  Tricky Mouse  
Designer  Manufacturer  Year  
Philos  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  loop  Θ( 2^{m} )  
Remarks  Variant: CR032  
References  [1]  
CR085  Name  Uhrwerk  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  ball/gear  2·(n^{m}—1)  160  
Remarks  Mechanism similar to CR084. Goal: Move the one ball with the special starting position to its third hole and remove (only) this ball from puzzle. The two pictures show second (more stable) and first edition.  
References  [1], [2]  
CR138  Name  Unknown Disentanglement  
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  loops  
Remarks  Choosing one of the sides, the consecutive loops on that side will act like a Chinese Rings puzzle. All other loops are not part of the solution.  
References  [1]  
CR152  Name  Viking Box  
Designer  Manufacturer  Year  
Sven Baeck, JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  switches  
Remarks  The basic mechanism of the box is a ternary mechanism consisting of discs with the switches attached and visible to the puzzler, and some ball bearings. These will move into some cutouts of the discs and block them in various positions, same general concept as in CR064. Additionally, there are two mechanisms interacting with several discs each: One visible as the bottom horizontal slider, the other hidden, but with its state visible through a small hole below the left disc. This mechanism and the ball bearings have to be manipulated via tilting. The lid contains the mechanism and is firmly closed. However, a second variant was released with a transparent top, allowing the puzzler to see most of the mechanism.  
References  [1]  
CR103  Name  Wheel  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  24  
Remarks  
References  Reference Section [7] and [8]  
CR183  Name  xBrain binary  
[1] [2] [3] 
Designer  Manufacturer  Year  
David Guo  David Guo  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  switch  [2^{m+1}/3]  42  
Remarks  This puzzle is based on: CR057. Variants: CR184 and CR185. The second picure shows the goal configuration (all sliders moved to the border), and the third picture a different colour variant in a configuration during the solution.  
References  [1]  
CR184  Name  xBrain ternary  
[1] [2] [3] 
Designer  Manufacturer  Year  
David Guo  David Guo  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  switch  2·3^{m — 1} — 1  485  
Remarks  This puzzle is based on: CR057. Variants: CR183 and CR185. The second picure shows the goal configuration (all sliders moved to the border), and the third picture a different colour variant in a configuration during the solution.  
References  [1]  
CR185  Name  xBrain quarternary  
[1] [2] [3] 
Designer  Manufacturer  Year  
David Guo  David Guo  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  6  switch  0.1 · (—1)^{m} + 0.4 · 4^{m} — 0.5  1638  
Remarks  This puzzle is based on: CR057. Variants: CR183 and CR184. The second picure shows the goal configuration (all sliders moved to the border), and the third picture a different colour variant in a configuration during the solution. The solution length function for the number of moves f(m) is a solution of the recursion f(m) = 3f(m1) + 4f(m2) +3 with f(0)=0 and f(1)=1 derived from solving the puzzle with m pieces.  
References  [1]  
This compendium contains a special collection of puzzles which are somehow related to the famous Chinese Rings puzzle. For a definition which puzzles are included in this compendium and for a clear understanding why they are included, we will provide a structural definition of the class of puzzles in this compendium, the CR recursive puzzles. We will provide a definition, with some examples, and with some interesting properties of these puzzles.
A CR recursive puzzle is a puzzle that contains m special similar pieces (with m ≥ 1) and

Note that beside the special pieces in the definition above, there may be other pieces. For a distinction from the others, the special pieces are sometimes called "ring pieces", in analogy to the classic Chinese Rings puzzle.
This is a short and formal definition related to the structure of the puzzle. Some examples might be useful.
In the picture, a typical wooden version of CR with 5 rings is shown. Each ring may be positioned (diagonally) on the horizontal loop or off the loop. These states may be denoted as: 1  on, 0  off the loop, so in this example we have:
To conclude the matching of the particular classic CR puzzle of this example with our definition of a CR recursive puzzle, we note that there exist many different classic CR versions, with various number of rings, that correspond to the different values of m in our definition of CR recursive puzzles.
In this puzzle, we have a slider carrying a line of discs. Each disc can be either in a vertical position (denoted by 0) or horizontal position (denoted by 1). This puzzle is equivalent to CR, if we restrict the moves to the ones that are used in the solution: From the vertical position, each disc can be turned left into the horizontal position, or to the right to a different horizontal position. We disregard this (right turned) position, as it is not needed for solving the puzzle. To see the uniform condition for this puzzle, we have a look at the pictures above and note: A disc can be turned between 0 and 1, if the disc immediately to the right is 0 (in vertical position) and all discs further right are 1 (in horizontal position). For the solution, two additional restrictions are implemented: Only a disc at the position with the additional space (second from the right) can be turned. Discs can only be moved out to the right when in position 1 (horizontal).
The Crazy Elephant Dance is a generalized version of SpinOut. Instead of discs, we have a line of 5 elephants on a slider, and each elephant has three possible states: 0  facing upwards, 1  facing to the right, and 2  facing downwards.
The uniform condition is split into two parts in this case: 1. An elephant (the second from the right in the picture) may move between 0 and 1, if the one immediately to the right is in position 2, and (not shown in the picture) all further right are in position 2.
2. An elephant (again the second one) may move between 1 and 2, if the one immediately to the right is in position 0, and (not shown) all further right are in position 2.
Again, as for the SpinOut, the second part of the conditions above arises from the fact that the slider and elephants may only move out to the right when in position 2.
The pictures demonstrating the two parts of the condition also show an example how to move the second elephant from 0 to 2: It first has to be moved from 0 to 1 (first two pictures), then the elephant to the right of it is moved from 2 to 0 (third picture), then the second elephant may finally move from 1 to 2. This gives an idea what is necessary to move the leftmost elephant from 0 to 2, which is a vital step in the solution sequence.
The Kugellager has four balls, which are the special pieces in our definition and one slider containing some mazes for these balls. The four balls move up and down (maze in the slider permitting, green arrows), and the slider moves left and right (blue arrow). Each of the balls has 5 regular positions {0,1,2,3,4} (or {1,2,3,4,5} in the picture), and then there is an additional position 5 (or 6 in the picture), which can only be used if all balls are already in position 4, to remove the slider afterwards. This is why we may disregard this position 5.
The pictures are taken from the article [1] which also describes the movement in more detail and also lists the uniform condition for ball movement. Shortly summarized, a ball may move between positions i and (i+1), if all balls to the left are in a certain set of positions and all balls to the right are in a certain (different) set of positions.
This puzzle can not only be generalized to more balls, as the definition requires, but also to a higher or lower level, as the Kugellager 7 puzzle (n=7), or the Auf dem Holzweg puzzle (n=3) show.
At first sight, Tower of Hanoi looks very different from the puzzles we have seen so far, but it is a CR recursive puzzle and complies to our definition: It has m discs (m=9 in the picture), and each of the discs can be on one of the three piles built on the poles, so n=3. There are different variants with different numbers of discs, so the generalization to other values of m (even other values of n with more poles) is easy. All these variants will have to obey simple rules: Move only one disc at a time, and only the top disc of a tower, and a disc may only be laid down on discs that are bigger than itself. The rules deliver the uniform condition we need for our CR recursive definition and can also be translated to: To move a disc, all smaller discs have to be on a pole different from the start and destination positions of the move.
The uniform definition covers a property that is independent of the actual number of pieces and also allows the same condition to apply to each one of them. This condition states that for all suitable indices i and j, piece number i can move between positions j and j+1 if and only if the "lower" pieces (left of i) and "higher" pieces (right of i) are in certain positions. This works independently of i: No matter if the second piece (i=2) or the fifth piece (i=5) is to be moved.
There are also puzzles for which the "higher" pieces are irrelevant, for example:
All puzzles contained in this compendium allow a recursive description of their solution. As an example, take the Tower of Hanoi. This puzzle has three positions, two of which are initially empty and one carries a stack of discs that are ordered from biggest in the bottom to smallest on top. The aim of the game is to move the stack of discs to the third position (whichever that may be) obeying the following two rules:
A typical Algorithm to solve this problem can be described informally as follows:
Move Tower of n discs from startTower to endTower:

This algorithm works by moving the n—1 top discs away on the auxiliary tower, then disc n, then the ones on the auxiliary tower to the destination tower.
What algorithm do we use in lines 3 and 6 in order to move an n—1 disc tower? It is our very same algorithm, that calls itself recursively, and now we have our justification to call this puzzle "recursive", as it can be solved by such a recursive algorithm. More details about Tower of Hanoi can be found e.g. here: [4]
While for this puzzle it may seem obvious, the question remains for the other puzzles: Why are the other puzzles in this compendium also recursive?
Well, this drills down to the core of the matter. What do all these puzzles have in common, and how are they related to the "classic" Chinese Rings puzzle? A first insight might be to look at a solution method for Chinese Rings. The goal of this puzzle is to remove all the rings from the loop.
This can be established by a recursive algorithm with the following ideas:

Before the formalization of the recursive puzzles as above, a different notation was used in prior discussions: "nary Puzzles". This notation has its roots in well known puzzles: Chinese Rings, The Brain, SpinOut, The Key, and Binary Burr. These are typically called "binary" puzzles, because their "ring pieces" have two different states each, and their solution length function are asymptotically 2^{m}. Ternary Burr, Tern Key, Crazy Elephant Dance are called "ternary" puzzles because they generalize the binary concepts to pieces having three different states. However, interestingly enough, their solution length functions are still asymptotically 2^{m}, which is a justification for our structural definition. Why ternary puzzles can have 2^{m} as solution length function is discussed below.
A mathematical argument for calling these puzzles "nary" is that their current state can be represented by an mtuple of entries ranging in {0,...,n—1}. For example, the SpinOut starting configuration would be: (0,0,0,0,0,0,0) and the goal configuration: (1,1,1,1,1,1,1). A solution could then be described as a sequence of such tuples:
A ternary example is the Crazy Elephant Dance, with the following encoding:
You may have noticed that In the definition of CR recursive puzzle we did not refer to the number of moves required to solve the puzzles, which is a central property in a different definition of the class of puzzles in this compendium (see discussion below). The number of moves seems related to the parameters in our definition, but no uniform relation has been determined for all the puzzles of this compendium, and this seems impossible, as we will see: The key count is the number of moves that the special pieces (or "ring pieces") move during the solution process. Similar to approaches in Computer Science, we will sometimes not provide an exact function of the number of moves, but will use an approximate notation. In such cases the exact number of moves might not have been calculated yet, but by analogy one has a strong indication what it could be like.
This notation describes the asymptotic growth and we are only interested in the fastest growing elements of this number of moves function. Following are some examples for this notation:
Exact function  Approximation  Note 

2^{m}+m+3  Θ( 2^{m} )  Linear and constant summands neglectable 
2 · 5^{n}  Θ( 5^{n} )  Constant factor neglectable 
2^{(m—1)}  Θ( 2^{m} )  2^{(m—1)}= (1/2)·2^{m}, constant factor neglectable 
3 · (2^{m}—1) — 2·m  Θ( 2^{m} )  Combination of examples above 
The Θ notation is taken from Computer Science and Mathematics, the formal definition and details are explained in [5].
Why do some CR recursive puzzles with n>2 have a solution with only ~2^{m} moves, not ~n^{m}? CR recursive puzzles with solution length ~n^{m} obviously use all different combinations of piece positions in their solution. To see this, just recall that the number of mtuples over a set with n different values is exactly n^{m} and so all these tuples occur in the description of the solution (see tuple representation above). So the puzzles in question that have solution length ~2^{m} will not use all these tuples in their solution, but leave some out. For example, on the (shortest) solution path for the Ternary Burr, you will never find a configuration corresponding to tuple (1,0,0,0)  this configuration is not needed. If you have this puzzle or the equivalent Crazy Elephant Dance, just try it out (with the lowest 4 elephants)! When you try the solution for on of these puzzles, you will find that directly before reaching this position, you will have the configuration (1,0,0,1)  which is not part of the shortest solution either  and this will be the only successor configuration after (1,0,0,1). Shortly said: only from (1,0,0,1) you reach (1,0,0,0), and your only option is going back to (1,0,0,0), and this is a detour way back from the solution from (0,0,0,0) to (2,0,0,0). Please see picture for these solution steps in the actual puzzle.
This effect occurs in several different puzzles, but what are the reasons for some puzzles to use all possible configurations, and for some others to omit configurations in their solution? Several reasons have been observed so far:
In the paragraphs above the relation between binary and ternary regarding the solution length has been discussed. There is also a binary representation that can be used for describing the solution of Tower of Hanoi, for details, please see [4].
Recently Goh Pit Khiam created a nice illustrated example of a variant of Tower of Hanoi: Linear Tower of Hanoi. In this variant, the three poles are in a line and a disc may only move from a pole to an adjacent pole. The obvious implications are that there are no direct moves between pole 0 and 2, and that a bigger disc may not move between poles 0 and 2, whenever there is a smaller one on pole 1. This makes it very similar to a Rudenko Clips (see previous section above). The less obvious implication is that the puzzle follows a ternary gray code. Please see [10] for the illustrated example of this puzzle, which also shows a nice ternary representation of Tower of Hanoi.
Our definition of CR recursive puzzle is based on the structure of the puzzle, which makes it (relatively) easy to spot if a puzzle belongs to this class. However, there is another different and commonly used definition of nary puzzles that first requires the puzzle to be analyzed and solved fully before it can be classified. Once one has determined that there are m special pieces and the solution length function is asymptotically equal to n^{m}, it is classified as nary (in this solution length based notation). We are using the structural definition provided above (as it seems easier to apply it in most cases), but there might be some confusion. Some ternary puzzles (our definition) may have a solution with (asymptotic) length 2^{m}, while the solution length function based definition would call them "binary" for this reason. One prominent example is the Ternary Burr by Pit Khiam Goh. This ternary (sic!) variation of the Binary Burr by Bill Cutler would be classified as binary following the solution length based definition.
[1] Goetz Schwandtner. Kugellager.pdf.
[2] Goetz Schwandtner. nary Puzzle Group.
[3] Ring of Linked Rings. Sydney N. Afriat. Gerald Duckworth & Co Ltd (November 1982). ISBN 0715616862
[4] Tower of Hanoi (Wikipedia).
[5] Theta Notation (Wikipedia).
[6] The Tower of Hanoi — Myths and Maths Andreas M. Hinz, Sandi Klavzar, Uros Milutinovic, Ciril Petr. Springer Basel 2013.
[7] Ingenious Rings. Yu Chong En and Zhang Wei. Beijing, 1999. The diagrams shown in the puzzle list of this Compendium for the Ingenious Rings Puzzles are taken from this book and were created by Wei Zhang.
[8] ChinesePuzzles.org: Ingenious Rings Wire puzzles
[9] ChinesePuzzle.org: Nine Linked Rings
[10] Goh Pit Khiam. The Linear Tower of Hanoi and the Ternary Gray Code.
[11] Goh Pit Khiam. Design of Nary Mechanical Puzzles. CFF95. Rijswijk, 2014. The next entry [12] is the most recent updated version
[12] Goh Pit Khiam. Design of Nary Mechanical Puzzles. (extended version, latest update 20141215; main updates are from page 28 on: The Power Box, Racktangle, Mixed Base Power Tower illustrated overview and simplification)
[13] New Book of Puzzles. Jerry Slocum and Jack Botermans. New York, 1992.
[14] Denkspiele der Welt. Pieter van Delft and Jack Botermans. München, 1977.
[15] Rik van Grol (Ed.). CFF 100 (Cubism For Fun 100). Rijswijk, 2016.
The idea for this compendium dates back a few years, and in 2012 first steps were taken for implementation, starting to collect data, searching for new puzzles and determining a common property to create a formal definition.
I wish to thank Dan Feldman for big support in the creation of this compendium during many discussions, with research on certain puzzles and editorial work on this compendium. My thanks also go to Nick Baxter and Michel van Ipenburg, with whom I had some detail discussions about the compendium and some puzzles included.
Of course I do not own all the puzzles and need pictures of puzzles that I do not have, of course observing the copyright. Thank you for picture contributions or puzzle samples for taking pictures to: Dan Feldman, Jack Krijnen, Namick Salakhov, Rob Stegmann, Dirk Weber, Yvon Pelletier, Claus Wenicker, Allard Walker, Michel van Ipenburg, Nick Baxter, Robert Hilchie, Kevin Sadler, Jerry McFarland, Stephen Miller, Jeremy Rayner, James Dalgety, and Fredrik Stridsman. Thanks to Jan de Ruiter for pointing out the similarity between Quatro and Chinese Rings. Thanks to Pit Khiam Goh for some interesting discussions around BurrTools models of the puzzles and for confirming some puzzle entry details, and also nice illustrations of puzzles and puzzle examples. Many thanks to the designers and craftsmen who provided some of their puzzles for my collection or some detail descriptions of the puzzles.
Ingenious Rings: Many thanks to Wei Zhang, Peter Rasmussen and Nick Baxter for providing me material on these wire puzzles, of which I selected the ones that seem to fit the definition well. Beside the book [7] they also have a nice web site [8] and [9] on this topic. (see references above)
This compendium is not a static collection of puzzles, but a dynamic overview which will be updated when new puzzles, new details, pictures or references are available. If you would like to send me some feedback on the compendium, submit additional material or information to be added, or update some entries, please send a mail to me:
Your feedback and contributions are welcome, so please do not hesitate. I am always interested to hear some interesting background stories about the puzzles.
If you are sending pictures for publication in the compendium, please clearly indicate that you are the holder of the rights on these pictures and that you allow the use in this compendium.