Compendium of Chinese-Rings-Like Puzzles


© 2013 by Dr. Goetz Schwandtner

1 Introduction

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].

Chinese Rings
Chinese Rings puzzle

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 "Chinese-Rings-like 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
SpinOut
Crazy Elephants Dance
Crazy Elephants Dance
Kugellager
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 "n-ary puzzle" was termed for these puzzles: [2]. This term n-ary was also used in a nice article [11] about designing n-ary puzzles which appeared in CFF 15 in November 2014. The most recent exteded version of this article can be found in [12].

1.1 Presentation of the Puzzles

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.

Puzzle-ID 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) or n' [n], see note below special pieces only of special pieces (m) exact or asymptotic (Θ) function of n and m counted/calculated
RemarksRemarks about special features, similar puzzles.
References
Symbols: §=counting moves of special pieces only; =counting moves until first piece comes out
Record Layout — Structure of each puzzle entry in the list

Note on the Arity: While n (and hence the arity) by Definition 3.1 in this compendium is the number of different positions each piece can have (including possibly the "removed" state if it occurs regularly during the n-ary sequence, not only at the end when all pieces are removed at once), there are puzzles, for which a generally accepted arity has been defined by the designer of the puzzle, and which is usually aligned to the solution length, and the base of the exponential function describing the solution lengths. In this cases, a bracket notation is used in the arity field for the defined arity n' and the number of levels n: n' [ n ]
For example, the Racktangle puzzle would have defined arity 3, yet the pieces have 5 different positions (two additional positions to ensure the solution length proportional to 3m), and this would be denoted by: "3 [5]".
If there are single pieces with different number of positions (e.g. when only one piece comes out of the puzzle in the n-ary sequence), then only the number of positions/levels for the majority is provided.

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 Ctrl-F 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.

1.2 Table of Contents/Sitemap

1   Introduction
1.1   Presentation of the Puzzles
1.2   Table of Contents/Sitemap
2   List of puzzles
3   Definitions, Examples and More
3.1   Definition of CR Recursive Puzzle
3.2   Examples
3.2.1   Classic CR puzzle
3.2.2   SpinOut
3.2.3   Crazy Elephants Dance
3.2.4   Kugellager
3.2.5   Tower of Hanoi
3.3   What does "uniform" mean in the definition?
3.4   Where does the term "recursive" come from?
3.5   Tuple Representation and a Different Notation: n-ary Puzzles
3.6   Puzzle Parameter and Different View: Number of Moves
3.7   CR recursive puzzles with solution length only ~2^m
3.8   Tower of Hanoi - binary or ternary?
3.9   A different definition for n-ary puzzles based on number of moves
4   References
5   Acknowledgements
6   Feedback

2 List of puzzles

Puzzle-ID 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) or n' [n], see note in Section 1.1 special pieces only of special pieces (m) exact or asymptotic (Θ) function of n and m counted/calculated
RemarksRemarks about special features, similar puzzles.
References
Symbols: §=counting moves of special pieces only; =counting moves until first piece comes out


CR226 Name4L Bin

[1]
[2] [3]
Designer Manufacturer Year
Goh Pit Khiam Tom Lensch 2021
Arity No of pieces Piece type Solution length function Number of moves
2 [4] 4 L-block 2m+1—2 30
RemarksVariant: CR237. Goal is to pack all the L-blocks into the box, which only has an opening at the top/front (and two smaller openings on the back/bottoms sides for handling of the pieces). The first 3 pieces can be packed into the box with a few moves, the last one requires a binary sequence (with additional auxiliary positions, e.g. like for CR126, CR136 and CR167). The pieces come in left and right handed shapes, two of each. The first and last pieces are different, with the required grooves and blocks only on one side.
References

CR237 Name5L Bin

[1]
[2]
Designer Manufacturer Year
Goh Pit Khiam Eric Fuller 2022
Arity No of pieces Piece type Solution length function Number of moves
2 [4] 5 L-block 2m+1—2 62
RemarksVariant: CR226. Goal is to pack all the L-blocks into the box, which only has an opening at the top/front (and two smaller openings on the back/bottoms sides for handling of the pieces). The first 4 pieces can be packed into the box with a few moves, the last one requires a binary sequence (with additional auxiliary positions. The pieces come in left and right handed shapes, two of each. There is no special first/last piece. Pieces can be rotated by 180° and then a change in the order of the solution can be observed, or a change in orientation, if the box is rotated as well after inserting the pieces.
References

CR214 Name5 times 5 times 5
Designer Manufacturer Year
Hiroshi Iwahara Hiroshi Iwahara 2020
Arity No of pieces Piece type Solution length function Number of moves
3 6 panel   125
RemarksVariant: CR212. This box has one compartment and follows the basic move scheme of CR172.
References

CR091 NameAlgorithme 9
Designer Manufacturer Year
Patrick Farvacque Patrick Farvacque  
Arity No of pieces Piece type Solution length function Number of moves
3 9 discs    
RemarksThe 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

CR174 NameAlken/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 [4] 6 panel   321
RemarksVariant 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 6-ary (321 moves) in the other. Kenal has a binary (135 moves) and 4-ary (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 re-inserting 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

CR127 NameAlles Schiebung
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2014
Arity No of pieces Piece type Solution length function Number of moves
2 6 slider   42
RemarksAdditional locking mechanism; AKA: Sternary
References

CR212 NameAquarius Box (small)
Designer Manufacturer Year
Hiroshi Iwahara Hiroshi Iwahara 2019
Arity No of pieces Piece type Solution length function Number of moves
3 6 panel    
RemarksVariant: CR214. This box has two compartments and follows the basic move scheme of CR172. In this puzzle, there are two chains of 3 panels each, in two different species of wood. The first one opens the first compartment, but somewhere in the middle of the sequence with a special move also unlocks the starting move for the second chain of panels. It is up to the puzzlers choice which compartment to open first, both ways work.
References

CR172 NameAquarius 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
RemarksFive 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

CR061 NameA Slide-ly Tricky Tower

[1]
[2] [3] [4]
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( 3m ) 485
RemarksDifferent movement schemes by using additional blocking pieces to block the tunnel for some larger sizes of the blue sliding pieces. In the worst case (all blocking pieces), it has 2·3m—1—1 moves. Other cases have just Θ(2m) moves. The configuration without blocking pieces is equivalent to Tower of Hanoi (obeying the rules!), while the one with all blocking pieces is equivalent to a one-tower Panex.
References

CR046 NameApricot
  Designer Manufacturer Year
Akio Kamei Akio Kamei 2002
Arity No of pieces Piece type Solution length function Number of moves
2   panel    
Remarks 
References

CR023 NameAuf dem Holzweg
Designer Manufacturer Year
Juergen Reiche Siebenstein 2011
Arity No of pieces Piece type Solution length function Number of moves
3 4 slider    
RemarksTwo arity 3 puzzles in one
References

CR177 NameBald Eagle
Designer Manufacturer Year
DDK, Aaron (Yulong) Wang Aaron (Yulong) Wang 2017
Arity No of pieces Piece type Solution length function Number of moves
1 [2] 5 ring+connector Θ( m )  
RemarksGoal 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 zig-zag chain of rings on the main loop looks like the structures used in others of Aaaron's n-ary puzzles.
References

CR039 NameBarcode 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 2m+1—4 124
RemarksVariants: CR137, CR199; some shortcuts exist
References

CR137 NameBarcode Burr (3D printed)
Designer Manufacturer Year
Lee Krasnow Steve Miller 2014
Arity No of pieces Piece type Solution length function Number of moves
2 6 burr piece 2m+1—4 124
Remarks3D printed reproduction of CR039 in limited run; variant:CR199. Each of the six pieces is printed as one piece and has some additional metal pins.
References

CR199 NameBarcode Burr (3D printed, Master Sets)

[1]
[2] [3] [4]
Designer Manufacturer Year
Lee Krasnow, Derek Bosch Lee Krasnow/pacificpuzzleworks 2018
Arity No of pieces Piece type Solution length function Number of moves
4 6 burr piece Θ(4m) 1233
Remarks3D printed reproduction of CR039 by original designer; variant:CR137. Each of the six pieces is assembled from three 3D printed pieces (one silver, two black), and some screws. The second picture and second reference show the add-on to the "Master Set", which contains an additional set of body pieces, so that two full cubes can be built in parallel, an extra bronze colored piece for keeping track of the orientation, and additional inserts, so that the following puzzles can be built: Barcode burr (black, binary, by Lee Krasnow), TernCode Burr (orange, ternary, level 115, by Derek Bosch), QuadCode Burr (yellow, quarternary, level 1233, by Derek Bosch), SuperCode Burr (red, level 81.38.11.11.6, by Lee Krasnow), ExtremeTortureCode Burr (white, red, orange, level 139.6.1.17.6, by Lee Krasnow and Derek Bosch), CoordiCodeBurr (blue, coordinate motion and binary mixed, level 7.5.3.4.1, by Lee Krasnow). The third picture shows the paperwork coming with this puzzle, including some overview, detail cards for each puzzle, an assembly guide, a hint and solution guides, solution (Grey code printed in shades of grey), and diagram plans that can be used to keep track of the maze positions during the solution, for which some small nuts are included as markers. In the beginning of 2019, some more inserts were designed by Lee for his BarcodeBurr, but with a focus on coordinate motion and shorter, less regular solutions, not the long n-ary sequences. This set can be seen in the fourth picture and third reference.
References

CR257 NameB-Bar
Designer Manufacturer Year
Felix Davis FADplus 2023
Arity No of pieces Piece type Solution length function Number of moves
2 8 slider 2m 256
RemarksGoal of this counter is to run through all 256 configurations, starting from 00000000 via 11111111 to the goal of 10000000. The synchronizing mechanism can be seen through the open back side and works a bit like the CR057. The configuration shown in the picture is a few moves into the solution.
References

CR160 NameB-Box

[1]
[2]
Designer Manufacturer Year
Goh Pit Khiam Eric Fuller 2016
Arity No of pieces Piece type Solution length function Number of moves
2 [4] 6 panel   135
RemarksThis 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

CR115 NameBicomplementary 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
RemarksV1, 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 n-ary scheme and with half-notches. The number of moves contains the binary sequences and some of the burr like moves.
References

CR134 NameBi-Nary

[1]
[2]
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2014
Arity No of pieces Piece type Solution length function Number of moves
3 4 slider-pair+ball   259
RemarksThis 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

CR247 NameBinary Disk

[1]
[2] [3] [4]
Designer Manufacturer Year
Oskar van Deventer Oskar van Deventer 2023
Arity No of pieces Piece type Solution length function Number of moves
2 8 sliding knobs    
RemarksThere is also a video referenced [2] below with the description. Goal of the puzzle is to slide the coloured knobs to their corresponding positions with the same colours indicated in the frame, and with the line/arrow indicator of the bronze disk segment pointing to the target colour, consequently there are 8 challenges, one for each colour. The coloured/rainbow knobs each have their own groove in the top and bottom. There is a central disk consisting of two segments (bronze, golden coloured), and a rainbow knob can only move to the other end of its channel, if one of the two gaps between the golden/bronze slider disk segments is adjacent. The red and blue knobs have special grooves that stay on the inner/outer ring, and they can be moved either with one of the two gaps between the disc segments, or using the special cutouts in the bronze segment surrounded by a half circle indicator. The interaction between the two disk segments and the knobs are the main aspect of the puzzle. Each move of a rainbow knob will also move the two golden/bronze segments, and unlock other moves (or block some). The channels for the two green knobs, yellow and orange are oriented in parallel, the purple and pink ones in the opposite direction, and then there are the special blue/red ones mentioned before. In some cases it is also possible to move two knobs simultaneously, one of red/blue, and one of the others, adding further complexity. The additional pictures [2] to [5] above show some more details for the construction, also the reset feature of unscrewing knobs. The two disk segments are kept in place by magnets, and more magnets are used for keeping the knobs in their end positions. The original design by Oskar is from May 1988, but only recently 3D printing enabled the construction of prototypes, also for optimizing the channel layout, and the initial design had all of them oriented in parallel. Unscrewing the knobs it is possible to set up random starting configurations (with each knob in its channel of the same colour) and there are some completely blocked. It has yet to be determined if any configuration with at least on possible move will be a solvable starting configuration.
References

CR006 NameBin 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
RemarksPartially ternary and modified sequence
References

CR150 NameBin 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    
RemarksAdditional 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

CR073 NameBinary 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( 2m )  
RemarksGoal: start with all 6 petals having the small protrusion poiting to the top (picture [1]), and find a sequence so that sll end up with the protrusions inside the puzzle (picture [5]). Each petal has two different orientations, the starting one with the protrusion pointing upwards, and the goal one rotated so that the protrusion points inwards. Each petal interlocks with the next petal. For all but one petal, the starting orientation will allow the next one to move, the other orientation blocks the next petal. There is one petal that has locking and unlocking swapped between the two orientation. Additionally, all petals interact with the white part of the rotator on top, which allows two neighboring petals to move, and blocks all others. The puzzle contains different challenges: In the starting configuration (all protrusions pointing up), the central column can be pushed upwards and then the rotator on top be rotated for one of the 6 challenges. One of these challenges only allow one move and is othewise unsolvable, the others different solution sequences. One allows a genuine binary sequence of all six petals, the others modified sequences with shortcuts.
References

CR169 NameBinary Ladder Disentanglement
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin  
Arity No of pieces Piece type Solution length function Number of moves
2 6 ring    
RemarksName unknown; this version is of early 1990s or shortly before.
References

CR063 NameBinary 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 16 [—7·(—1)m+2m+4—9] 85
RemarksVariation of CR058
References

CR207 NameBlack Bow-Tie

[1]
[2] [3]
Designer Manufacturer Year
Aleksandr Leontev Aleksandr Leontev 2019
Arity No of pieces Piece type Solution length function Number of moves
9 4 blocks 2·9m 13122
RemarksVariant: CR215. The puzzle consists of a sleeve with 4 mazes, and 4 block pieces with the goal to remove these 4 block pieces. The maze and sequence is inspired by the Kugellager puzzles, and this could be called a 9-ary Kugellager. During the solve, the maze can only be seen partially (from the bottom, like in the third pictures), and it is a partially blind solve (while the piece positions can be seen clearly).
References

CR163 NameB-Nary
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2016
Arity No of pieces Piece type Solution length function Number of moves
3 4 slider Θ( 3m ) 220
RemarksThe 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

CR182 NameBuggin
Designer Manufacturer Year
Stuart Gee Stuart Gee 2017
Arity No of pieces Piece type Solution length function Number of moves
2 6 loop    
RemarksVariant 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

CR248 NameCaged Stairs
Designer Manufacturer Year
Ad van der Schagt Hobbytik 1999
Arity No of pieces Piece type Solution length function Number of moves
2 [4] 3 ring pairs    
RemarksGoal is to remove the rope from the frame. There are pairs of rings, each consisting of a ring mounted to the top bar, and one mounted to the bottom bar. The puzzle is based on CR032 by adding the top half (left on the picture) introducing additional restrictions. The solution is roughly binary, but one has to choose the correct ring of each pair and will traverse the rings multiple times. The rope can go through no ring of a pair, each of the rings, and both rings, accumulating to 4 different possibilities for each pair. Designed for IPP19 as an unofficial exchange puzzle.
References

CR166 NameCast Infinity
Designer Manufacturer Year
Vesa Timonen Hanayama 2016
Arity No of pieces Piece type Solution length function Number of moves
6 2 disc    
RemarksTwo interlocking discs which can rotate between six positions and can move up and down. Objective is to remove the discs.
References

CR059 NameChinese Rings 5

[1]
[2] [3]
Designer Manufacturer Year
     
Arity No of pieces Piece type Solution length function Number of moves
2 5 ring [2m+1/3] 21
RemarksVariants: CR042, CR208. The pictures 2 and 3 show other versions with 5 rings. Reference [14] shows a 7 ring variant including solution.
References

CR042 NameChinese Rings 9
Designer Manufacturer Year
     
Arity No of pieces Piece type Solution length function Number of moves
2 9 ring [2m+1/3] 341
RemarksVariants: CR059, CR208
References

CR208 NameCatacombs / Chinese Rings 12
Designer Manufacturer Year
  Puzzlemaster.ca  
Arity No of pieces Piece type Solution length function Number of moves
2 12 ring [2m+1/3] 2730
RemarksVariants: CR042, CR059
References

CR202 NameChinese Soft Rings

[1]
[2]
Designer Manufacturer Year
Jim Wu, Aaron Wang Aaron Wang 2018
Arity No of pieces Piece type Solution length function Number of moves
2 7 rope loop Θ( 2m )  
RemarksVersion with red and white rope loops was introduced at IPP39 (Design Competition, Exchange with Dirk Weber). The IPP version had 3 loops in the base configuration, and others added as additional challenge. A version with more rings and 7 loops in two colors was offered for sale on-line, with additional challenges: Loop with 4 rings and (one or) two rope loops in between each, star shaped with 3 rings and binary chains of 2 loops meeting in a common additional rope loop in the middle, and star shaped with 4 rings and 4 binary chains (2 of length 1, 2 of length 2).
References

CR236 NameCoherent Convoys
Designer Manufacturer Year
Namick Salakhov, Goetz Schwandtner Namick Salakhov 2021
Arity No of pieces Piece type Solution length function Number of moves
3 14 ships Θ( 2m ) 296
Remarks The plastic body of this puzzle contains two channels (red, blue), and a lock chamber in between, with two gates between the lock and each of the channels and an acrylic cover with 14 ship pieces sliding in grooves in the cover. Ships can move between the channels and the sluice chamber depending on the configuration of ships. Ships can open one or the other gate for another ship to pass. There are several challenges which can be be set up by adding one of the spacer pieces into the lock chamber. The challenges from the Design Competition version are: (#1, 100 moves) Move all ships from the starting (blue) channel through the lock (gray channel) and into the red channel. (#2, 126 moves) Add the small spacer at the blue end of the lock, then move all ships from the red channel to the blue channel, except that the guard ships (light red and light blue) will remain in the lock. (#3, 296 moves) Add the large spacer at the red end of the lock (remove the small spacer), then move all ships from the blue channel to the red channel, again leaving the guard ships in the lock. This version of the puzzle has two extra spacers for additional challenges, which add up to 21 possible challenges in total. The puzzle won the first prize in the 2021 IPP Design Competition. A simpler ancestor is CR210.
References

CR123 NameComplementary p-arity

[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
RemarksComplimentary combination of several different sequences: Top 5 bars run in a 3-ary sequence, together with the 5 bottom bars, who run (slower) in a 2-ary sequence. These interact with the 4 loop-pieces, which run accross in a 3-ary 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

CR054 NameComputer Loops
Designer Manufacturer Year
  Mag-Nif 1975
Arity No of pieces Piece type Solution length function Number of moves
2 8 ring [2m+1/3] 170
Remarks 
References

CR031 NameComputer 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( 2m )  
Remarks 
References

CR034 NameComputer Puzzler No 5

[1]
[2]
Designer Manufacturer Year
  Tenyo  
Arity No of pieces Piece type Solution length function Number of moves
2 4 loop    
Remarkswas No 3 earlier; Variants: CR003, CR013, CR024, CR045, CR081, CR122
References

CR010 NameCrazy 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·(2m—1)—2·m 83
RemarksThe second and third pictures show the original prototype of the puzzle.
References

CR219 NameCrazy Elephant Dance (3D printed)

[1]
[2] [3]
Designer Manufacturer Year
Markus Goetz, Samuel Farinas Samuel Farinas 2019
Arity No of pieces Piece type Solution length function Number of moves
3 7 lever 3·(2m—1)—2·m 367
Remarks3D printed design based on CR010. Goal is to run through the ternary sequence (like shown in second picture) and then to get all elephant pieces pointing downwards, to remove the slider from the frame (third picture).
References

CR175 NameCorn on the Cob I
Designer Manufacturer Year
  Aaron (Yulong) Wang 2017
Arity No of pieces Piece type Solution length function Number of moves
2 [4] 9 ring pairs Θ( 2m )  
RemarksThis 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

CR178 NameCorn 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 [4] 9 ring pairs Θ( 2m )  
RemarksThis 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

CR188 NameCorn 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 [4] 9 ring pairs Θ( 2m )  
RemarksLike 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 zig-zag 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 re-assembly (entanglement): When the handlebar is at the rightmost free/zig-zag ring pair, it should break the rule before and go through the zig-zag ring.
References

CR203 NameCorn on the Cob IV
Designer Manufacturer Year
Jianjiang Wu, Aaron Wang Aaron (Yulong) Wang 2018
Arity No of pieces Piece type Solution length function Number of moves
2 [6] 9 ring pairs Θ( 2m )  
RemarksThis fourth puzzle of the series is basically a binary puzzle like the others. The rings are occurring in pairs again, and one ring is part of a zig-zag backbone, while the other ring is only attached to one connector and can be on the main handle or off. The zig-zag character of the main chain makes it difficult to determine the correct orientation of the free rings, but after some analysis it is easy to see that only one orientation will work for each ring. This can be visualized by creating little "huts" of four rings each: two backbone rings for the roof, and two free rings for left and right wall. The handlebar can freely pass through such a "hut". During the solution, the binary sequence is traversed a couple of times with the main aim to unlock all rings up to the last ring (all of them sitting on the handle in wrong orientation initially) and transform the chain into a hut only shape; then the handlebar can be pulled out completely.
References

CR204 NameCorn on the Cob V
Designer Manufacturer Year
Aaron Wang Aaron (Yulong) Wang 2018
Arity No of pieces Piece type Solution length function Number of moves
2 [4] 9 ring pairs Θ( 2m )  
RemarksThis fifth puzzle of the series is basically a binary puzzle like the other, and for this one it is more apparent: There are 9 pairs of rings each connected via the usual connector, but in a zig zag pattern each two adjacent are connected via a small additional ring. With this modification, the two rings of each pair assume roles, and while the ring next to the small additional ring only serves as secondary ring only sitting on the main handlebar when the pair is in the initial state, the other ring is part of a binary chinese rings chain. The main challenge is to choose the right ring of each pair (after unlocking both for the first time), and then perform a classic chinese rings solution sequence, just in a zig zag fashion.
References

CR206 NameCorn on the Cob VI
Designer Manufacturer Year
Jianjiang Wu, Aaron Wang Aaron (Yulong) Wang 2018
Arity No of pieces Piece type Solution length function Number of moves
2 16 rings Θ( 2m )  
RemarksThis sixth puzzle in the series is an easier one, and actually a direct variation of the classic Chinese Rings puzzle. There are two main frame bars on top and bottom, and the usual long handlebar in the middle, going through all the rings. The first pair of rings is simply attached to the end of the frame bars, and then the other attached via connectors to these frame bars, like in a Chinese Rings puzzle. These two copies from top and bottom are interweaved so that there are top and bottom rings in an alternating way, and additionally the connectors go though the adjacent ring of the opposite chain. That way, both chains have to be solved simultaneously and actually form one big chain of Chinese Rings of 16 rings, taking many moves to solve.
References

CR047 NameCross 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 2·5m 1250
RemarksVariants: CR120, CR121, CR158
References

CR120 NameCross 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 2·5m 1250
RemarksReproduction based on the original patent; Variants: CR047, CR121, CR158
References

CR121 NameCross 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 2·7m 4802
RemarksVariants: CR047, CR120, CR158
References

CR140 NameCrossing

[1]
[2]
Designer Manufacturer Year
Jack Krijnen Jack Krijnen 2014
Arity No of pieces Piece type Solution length function Number of moves
2 4 sliding piece    
RemarksGoal: slide the pieces so that the left black L shape ends up in the bottom left corner
References

CR056 NameCUBI
  Designer Manufacturer Year
Akio Kamei Akio Kamei 1985
Arity No of pieces Piece type Solution length function Number of moves
2 6 panel 2m—1 32
RemarksVariant: CR048, CR162
References

CR092 NameDelirium

[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 (2m+2—1 — (m mod 2))/3 357913941
RemarksSimplified 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

CR154 NameDelirium 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 (2m+2—1 — (m mod 2))/3 5461
RemarksSimplified version of: CR012, CR076. Reference 1 shows form for arbitrary many special pieces. Variant: CR092
References

CR250 NameDevil
Designer Manufacturer Year
Stephan Baumegger Stephan Baumegger 2023
Arity No of pieces Piece type Solution length function Number of moves
7 6 sliding panel   663
RemarksGoal is to remove the 6 plates of this interlocking box. All the plates have a wooden pin running in grooves in the neigboring plate (one plate without groove), and these grooves have different shapes and create mixed-base mazes of arity 7 and lower. Not only have the mazes different number of levels/arity, but also different lengths, which influences the interaction with the neighbors and makes the solve more challenging. Additionally, there are some initial moves required before the long n-ary sequence starts. Missing these moves will lead to a sequence ultimately ending up in a dead end situation. The panels have some engraving of the mazes on the outside to serve as a map for solving, and there are holes in the frame sides to have a (partial) look at these engravings. At the beginning the plates are well aligned by each other, but after a while some of the plates are partially extracted and don't provide this alignment guidance to their neighbors. Not taking care of the alignment in these situations can lead to slight tilting of the plates and may also cause skipping of moves. This puzzle was inspired by puzles like CR174. Variant: CR258
References

CR075 NameDevil'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 3m — 1 80
Remarks Variants: CR014, CR030, CR067, CR068, CR069, CR070
References

CR060 NameDie Welle
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2010
Arity No of pieces Piece type Solution length function Number of moves
5 3 ball 5m—1 124
Remarks 
References

CR124 NameDigi Fork Lock

[1]
[2] [3] [4]
Designer Manufacturer Year
Namick Salakhov Namick Salakhov 2014
Arity No of pieces Piece type Solution length function Number of moves
4 5 slider    
RemarksEnhancement of CR093. The first two pictures show the enhanced version built in 2021, with an improved mechanism and some additional design elements, the other two pictures were taken directly of the IPP34 design competition entry at IPP34. The goal is to remove the long slider in the bottom of the picture.
References

CR159 NameDigits' 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
RemarksGoal 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 different-length 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

CR158 NameDisc & 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 2·3m 54
RemarksLimited edition of 500 that was a gift with CFF issue 100. Variants: CR047, CR120, CR121
References

CR192 NameDisordered 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    
RemarksWhile 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

CR074 NameDispersed 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
RemarksCode corresponds to setting 1100 of CR020
References

CR143 NameDITWIBIN

[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( 2m )  
RemarksOne 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

CR170 NameDouble 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
RemarksThis 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

CR194 NameDouble 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    
RemarksThe 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

CR135 NameDouble Loop
Designer Manufacturer Year
     
Arity No of pieces Piece type Solution length function Number of moves
3 2 loop pairs 3m — 1 8
RemarksVariant: CR067 (other variants see there)
References

CR101 NameDragonfly

[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
Remarksextra rings for symmetry; second picture shows Airplane puzzle
References

CR146 NameDrunter & Drueber
Designer Manufacturer Year
Juergen Reiche Siebenstein 2015
Arity No of pieces Piece type Solution length function Number of moves
2 4 loop Θ( 2m )  
Remarks 
References

CR014 NameElectro 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 3m — 1 26
RemarksThe second picture shows an unknown variant. Variants: CR030, CR067, CR068, CR069, CR070, CR075
References

CR015 NameElectro 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

CR153 NameElephant 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    
RemarksVariant of: CR031 with a more irregular shape. The instructions lists 11 different starting positions as challenges.
References

CR198 NameEntwined 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( 3m ) 80
RemarksThis 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 7-ary 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 5-ary, and the actual solution length is 3-ary. 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

CR245 NameEurofalle 8 / Auf dem Holzweg
Designer Manufacturer Year
Juergen Reiche Siebenstein 2022
Arity No of pieces Piece type Solution length function Number of moves
3 4 slider    
RemarksVariant of: CR023, Two arity 3 puzzles in one. Goal is to remove the top slider and extract the coin.
References

CR071 NameExpansion 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 2m—1+3 35
RemarksSimpler variant of: CR094
References

CR094 NameExpansion 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( 2m ) 83
RemarksMore complicated variant of: CR071
References

CR157 NameExtended Chinese Rings
Designer Manufacturer Year
Ruan Liuqi Bob Easter  
Arity No of pieces Piece type Solution length function Number of moves
2   rings Θ( 2m )  
RemarksVarious extended Chinese Rings, based on the designs from the book given in the references section. These designs are e.g.: CR108, CR110, CR111
References

CR228 NameFaraday Cage
Designer Manufacturer Year
Heping Gao Heping Gao 2021
Arity No of pieces Piece type Solution length function Number of moves
2 6 loop    
RemarksGoal is to remove the rope with the wooden ball. The sequence is similar to some classic loop and rope based n-ary puzzles.
References

CR072 NameFerris Wheel
Designer Manufacturer Year
Jean Carle Eureka 3D Puzzles
Arity No of pieces Piece type Solution length function Number of moves
2 3 loop    
RemarksVariant: CR144
References

CR147 NameFibula 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

CR052 NameFidgety 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( 2m ) 170
RemarksVariant: CR018
References

CR018 NameFidgety 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( 3m ) 230
RemarksVariant: CR052
References

CR129 NameFind my Hole
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2014
Arity No of pieces Piece type Solution length function Number of moves
3 3 discs    
RemarksThis 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

CR098 NameFish

[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
RemarksThe first picture shows the "Wicked Wire" version by Professorpuzzle.
References

CR161 NameFishing Hook Chain 9-Ring
Designer Manufacturer Year
DDK Aaron (Yulong) Wang 2016
Arity No of pieces Piece type Solution length function Number of moves
3 9 rings+loops    
RemarksThe 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

CR114 NameFootball
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

CR110 NameFortune
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

CR081 NameFrame & 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 NameFrame & 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    
RemarksVariant of Computer Puzzler No 5; Variants: CR003, CR013, CR034, CR045, CR081, CR122
References

CR003 NameFrame & 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

CR122 NameFrame & 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

CR045 NameFrame & 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 Re-released for IPP34 Exchange; Variants: CR003, CR013, CR024, CR034, CR081, CR122
References

CR013 NameFrame & 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    
RemarksVariants: CR003, CR024, CR034, CR045, CR081, CR122
References

CR079 NameFrequency 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·(m2+2·m—1) 28
RemarksVariants: CR080, CR090 older design, but first made in this version in 2012
References

CR080 NameFrequency 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·(m2+2·m—1) 56
RemarksVariants: CR079, CR090 older design, but first made in this version in 2012
References

CR090 NameFrequency 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·(m2+2·m—1) 92
RemarksVariants: CR079, CR080, second picture shows solved state, older design, but first made in this version in 2012
References

CR229 NameGears Box

[1]
[2]
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2021
Arity No of pieces Piece type Solution length function Number of moves
4 7 sliders and gear rows    
RemarksGoal is to open the box. For this, first the additional cover needs to be removed and then the n-ary sequence has to be performed so that all gears are in the position allowing the sliders to move freely. Pushing the sliders near the top position, the locking mechanism can be slid sideways and then the lid be taken off. The sliders have 3 positions each (and are therefore ternary), the gears have 4 positions each (therefore quaternary) and the gears are linked in rows while the rows can rotate independently. This puzzle revisits the general maze ideas of some other puzzles by the same designer, but the overall design is a new one. For closing the top lid, the gears and sliders need to be in their initial positions, which is enforced by pins and the structure of the lid. The second picture shows the puzzle in mid solution and the upper lid removed and lying behind the box.
References

CR089 NameGC 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
RemarksGoal is to move all switches to the "far out" position
References

CR065 NameGeneration Lock

[1]
[2]
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2013
Arity No of pieces Piece type Solution length function Number of moves
15 8 slider 2·15m—1 341718750
Remarkssecond picture shows comparison with CR037; Variant: CR037
References

CR067 NameGordian Knot
Designer Manufacturer Year
  Eureka 3D Puzzles  
Arity No of pieces Piece type Solution length function Number of moves
3 2 pair of loops 3m — 1 8
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

CR068 NameGordian 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 3m — 1 2
Remarks The second picture shows a variant built by Jan Sturm (new in 2014). Variants: CR014, CR030, CR067, CR069, CR070, CR075
References

CR069 NameGordian 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 3m — 1 8
Remarks Variants: CR014, CR030, CR067, CR068, CR070, CR075
References

CR070 NameGordian 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 3m — 1 26
Remarks Variants: CR014, CR030, CR067, CR068, CR069, CR075
References

CR112 NameGourd
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

CR118 NameGrydlock

[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 3m/2—1 242
RemarksThe puzzle can be built with various slider shapes, leading to different mazes. Most of them are not n-ary, like the one shown in the pictures. Several puzzles have been implemented as online version (see reference [2]), an n-ary one has also has been implemented — please see reference [3], and for this the solution length and other details are provided here.
References

CR108 NameHappiness
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

CR043 NameHanui
  Designer Manufacturer Year
Yoshiyuki Kotani   1994
Arity No of pieces Piece type Solution length function Number of moves
3 5 U piece 3m—1·2i—1 242
RemarksPiece i not allowed on middle position; 242 moves for i=biggest piece
References

CR020 NameHexadecimal 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( 2m ) 170§
RemarksBinary and 170 move sequence for setting 1110; Variants: CR040, CR066
References

CR040 NameHexadecimal 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( 2m ) 170§
RemarksBinary and 170 move sequence for setting 1110; Variants: CR020, CR066
References

CR066 NameHexadecimal 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( 2m ) 170§
RemarksBinary and 170 move sequence for setting 1110; Variants: CR020, CR040
References

CR195 NameJack-in-the-Box

[1]
[2]
Designer Manufacturer Year
Jack Krijnen Jack Krijnen 2017
Arity No of pieces Piece type Solution length function Number of moves
3 [5] 4 wheel    
RemarksFrom the description: It's sequential discovery, it's riddle solving, it's ternary and in the end it's challenging. The ternary puzzle inside is used as a lock for one of the sliding panels and consists of 4 wheels with pins and rails. These wheels are basically a round version of the stick pieces of CR126, and like in that puzzle, the wheels only interact locally with their immediate neighbors and not requiring any synchronizing piece. The wheels are arranged in an alternating pattern of 3 layers (1 middle layer, 2 wheel layers). The goal is to rotate all pieces as far anti-clockwise as possible to unlock a panel.
References

CR216 NameJack's Ladder
Designer Manufacturer Year
DDK Aaron (Yulong) Wang 2020
Arity No of pieces Piece type Solution length function Number of moves
10 2 group of rings    
RemarksGoal is to remove the rope loop with the ball from the frame. The ball is too wide to fit through the main handlebar loop, separating the puzzle in an upper and lower half. Each group of rings consists of a U bend in the zig zag part of the frame, and three rings: left, right, bottom. The bottom ring controls access to the left ring. Each group has the following states (part of the solution sequence, ignoring others): the rope off the group, through the bottom ring only, through the left ring only, through left and right rings, through left and bottom rings. For each ring there is only one orientation for the rope to go through it, so the total number of states of the group is 5 different possibilities, and then multiplied by the cases: rope above the main handlebar loop, and below (and this as transition for each of the groups, possibly with multiple such transitions along the handlebar). Thus, these are 5·2=10 sttes, leading to the arity of 10. There is an additional single ring controlling the right hand end of the two ends of the frame (zig-zag part, handlebar loop).
References

CR235 NameJacob's Ladder

[1]
[2] [3] [4]
Designer Manufacturer Year
A.J. Jacobs, Oskar van Deventer Oskar van Deventer 2021
Arity No of pieces Piece type Solution length function Number of moves
4 55 pins 4m—1 1298074214633706907132624082305023
RemarksGoal is to remove the central long helix piece. For this, in an alternating sequence, the pins and the helix have to be rotated. Each pin has four orientations and interacts with the central helix and its upper and lower neighbor. The pins are arranged in a helical pattern around the central helix, and the first one to move is the bottom one (which only has 2 states, while all other pins have 4 states, transitioned via 90° rotation of the pin). The first picture shows the world record puzzle with 55 pins, which has approximately 1033 moves in the solution, and which was presented at MoMath event in February 2022. The second picture shows a close-up of the top of the puzzle, the third some details of the pins. The fourth picture shows a smaller prototype with 5 pieces and 1023 moves. Reference [1] below is Oskar's presentation of the puzzle demonstrating it in detail and [2] is a detailed post on the Twistypuzzles forum with many pictures and behind the scenes pictures *some of them here with permission.
References

CR259 NameJellyfish

[1]
[2]
Designer Manufacturer Year
Stephan Baumegger Stephan Baumegger 2024
Arity No of pieces Piece type Solution length function Number of moves
9 4 sliding panel   687
RemarksGoal is to remove the panels by sliding them through the solution, with the handlebar (with the puzzle name engraved) moving through the grooves of the panels. The panels have partially a regular n-ary structure, but also some more irregular structure as well which can be seen in the second picture. The overall solution is still the n-ary one, but the mazes allow for some shortcuts on one hand, and also some dead ends leading to a possible longer solve on the other hand. The panes are slid through the main frame with the handlebar and the mazes are mostly visible from the sides, which makes this not a blind solve. Care has to be taken about the length of the regular grooves to be able to progress with some panels. Because of this, some panels need to be traversed completely again and again between moves of the other panels, a typical n-ary solution property. The first two panels to be extracted can be removed simlutaneously, the others require another short sequence and then also leave the frame simultaneously. The 4th panel to move has a mainly regular maze in the upper part, and then a small orthorgonal one in the bottom (the left panel in the second picture). This leads to an interesting change of the sequence for the last part of the solution sequence.
References

CR164 NameJUNC

[1]
[2] [3]
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2016
Arity No of pieces Piece type Solution length function Number of moves
2 5 slider pair    
RemarksGoal 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 425≅1015 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 top-left 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 exponential solution length. The letters of the name depict the various configurations of the small squares.
References

CR049 NameJunk'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( 3m ) 161
RemarksVariation: Israelogi by ThinkinGames / Ili Kaufmann. The image shows a different version created by Dirk Weber.
References

CR053 NameK-323

[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
RemarksVariants: CR016, CR038
References

CR038 NameK-419
Designer Manufacturer Year
Kim Klobucher Kim Klobucher 2010
Arity No of pieces Piece type Solution length function Number of moves
4 6 block   419
RemarksVariants: CR016, CR053
References

CR017 NameKing-CUBI
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

CR051 NameKugellager
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2009
Arity No of pieces Piece type Solution length function Number of moves
5 4 ball 2·5m 1250
RemarksVariants: CR027, CR028
References

CR028 NameKugellager 7
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2010
Arity No of pieces Piece type Solution length function Number of moves
7 4 rivet 2·7m 4802
RemarksVariants: CR027, CR051
References

CR027 NameKugellager 8
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2010
Arity No of pieces Piece type Solution length function Number of moves
5 4 ball 2·5m 1250
RemarksSmaller Version and upside-down to original Kugellager; AKA: Kugellager 2; Variants: CR028, CR051
References

CR088 NameLabynary

[1]
[2]
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2013
Arity No of pieces Piece type Solution length function Number of moves
2 4 slider pair+switches    
RemarksBeside 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

CR240 NameLager Lock
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2022
Arity No of pieces Piece type Solution length function Number of moves
5 4 ball 2·5m 1250
RemarksBased on: CR051. The goal is similar to the Kugellager: traversing all 4 balls to the bottom of the maze, then pull the slider to the end an swing the shackle open. This puzzle has two mazes/balls on each side, which are running on a common slider which is pulled/pushed as one piece.
References

CR029 NameLeft-Right Chinese Rings
Designer Manufacturer Year
  Jan Sturm  
Arity No of pieces Piece type Solution length function Number of moves
2 9 ring    
Remarks 
References

CR078 NameLego 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·(2m—1)—2·m 177
RemarksLego 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

CR100 NameLock
Designer Manufacturer Year
Ruan Liuqi Ingenious Rings  
Arity No of pieces Piece type Solution length function Number of moves
2 5 rings   23
Remarksextra ring for symmetry
References

CR130 NameLock 14
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2014
Arity No of pieces Piece type Solution length function Number of moves
3 3 slider+ball    
RemarksFirst shackle part has ternary sequence, second part additional trick. Mechanism is like in CR064; AKA: Alphalock
References

CR037 NameLock 250+
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2010
Arity No of pieces Piece type Solution length function Number of moves
6 4 slider Θ( 5m—1 ) 310
RemarksLowest (4th) ring piece has only 2 position and acts as slider, AKA: Big Sliding Lock, Schloss 250+; Variant: CR065
References

CR102 NameLongevity
Designer Manufacturer Year
Ruan Liuqi Ingenious Rings  
Arity No of pieces Piece type Solution length function Number of moves
2 6 rings   37
Remarksextra rings for symmetry
References

CR030 NameLoony Loop
Designer Manufacturer Year
  Trolbourne Ltd 1975
Arity No of pieces Piece type Solution length function Number of moves
3 2 pair of loops 3m — 1 8
Remarks Variants: CR014, CR067, CR068, CR069, CR070, CR075
References

CR196 NameLoopary 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( 2m ) 127
RemarksThe 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

CR271 NameLost
Designer Manufacturer Year
Jürgen Reiche Siebenstein 2024
Arity No of pieces Piece type Solution length function Number of moves
2 5 loop Θ( 2m )  
RemarksGoal is to free the rope. The design follows the standard binary disentanglement puzzle approach.
References

CR243 NameMagestic 3
Designer Manufacturer Year
Goh Pit Khiam, Alfons Eyckmans Alfons Eyckmans 2022
Arity No of pieces Piece type Solution length function Number of moves
3 3 sliders   64
RemarksVariation of CR125 with reduced piece counts and slight modification of the pieces leading to a slighly less regular sequence.
References

CR008 NameMagnetic 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( 3m ) 83
Remarks 
References

CR111 NameMandarin 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

CR099 NameMaze

[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
RemarksThe first picture shows "Rat Race" by Puzzlemaster
References

CR162 NameMechanic CUBI
Designer Manufacturer Year
Akio Kamei Akio Kamei 2005
Arity No of pieces Piece type Solution length function Number of moves
2 6 panel 2m—1 32
RemarksVariants: 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

CR077 NameMeiro Maze Variant
Designer Manufacturer Year
  Fujita  
Arity No of pieces Piece type Solution length function Number of moves
3 3 pair of loops    
RemarksFirst 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

CR167 NameMerry-go-round

[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 [8] 6 burr sticks   13432
RemarksVariants: 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 2-ary, 3-ary, 4-ary, 5-ary, and 6-ary (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 6-ary). 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 (mid-solution). While the Power Tower has pairs of mirror-symmetric 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

CR260 NameMiBinity I

[1]
[2]
Designer Manufacturer Year
Michel van Ipenburg Jack Krijnen 2024
Arity No of pieces Piece type Solution length function Number of moves
4 [6] 3 Sliding plates   25
RemarksGoal is to slide the pieces until they are apart. The central piece serves as a frame pieces with mazes on both sides, and the two other pieces are identical and have two dowels each, one piece running in the front maze, the other running in the back one. The two dowels run in paralell mazes added for stability, and the back maze is oriented vertically and binary. The front maze features two copies of a binary maze (one for each dowel). As the left dowel (as seen on the picture) first traverses its own binary maze, and then the one for the right dowel, this leads to four positions (plus two additional ones for the initial locking position and the "slide out" position. The back maze is binary (with two extra positions as before) and oriented in a vertical manner. Hence this can be considered as a mixed-base puzzle with binary and quaternary mazes. When the first piece (longer maze) slides out, the other slider is in the initial position and afterwards needs to traverse its maze fully to be extracted. The middle frame piece will always perform moves orthogonally to the two identical pieces (i.e. move up/down). With the current arrangement of the pieces, the number of dowels/mazes and also bends in the mazes could be increased leading to other arities/numbers of states for each piece. Similar mazes can be seen in the puzzle CR142.
References

CR139 NameMini 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    
RemarksVariants: 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

CR180 NameMiSenary 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( 7m )  
RemarksThe 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

CR149 NameMixTer-MaxTer

[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( 3m ) 342
RemarksOne of a whole puzzle family, with different number of sliders, disks, and arities. CR143 is a simpler variant. The goal of MinTer-MaxTer is to move the sliders from the outer discs with two slots to the outer disc with 8 slots and collect them there.
References

CR016 NameMMMDXLVI
Designer Manufacturer Year
Kim Klobucher Kim Klobucher 2010
Arity No of pieces Piece type Solution length function Number of moves
4 9 block   3546
RemarksVariants: CR038, CR053
References

CR171 NameMountain 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    
RemarksMain 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 99-ring series.
References

CR193 NameMountain 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    
RemarksThis 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 99-ring series.
References

CR033 NameMysterians
Designer Manufacturer Year
Oskar van Deventer George Miller 2002
Arity No of pieces Piece type Solution length function Number of moves
5 3 plate 5m—1 124
Remarks 
References

CR232 NameN3-Box

[1]
[2]
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2021
Arity No of pieces Piece type Solution length function Number of moves
3 3 slider-disc pair Θ(3m)  
RemarksBox with a round variant of the series: CR131, CR132, CR087, CR133; The box has a lid with an n-ary sliding piece puzzle, which consists of 3 layers of discs with mazes, and 3 rivets sliding in those. These correspond to what would be the pairs of sliders in the N52 puzzle. At the start, the rivets are in the center start positions marked with circles, and the discs have the little triange/square/circle symbols aligned and stacked. To solve the box, all three layers need to be rotated to the end of the maze so that the rivets can fall out when turning the box over. After that, the lid can be unscrewed by rotating the top disc. Variant: CR242
References

CR131 NameN5
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2014
Arity No of pieces Piece type Solution length function Number of moves
3 2 slider-pair Θ(3m) 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 Burr-Tools, see second reference), with one additional move of the left slider to remove the ball, totalling 21.
References

CR132 NameN52
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2014
Arity No of pieces Piece type Solution length function Number of moves
3 3 slider-pair Θ(3m) 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 Burr-Tools, see second reference), with three additional moves of the left slider to remove the ball, totalling 71.
References

CR087 NameN522

[1]
[2]
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2013
Arity No of pieces Piece type Solution length function Number of moves
3 4 slider-pair Θ(3m) 212
RemarksAKA: "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 Burr-Tools, 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

CR133 NameN522222222
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2014
Arity No of pieces Piece type Solution length function Number of moves
3 10 slider-pair Θ(3m) 137334
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. This is the biggest of the series actually built.
References

CR223 NameN-Airy Box
Designer Manufacturer Year
Fredrik Stridsman Fredrik Stridsman 2021
Arity No of pieces Piece type Solution length function Number of moves
3 4 slider Θ( 3m ) 85
RemarksThis is a puzzle box based on the ReTern Key with Circular pieces, and the transparent cover features exactly such a puzzle. The goal is to open the box, and for that, the sping loaded sliders on the top and bottom left need to be slid to the middle of the puzzle. Of course, this cannot happen at the same time because of the middle slider on the left, so these moves need to be performed one after another, and the little spring mechanisms are part of the solution to this problem. These springs are also part of a quick reset mechanism so that the lid can be closed regardless of the sliding puzzle configuration. The starting configuration of the box is in the middle of the ternary sequence. As both ends of the sequence need to be visited for opening, the ternary sequence is approximately 1.5 times. A smaller version with only 3 special pieces was built as well. Variants: CR155, CR168, CR224.
References[1]

CR116 NameNew Puzzle Rings 3
Designer Manufacturer Year
     
Arity No of pieces Piece type Solution length function Number of moves
2 3 ring    
RemarksVariant: CR117
References

CR117 NameNew Puzzle Rings 5
Designer Manufacturer Year
     
Arity No of pieces Piece type Solution length function Number of moves
2 5 ring    
RemarksVariant: CR116
References

CR187 NameNew 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 2m—1 32
RemarksVariants: CR048, CR056, CR162. Mechanism is completely made out of wood, no metal (pins) used.
References

CR106 NameNine 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

CR179 NameNo 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
RemarksStarting 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 teacher-choreographer 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

CR125 NameNum 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 (3m—2) —1  143
RemarksVariants: CR139 and CR176
References

CR176 NameNum 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 n0··· nm—1(nm+1) —1  50009399
RemarksVariants: 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 nm of the leftmost piece and the product n0··· nm—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: 3-ary: 7+1 (1 block attached), 5-ary: 4+1 (2 blocks), 7-ary: 3+1 (3 blocks), 9-ary: 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

CR151 NameOh Sh*t! Puzzle
Designer Manufacturer Year
  Woodenworks  
Arity No of pieces Piece type Solution length function Number of moves
2 8 loop Θ( 2m )  
RemarksVariants: CR032, CR145
References

CR258 NameO.M.G

[1]
[2]
Designer Manufacturer Year
Stephan Baumegger Stephan Baumegger 2023
Arity No of pieces Piece type Solution length function Number of moves
9 6 sliding panel   1719
RemarksGoal is to remove the panels by sliding them through the solution, with many moves for the first and subsequent panels (level 1719.321.61). This is a larger variant of the Devil (see below) with more moves by higher arity. The panels have each a wooden peg running in a neigbouring panel's groove, and the grooves are cut in a zig-zag-shape. Like for the Devil, the start of the solution requires some higher panels to move first (which was added to reach a unique solution), otherwise a dead end is reached when that respective panel should move after many moves. While the panels have the groove for the mechanism engraved on the inner side, an outline of the groove was engraved for the puzzler to have some orientation about the actual maze layout inside, which is also shown in the second picture. The panels also have different exit points, which lead to the higher level for the 2nd and 3rd panels. After the removal of the 1st panel, the 3rd panel has only seen half of rhe groove before, and the other half will be used to increase the level for the subsequent panels. Variant: CR250
References

CR107 NamePagoda

[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
RemarksThe third picture shows the simpler variant "Tree Puzzle" by Puzzlemaster
References

CR009 NamePanex Gold
Designer Manufacturer Year
Toshio Akanuma TRICKS 1983
Arity No of pieces Piece type Solution length function Number of moves
3 20 slider   31537
RemarksVariant: CR035. Goal is to slide the pieces (without turning) to exchange the left and right stacks.
References

CR231 NamePanex Galaxy

[1]
[2]
Designer Manufacturer Year
Oskar van Deventer Oskar van Deventer 2021
Arity No of pieces Piece type Solution length function Number of moves
4 6 slider    
RemarksVariant: CR035. Goal is to slide the pieces to exchange the silver and gold pieces. The second picture shows the wooden mass produced version (by manufacturer Project Genius) from 2022. Here, colours have been replaced by chess piece icons (with some hieroglyph elements included). In this version, the arrangement of the channels was changed, so that the bronze pieces now occupy the longer channel. This changes the solution sequence and makes it possible to solve the goal without moving any of the bronze pieces.
References

CR230 NamePanex Junior
Designer Manufacturer Year
Oskar van Deventer Oskar van Deventer 2021
Arity No of pieces Piece type Solution length function Number of moves
2 [3] 6 slider    
RemarksVariant: CR035. Goal is to slide the pieces (without turning) to move stack between left and right channels. There is an additional one piece parking position on top of the left channel.
References

CR035 NamePanex Silver
Designer Manufacturer Year
Toshio Akanuma TRICKS 1983
Arity No of pieces Piece type Solution length function Number of moves
3 20 slider   31537
RemarksVariant: CR009. Goal is to slide the pieces (without turning) to exchange the left and right stacks.
References

CR128 NamePanex 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
RemarksVariant 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

CR113 NamePear
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

CR036 NamePharaoh's Dilemma
Designer Manufacturer Year
  Mag Nif 1970
Arity No of pieces Piece type Solution length function Number of moves
3 6 disc    
RemarksTower of Hanoi variant
References

CR109 NamePhoenix

[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

CR217 NamePiano
Designer Manufacturer Year
DDK Aaron (Yulong) Wang 2020
Arity No of pieces Piece type Solution length function Number of moves
2[4] 10 rings    
RemarksGoal is to remove the handle going through the upper row of rings. The puzzle consists of two binary Chinese Rings chains of 5 rings. The upper (with the handle) attached to short connectors, the lower one to longer connectors. To solve, the handle has to be moved out of the upper chain, and for each transitions, some move sequences of the lower chain are required. The arity is 2 in general, and could be viewed as 4 if pairs of upper/lower rings are grouped together.
References

CR119 NamePin 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( 2m ) 38§
RemarksBinary sequence, which is non-GC based and uses a pin-maze-mechanism, 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

CR186 NamePlanex
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
RemarksVariant: 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

CR126 NamePower 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 [5] 4 burr sticks 3mm—1  76
RemarksVariants: CR136, CR167
References

CR136 NamePower 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 [7] 6 burr sticks 2·(nm—1)/(n—1)—m 7806
RemarksVariants: 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 n-ary 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

CR141 NamePower 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 [4] 6 panels    
Remarks 
References

CR032 NamePuzzle H
Designer Manufacturer Year
  Eureka 3D Puzzles 1997
Arity No of pieces Piece type Solution length function Number of moves
2 5 loop Θ( 2m )  
RemarksVariant: CR145
References

CR004 NamePyraCircle
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2008
Arity No of pieces Piece type Solution length function Number of moves
3 10 block   116
RemarksVariation of Panex, a non-disjoint union of several such puzzles; 116 is minimum number of moves
References

CR266 NamePython
Designer Manufacturer Year
DDK Heping Gao, Aaron (Yulong) Wang 2024
Arity No of pieces Piece type Solution length function Number of moves
2 7 ring Θ( 2m )  
RemarksGoal is to remove the long handlebar piece, starting from the configuration shown in the picture. This puzzle is basically a classic chinese rings puzzle, where the rings have been split into groups and the main backbone is bent in a way so that access to the rings happens from two different sides for the various rings. The group of rings 5, 6, and 7 have a special arrangement, with ring 7 serving as a gate for the goal position.
References

CR197 NameQuadrupled Quadlooplet
Designer Manufacturer Year
Namick Salakhov Namick Salakhov 2018
Arity No of pieces Piece type Solution length function Number of moves
5 4 loop 3m 81
RemarksThis puzzle contains multiple 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

CR082 NameQuatro
Designer Manufacturer Year
Eric Johansson Eureka 3D Puzzles  
Arity No of pieces Piece type Solution length function Number of moves
2 4 loop Θ( 2m ) 7
RemarksOne of the solutions (reference 2) acts like Chinese Rings, please see reference 3. There are also other solutions.
References

CR148 NameRacktangle
Designer Manufacturer Year
Goh Pit Khiam Tom Lensch 2014
Arity No of pieces Piece type Solution length function Number of moves
3 [5] 4 plate    
RemarksVariable 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

CR241 NameRailings
Designer Manufacturer Year
DDK Heping Gao 2022
Arity No of pieces Piece type Solution length function Number of moves
2 10 ring Θ( 2m )  
RemarksGoal is to remove the rope. This puzzle is basically a 10 ring binary rope puzzle that was folded into three layers (4 rings, 3 rings, and 3 rings), and these layers attached to the same poles. The solution sequence is mostly a typical binary reflected Gray code. As 3 of the rings are reachable from the outside (one on each level), one has to plan when to use each of them. The layer structure sometimes introduces modification in the 10 ring sequence and planning for the next step on the lower layer is also required to avoid unneccesary moves. The puzzle also features a quick reset where the rope can be opened.
References

CR093 NameRailing 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    
RemarksQuaternary version is: CR124
References

CR218 NameRainbow
Designer Manufacturer Year
DDK Aaron (Yulong) Wang 2020
Arity No of pieces Piece type Solution length function Number of moves
2 [8] 11 rings    
RemarksGoal is to remove the handle from the puzzle. The puzzle consists of four concentric half circles/arcs and 3 separate binary chinese rings chains, one chain of length four at each end, and one of length three in the middle. The right hand side chain is traversed many times, to traverse through the middle chain, and in certain situations when dropping a ring off the middle chain, one (or more) rings of the left hand chain are dropped. This can be viewed as one chinese rings chain of 11 rings with some branches. An alternate view is to count the rainbow arcs, which have three rings each and therefore 8 states each (each ring on/off the handlebar). That would make it an 8-ary puzzle with four special elements.
References

CR270 NameRainbow Drawers

[1]
[2] [3]
Designer Manufacturer Year
Bram Cohen Puzzleguy 2024
Arity No of pieces Piece type Solution length function Number of moves
4 6 board 2m+1—2·m—3 113
RemarksThis puzzle comes is a 3D printed stack of boards with rails running in grooves in the next higher board and a pin running in the second next higher board. Goal is to disassemble and re-assemble the puzzle. This puzzle is a cuboidal variant of Ziggurat CR234 The boards come in two chiral variants, and the stack of boards alternates between left and right handed boards. The pictures show the assembled puzzle of 6 boards (but a higher or lower number of boards can easily be used), the puzzle mid-solution, and then the two flavors of boards, shown from top and bottom. This puzzle was Bram's Exchange puzzle for IPP41.
References

CR254 NameRatchet
Designer Manufacturer Year
Heping Gao, Aaron Wang Aaron (Yulong) Wang 2021
Arity No of pieces Piece type Solution length function Number of moves
2 6 oval rings Θ( 2m )  
RemarksGoal is to remove the string loop from the metal frame. The main sequence is a classic Chinese Rings like sequence. The rope can pass through each of the 6 rings or travel around it, which leads to the binary structure. The first oval ring has a special feature as an entry point: The slots of the frame are all too small to allow the circular rings to pass through, except for the one adjacent to the first ring. This slot needs to be used in a short sequence to change the rope configuration between through and off the first ring — which happens a lot during the binary sequence — and which is the main challenge of the puzzle. Special care has to be taken to keep the two halves/slings of the rope separate, or additional knotting will occur.
References

CR173 NameReflection
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    
RemarksVariation 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 99-ring series.
References

CR155 NameReTern 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 · 3m—1—8·m+1 185
RemarksThe full name is "The Return of Tern Key" and demonstrates a variant of CR125 without a long synchronizing slider piece. Variants: CR168, CR223, CR224.
References

CR168 NameReTern 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 Θ( 3m )  
RemarksThe 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. Variants: CR155, CR223, CR224.
References 

CR224 NameReTern Key with circular pieces (Coin Release)
Designer Manufacturer Year
Fredrik Stridsman Fredrik Stridsman 2021
Arity No of pieces Piece type Solution length function Number of moves
3 5 slider Θ( 3m ) 313
RemarksThe 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. This one is a newer, version with laser cut acrylic and 3D printed sliding blocks, with more pieces and the goal to release the coin. Variants: 2, CR168, CR223
References[1]

CR189 NameReverse 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·2m)  
RemarksThis 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

CR021 NameRings Bottle
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2012
Arity No of pieces Piece type Solution length function Number of moves
2 6 ring    
Remarks 
References

CR267 NameRippl
Designer Manufacturer Year
DDK Heping Gao, Aaron (Yulong) Wang 2024
Arity No of pieces Piece type Solution length function Number of moves
2 8 ring Θ( 2m )  
RemarksGoal is to remove the long handlebar piece. The main structure is like basic Chinese Rings puzzle, but with the frame bent in some spiraled fashion. There are two spirals which are connected via bridge offering two U bends for access, which both carry a ring and have a little indentation at the bottom. While solving the puzzle, these rings easily slip into these indentations suddenly blocking the move, and forcing the user to locate this block and move the ring aside. This bridge separates the rings into two groups. The first three form some simple binary sequence, with nice interaction between the handlebar, the rings, and the spiral frame, where the first ring can also move around nearly a whole rotation around the spiral. For solving the other 5 rings, a both U openings of the bridge is used several times.
References

CR041 NameRow to Row
  Designer Manufacturer Year
     
Arity No of pieces Piece type Solution length function Number of moves
3 8 disc Θ( 2m )  
RemarksA Tower of Hanoi like puzzle.
References

CR007 NameRudenko Clips
Designer Manufacturer Year
Valery Rudenko Roscreative 2011
Arity No of pieces Piece type Solution length function Number of moves
3 7 clip ( 3m—1 )/2 1093
RemarksTower of Hanoi with move restriction
References

CR019 NameRudenko Disc
Designer Manufacturer Year
Valery Rudenko Roscreative 2011
Arity No of pieces Piece type Solution length function Number of moves
3 7 disc Θ( 2m )  
RemarksTower of Hanoi with simplification
References

CR044 NameRudenko Matryoshka
Designer Manufacturer Year
Valery Rudenko Roscreative 2011
Arity No of pieces Piece type Solution length function Number of moves
3 7 slider Θ( 2m )  
RemarksTower of Hanoi equivalent with restriction of moves between the outer two rows
References

CR252 NameSalva
Designer Manufacturer Year
Rex Roxano Perez Rex Roxano Perez 2023
Arity No of pieces Piece type Solution length function Number of moves
6 2 slider   71
RemarksGoal is to free the Salva dog coin from the cage. The puzzle is a combination of a 6-ary maze puzzle and a sequential discovery puzzle that offers an additional prize. The 6-ary sequence occurs in two stages, and the two thin sliders interact with two different areas of the large maze board.
References

CR227 NameSea Horse
Designer Manufacturer Year
Xianyang Yang Aaron (Yulong) Wang 2021
Arity No of pieces Piece type Solution length function Number of moves
2 2 ring   6
RemarksGoal is to remove rope. Nicely made variant of CR031
References

CR086 NameSeestern
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2013
Arity No of pieces Piece type Solution length function Number of moves
11 3 Layers 11m—1 1330
Remarks 
References

CR190 NameSecond 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    
RemarksWhile 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

CR255 NameSensi Box

[1]
[2]
Designer Manufacturer Year
Alfons Eyckmans Alfons Eyckmans 2017
Arity No of pieces Piece type Solution length function Number of moves
2 [4] 6 panel   371
RemarksThis 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 Sensi by the same designer, a framed 6 pieces burr. This inner puzzle also adds to the stability of the movements of the box panels. Both ideas are based on CR160. The panel with the name on it and which is the lid of the box is 6-ary
References

CR209 NameSeptenary Cube

[1]
[2]
Designer Manufacturer Year
Aleksandr Leontev Johan Heyns 2019
Arity No of pieces Piece type Solution length function Number of moves
7 4 board   4802§
RemarksObjective of this puzzle is to remove the four acrylic boards by moving the pin connected to the central wooden block through the mazes, and then to find and open the secret compartment. This puzzle has the same maze structure like a Kugellager 7, just divided over the 4 pieces. In the end position.
References

CR201 NameSequence Cube
Designer Manufacturer Year
Aleksandr Leontev Aleksandr Leontev 2018
Arity No of pieces Piece type Solution length function Number of moves
4 12 burr sticks 2m+1—2 8190
RemarksThe cube in the picture is a version where only the first piece can be removed, called the "136 Minutes Cube". It comes with an alternate piece, which can be used to raise the number of moves to 12282 moves, calles the "206 Minutes Cube". These names refer to an estimate of solving the respective puzzles.
References

CR253 NameShoulder To Shoulder
Designer Manufacturer Year
Shuai Chi Heping Gao 2023
Arity No of pieces Piece type Solution length function Number of moves
3 [2] 9 rings    
RemarksGoal is to free the rope (withtout using the quick-reset feature). The main structure is a classic binary Chinese Rings like puzzle, but with an additional long metal loop through the rings. The vertical rods have been split up into U shapes, and this creates pairs of rings: One of the pair is going through the U below the long loop, the other ring of the pair going through the adjacent U shape above the long loop. The whole puzzle and solution structure is thereby changed into a ternary structure: Rope off the ring, rope through the ring and above the long loop, rope through the ring and below the long loop. In this aspect the puzzle is very similar to CR251 by the same designer/manufacturer from the same release. For the (disentanglement) solution, the rope has to be fed through all the rings that are accessible from above first (those linked to the lower U part), then some form of binary sequence follows from the open end to the closed one: The other rings have to be put onto the rope loop in a binary fashion, and for this the other rings have to be traversed on the way in shorter sequences. Care has to be taken so that the crossing of the rope with the long loop always happens on the inside. This can be achieved by "storing" some extra rope slings on the long loop, and this is possible while the rope runs through an uninterrupted chain of rings from the open end (where the extra slinging happens). The last phase of the solution happens mainly above the long loop and works towards the open end, even though some moves still work below that.
References

CR251 NameShuttle Run
Designer Manufacturer Year
Shuai Chi Heping Gao 2023
Arity No of pieces Piece type Solution length function Number of moves
3 [2] 11 rings    
RemarksGoal is to free the rope (withtout using the quick-reset feature). The main structure is two classic binary Chinese Rings chains of rings, just that they have been broken into an upper sequence (still binary) of 6 rings, and there is a lower one, which is segregated by a fixed long metal loop running through all of the rings. This long metal loop introduces additional rope+ring positions, incresing the arity to ternary, rougly: Off the ring/through the ring above the loop/through the ring below the loop. The solve is mainly a binary solve, but made more complicated by this loop, and for more moves the top binary chain interacts with the solution. The two chains are also of reversed orientation: For the first ring on the bottom (near the round loop end), the whole sequence above has to be traversed and is the longest run, while shorter runs on the top chain may appear later in the solution. For solving the bottom chain, a special trick is required: Solving it the usual way will make the loop end up on the wrong side of the long loop after a few moves (and later again), hence additional rope slings need to be stored around the long loop, and this is only possible at the open end, and when the rope traverses through an uninterrupted sequence of bottom rings from the rightmost/first ring. After running the sequence past all bottom rings, the loop will be slung around the last/leftmost vertical bar, and then the whole rope loop will move above the long bar. A few moves through the end of the top chain end will free this end, so that the rope has moved to the next gap between two poles, and the rope is then running through the puzzle only once — like in the beginning, but this time more in the middle. More sequences on the lower chain (padded by those filling sequences on the upper chain) will then lead to the rope coming off the frame.
References

CR064 NameSix Bottles
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2013
Arity No of pieces Piece type Solution length function Number of moves
3 6 slider+ball 4·(2m—1) 252
RemarksEach metal ball can be in a top-left, bottom-left, or a bottom-right 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

CR211 NameSix Keys Box
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2019
Arity No of pieces Piece type Solution length function Number of moves
3 6 key slider+ball slider pair 43 ·3m—3 969
RemarksMove all the keys down and then open the box. At first look similar to CR064, but no long synchronizing piece exists here. Instead there are two rows of acrylic sliders beneath the keys, each slider with one ball interacting with one of the keys. The slider work in a way similar to the Num Lock CR125, but the key pieces have a different layout. Move count: both keys and acrylic sliders.
References

CR011 NameSliding-Block Chinese Rings-style 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    
RemarksThe 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, non-ternary solution that was not intended, with goal configuration in third picture; under investigation.
References

CR249 NameSlidebox
Designer Manufacturer Year
Stephan Baumegger Stephan Baumegger 2023
Arity No of pieces Piece type Solution length function Number of moves
6 6 sliding panel   353
RemarksGoal is to disassemble the box into the 6 plates and 12 frame sticks. 5 of the plates have a brass pin running in grooves in the neigboring plate, and these grooves have different shapes and create mixed-base mazes of arity 6 and lower. After the first plate has been extracted, the disassembly of the stick frame starts. This is based on an idea first presented in CR160 and later shown in puzzles with fixed and disassemblable frame.
References

CR142 NameSlots 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    
RemarksThis version has mixed bases, i.e. binary and ternary pieces/piece parts.
References

CR210 NameSluice and Ships

[1]
[2] [3]
Designer Manufacturer Year
Namick Salakhov Namick Salakhov 2019
Arity No of pieces Piece type Solution length function Number of moves
3 12 ships   192
RemarksThe goal of this puzzle is to move the board with ships out of the puzzle by moving all ships from the lower chamber to the upper chamber. While travelling between upper and middle chamber is unrestricted as long as the ships reaches the opening, for travelling between the bottom and middle chamber, another ship needs to be in the chamber before and push the left or right gate aside. Only the first ship can always traverse here. There is an additional white block with blue rectangles that can be inserted into the left end of the middle chamber, reducing the length of the chamber (and therefore the left gate), and with a solution length of 102 moves, where a move is a move of a ship between the chambers, not one of the acrylic board or gate. The two configurations have the following names: 5:6/N12 (with 12 ships, left gate 5 ships wide, right gate 6), and with the extra block: 3:6/N12 (with the left gate now only 3 ships wide). To get ships out of the middle chamber quickly (in case of being lost in the solution) one can push the chamber gates open from below, or one can remove the black piece to open a shortcut between lower and upper gate (and the exit).
References

CR048 NameSmall CUBI
Designer Manufacturer Year
Akio Kamei Akio Kamei 2010
Arity No of pieces Piece type Solution length function Number of moves
2 6 panel 2m—1 32
RemarksVariants: CR056, CR162. Mechanism is completely made out of wood, no metal (pins) used.
References

CR022 NameSpinOut
Designer Manufacturer Year
William Keister Binary Arts 1970 / 2006
Arity No of pieces Piece type Solution length function Number of moves
2 7 disc [2m+1/3] § 85 §
RemarksVersion 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

CR050 NameSpinOut

[1]
[2]
Designer Manufacturer Year
William Keister Binary Arts 1970 / 1987
Arity No of pieces Piece type Solution length function Number of moves
2 7 disc [2m+1/3] § 85 §
RemarksThere exists an unintended shortcut solution with 49 moves (see Jaaps's page below). The second picture shows an unknown mini variant with rule scales in cm and inch, and inscription "PAT NO 23596" on the back side; Variants: CR022, CR026
References

CR026 NameSpinOut
Designer Manufacturer Year
William Keister ThinkFun 1970 / 2001
Arity No of pieces Piece type Solution length function Number of moves
2 7 disc [2m+1/3] § 85 §
Remarksreset shortcut. There exists an unintended shortcut solution with 49 moves (see Jaaps's page below); Variants: CR022, CR050
References

CR084 NameSpiralschloss
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2013
Arity No of pieces Piece type Solution length function Number of moves
3 4 shackle-layer 2·(nm—1) 160
RemarksMechanism similar to CR085. Goal: Open all shackle-layers completely.
References

CR233 NameSquare Tower of Hanoi
Designer Manufacturer Year
Jun-ichi Miyoshi, Mineyuki Uyematsu, Hajime Katsumoto MINE/DYLAN-Kobo 2020
Arity No of pieces Piece type Solution length function Number of moves
4 10 disc   108
RemarksGoal is to move the stack from the top left to the bottom right pole following the rules: The usual Tower of Hanoi rules (only one disc to be moved at a time, and no larger disc on a smaller one), moves only horizontally or vertically (not diagonally accross the center).
References

CR222 NameStacker
Designer Manufacturer Year
Jared Petersen CoreMods 2021
Arity No of pieces Piece type Solution length function Number of moves
3 5 ball bearing    
RemarksGoal is to slide ball bearings from the right to the left compartment (and back), using both the ball bearings and the horizontal slider. The cutouts allow the ball bearings of 5 different sizes only to decend to the same level of the three compartments where they started and not below, and the horizontal slider will only contain one ball bearing. This makes this puzzle similar to the Panex puzzle, just with one set of special pieces instead of two, and with a middle compartment that is two units shorter than the outer compartments, and containing at most 3 ball bearings. The usual solving method of Tower of Hanoi will work to some extent, until the smallest ball bearing needs to be relocated to the other outer compartment, then a different approach is required.
References

CR246 NameStern-Box/Star Box/Sun Box

[1]
[2]
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2022
Arity No of pieces Piece type Solution length function Number of moves
3 4 slider-pair    
Remarks Goal of this box is to open all four doors at the sides. To achieve this, a hidden N522 puzzle (CR087) in the top part of the box with 4 slider pairs needs to be solved. Unlike for the N522 puzzle, the sliders start in the middle position each. To open a door, the sliders all have to be moved to the other side. However, the order of the doors is also important (first door next to the first slider to move (right), then opposite (left), then the top one, then the bottom one last), which is accomplished by an additional locking mechanism that can be shifted to release the next door after removing a door. After opening each of the doors, the sliders also need to be arranged for the next one, solving the N522 maze on top blindly, which can be confusing. The second picture shows the box partially disassembled and the N522 puzzle visible. Behind the last door, there is a little prize. The name is Star Box (in German or English), and alternatively you can name it after the Sun, whatever you like better (statement from JC when explaining this box).
References

CR083 NameSteuerrad

[1]
[2]
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2013
Arity No of pieces Piece type Solution length function Number of moves
3 8 slider+switch 3·2m 768
RemarksRound 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). The second picture and reference show a box newly released in 2018, which features the same puzzle as lid. To open the box, all the sliders but the short one have to be moved to the outer position. This makes the solution shorter than the one of the original puzzle.
References

CR025 NameSuper-CUBI

[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
RemarksFirst image shows newer version (opposite panels following in solution), second and third the older version (panels following in 90° turn order); Variant: CR165
References

CR165 NameSuper-CUBI (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
RemarksSmaller version of original Super-CUBI 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

CR239 NameSwitched Maze
Designer Manufacturer Year
Kirill Grebnev Kirill Grebnev 2007
Arity No of pieces Piece type Solution length function Number of moves
4 2 pairs of switches   12
RemarksAKA: Life's Maze; goal is with all switches turned clockwise first, insert the runner into the right hole and guide it to the left hole to exit. In this puzzle, the switches can be rotated between two positions, and two of them are grouped as an n-ary piece "pair of switches": one from the lower row in the picture and the one right above next to it. The switches have two positions to accept the runner, and it can move to the other exit channel of this switch, if the switch can turn this way. This leads to a lot of setting and resetting switches during the solution sequence. The lower row of switches creates some binary sequence, but combined with the upper row they demonstrate a longer and more complicated sequence.
References

CR104 NameTeapot
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

CR242 NameTelefon Box
´ Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2022
Arity No of pieces Piece type Solution length function Number of moves
3 4 slider-disc pair    
RemarksBox with a round variant of the series: CR131, CR132, CR087, CR133; The box has a lid with an n-ary sliding piece puzzle, which consists of 4 layers of discs with mazes, and 4 rivets sliding in those. These correspond to what would be the pairs of sliders in the N52 puzzle. At the start, the rivets are in the center start positions marked with circles, and the markings aligned with the rivets. To solve the box, first the 3-ary puzzle needs to be solved, and then a second stage follows with several locks and tools to unlock the main door, in a sequential discovery manner. Variant: CR232
References

CR002 NameTern 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·(2m)—12·m—10 134
Remarks 
References

CR005 NameTernary 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 6·2m—4·m—5 § 75§
RemarksMove count includes control bar; Variant with only two frame pieces; Variants: CR055, CR095
References

CR055 NameTernary 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 6·2m—4·m—5 § 75§
RemarksMove count includes control bar; 95 moves for complete disassembly; Variants: CR005, CR095
References

CR095 NameTernary 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 6·2m—4·m—5 § 75§
RemarksMove count includes control bar; 95 moves for complete disassembly; Variants: CR005, CR055
References

CR272 NameTernary Key
Designer Manufacturer Year
Oskar van Deventer Oskar van Deventer 2024
Arity No of pieces Piece type Solution length function Number of moves
3 6 keys 2 · 3m — 1 + 1 487
RemarksGoal: Disassemble and reassemble. This was the DCD 2024 welcome gift, and is a variation of Oskar's classic Keys puzzle (with 2 keys) once produced by Hanayama and now re-relaeased as a 3 key version. This 6 key version has keys with a simpler shape leading to a ternary pattern. The red key only has two positions, and the move count includes a small initial step and the removal of the pack of keys at the end.
References

CR205 NameTernary / Quinary Cube

[1]
[2]
Designer Manufacturer Year
Aleksandr Leontev Johan Heyns 2019
Arity No of pieces Piece type Solution length function Number of moves
5 4 block   1251§
RemarksObjective of this puzzle is to move the four blocks on the sides and the central maze block with the two maze panels in a way that the four blocks on the side can all be removed. The puzzle comes initially in a ternary configuration, and with the allen wrench included (in the wooden storage plate), it can be disassembled partially, the maze plates can then be rotated to the other side and after reassmbling, the initial ternary 170 move solutions becomes quinary with 1257 moves. Jack Krijnen pointed out that also mixed base setups are possible, with 463 and 470 moves solutions. The second picture shows the puzzle partially disassembled and also somme of the ternary and quinary mazes included.
References

CR220 NameTernary Pin Burr

[1]
[2]
Designer Manufacturer Year
Aleksandr Leontev Aleksandr Leontev 2018
Arity No of pieces Piece type Solution length function Number of moves
3 4 block 2·3m § 162§
RemarksObjective of the puzzle is to move the four special pieces and the big slider piece until the special pieces come out, then completely disassemble the burr of 35 pieces in total. The second picture shows the puzzle in this second stage of disassembly. The mazes are based on the Kugellager mazes, and aside from ternary mazes, also a version with quinary mazes was designed.
References

CR181 NameThe Bell
Designer Manufacturer Year
Juergen Reiche Siebenstein 2017
Arity No of pieces Piece type Solution length function Number of moves
3 12 slider   881
RemarksVariant: 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

CR012 NameThe 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 + 2m+2 ) / 3  § 85§
RemarksMove count includes control bar; There is also a very rare 10 ring piece version, which is shown in the pictures; Variants: CR076, CR156
References

CR076 NameThe 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 + 2m+2 ) / 3  § 85§
RemarksMove count includes control bar; Variants: CR012, CR156
References

CR156 NameThe 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 + 2m+2 ) / 3  § 1385§
RemarksMove 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

CR057 NameThe Brain

[1]
[2] [3] [4]
Designer Manufacturer Year
Marvin H. Allison, Jr. Mag-Nif 1973
Arity No of pieces Piece type Solution length function Number of moves
2 8 switch [2m+1/3] 170
RemarksPictures 2, 3, and 4, and reference 2 show the newer version
References

CR096 NameThe 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

CR097 NameThe 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

CR058 NameThe 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
RemarksVariant: CR063
References

CR225 NameThe Tippenary Mystery Tour
Designer Manufacturer Year
Jack Krijnen Jack Krijnen 2021
Arity No of pieces Piece type Solution length function Number of moves
3 [5] 4 slider   55
RemarksFrom the description: It is sequential (puzzle) discovery, it is riddle solving, it is n-ary, and in the end there is a challenge waiting. This puzzle box has multiple stages of the solution, one of them being a ternary/binary mixed base puzzle, and also containing burr components. The goal for the ternary/binary mixed base puzzle is to solve it and unlock a locking mechanism, the overall goal is to work through the final challenge and solve this one. To avoid more spoilers, no further description is provided here. The design was first presented in 2019 with a prototype and in 2021, this box was released.
References

CR191 NameThird 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    
RemarksWhile 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

CR268 NameTower

[1]
[2]
Designer Manufacturer Year
Stephan Baumegger Stephan Baumegger 2024
Arity No of pieces Piece type Solution length function Number of moves
7 5 Maze board Θ( 7m ) 6746
RemarksGoal is to remove the maze boards from the frame. The burr level shows the number of moves required to remove each: 5642.939.155.8. All but the bottom boards have a wooden dovel running in the maze of the board below it. The top board does not have any labyrinth engraved, while the second board has a somewhat complicated and irregular labyrinth included, with several sections of similar moves, and with the final channels only being used for extracting the first piece, not before. The other three boards all have a very similar labyrinth (see second picture). The boards have two main directions, with the orientation differing by 90° in an alternating pattern, and the frame has some supporting structures with cut-outs (and 1 dovel) making the solution unique.
References

CR062 NameTower of Hanoi
Designer Manufacturer Year
Edouard Lucas Philos (and others) 1883
Arity No of pieces Piece type Solution length function Number of moves
3 9 disc Θ( 2m )  
Remarks 
References

CR105 NameTrapeze

[1]
[2] [3]
Designer Manufacturer Year
     
Arity No of pieces Piece type Solution length function Number of moves
2 5 rings   61
Remarksextra 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

CR144 NameTricky Frame
Designer Manufacturer Year
  Philos  
Arity No of pieces Piece type Solution length function Number of moves
2 3 loop Θ( 2m )  
RemarksVariant: CR072
References

CR145 NameTricky Mouse
Designer Manufacturer Year
  Philos  
Arity No of pieces Piece type Solution length function Number of moves
2 4 loop Θ( 2m )  
RemarksVariant: CR032
References

CR244 NameTvnary

[1]
[2]
Designer Manufacturer Year
Tamás Vanyó Rex Roxano Perez 2022
Arity No of pieces Piece type Solution length function Number of moves
5 4 Slider   1003
RemarksGoal is to disassemble this interlocking puzzle. The puzzle is a combination of an n-ary puzzle and a maze puzzle, in which the n-ary maze has been modified a bit to increase the number of moves and make the structure of the solution less regular and much more challenging to solve. The second picture shows one side of the central slider with two of the mazes, and there are two others (and different ones) on the back side. The overall structure of the solution is 5-ary, as can also be seen from the maze. On a higher abstraction level, each of the 4 sliders has 5 main positions, which consists of 2 (sometimes 3) adjacent positions in some of the mazes.
References

CR085 NameUhrwerk

[1]
[2]
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2013
Arity No of pieces Piece type Solution length function Number of moves
3 4 ball/gear 2·(nm—1) 160
RemarksMechanism 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

CR138 NameUnknown Disentanglement
Designer Manufacturer Year
     
Arity No of pieces Piece type Solution length function Number of moves
2 3 loops    
RemarksChoosing 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

CR213 NameVertical

[1]
[2] [3] [4]
Designer Manufacturer Year
Aleksandr Leontev Aleksandr Leontev 2020
Arity No of pieces Piece type Solution length function Number of moves
5 6 sliders 24 (5m—2) —1  14999
RemarksVariants: CR125, CR139, and CR176. This is is a round version of the Num Lock puzzle. The goal is to remove all (white) pieces from the black frame. The pictures show the puzzle in the start configuration, some pictures from the beginning of the solution, and then disassembled with all pieces.
References

CR152 NameViking Box
Designer Manufacturer Year
Sven Baeck, Jean-Claude Constantin Jean-Claude Constantin 2014
Arity No of pieces Piece type Solution length function Number of moves
3 4 switches    
RemarksThe 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

CR200 NameVisible 5-Ary Drawer (Quinary)
Designer Manufacturer Year
Hiroshi Iwahara Hiroshi Iwahara 2018
Arity No of pieces Piece type Solution length function Number of moves
5 3 drawers and plates 2 · 5m—1+1 51
RemarksA series of boxes with arity 2, 3, 4, and 5 was built and this is the highest arity one. All boxes have 3 drawers and two plates for the top mechanism, and a main drawer to open after the sequence has been completed. The models differ in their acrylic plates, which are engraved with a label stating their arity.
References

CR221 NameVoid Box
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2020
Arity No of pieces Piece type Solution length function Number of moves
5 3 slider 2·5m 250
Remarks Goal is to open the box. This is a box with an internal mechanism that (presumably) looks like CR001 and features the same sequence. The three knobs on the left side perform a quinary sequence together with the sliders on the front and back long sides. After the sequence is completed, the box can be opened by pulling out the knob on the right side.
References

CR001 NameVoid Lock

[1]
[2] [3]
Designer Manufacturer Year
Jean-Claude Constantin Jean-Claude Constantin 2009
Arity No of pieces Piece type Solution length function Number of moves
5 3 slider 2·5m 250
RemarksAKA: Kleines dickes Schloss; the second variant shown in picture and references is a metal version released in 2018 by Constantin
References

CR103 NameWheel
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

CR215 NameWhite Bow-Tie
Designer Manufacturer Year
Aleksandr Leontev Aleksandr Leontev 2019
Arity No of pieces Piece type Solution length function Number of moves
5 4 blocks 2·5m 1250
RemarksVariant: CR207. This puzzle is a 2-in-1 puzzle with two challenges, each with the same 4 blocks and two different mazes. One set of mazes (the initial configuration of the puzzle) starts from the top and is ternary, with a total of 162 moves, and the other starts from the other side with the 5-ary maze. Aside from the black and white colour, the four blocks have each one pin and seem to be identical. Goal is to slide the blocks through the maze until they can be extracted. Mixing 3-ary and 5-ary mazes does not seem to work, as the 3-ary mazes are not wide enough to allow for the 5-ary transitions.
References

CR183 NamexBrain 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 [2m+1/3] 42
RemarksThis 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

CR184 NamexBrain 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 2·3m — 1 — 1 485
RemarksThis 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

CR185 NamexBrain 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 · 4m — 0.5 1638
RemarksThis 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(m—1) + 4f(m—2) +3 with f(0)=0 and f(1)=1 derived from solving the puzzle with m pieces.
References

CR238 NameYPANEX
Designer Manufacturer Year
Javier Santos Jose Romero 2022
Arity No of pieces Piece type Solution length function Number of moves
2 [3] 7 slider   190
RemarksVariant: CR230. Goal is to slide the pieces (without turning) to move stack between left and right channels. There is an additional one piece parking position on top of the horizontal channel that can be used for swapping. This is a symmetric version of Panex Junior, with one additional space above the left channel (by moving it to the left one unit). This allows swapping moves in a symmetric way, while Panex Junior only allowed them in one orientation, and overall also some shorter sequences than in Panex Junior. In particular, move sequences involving sliders 1 and 2 can be shortened, as they require less swapping. Like the other recent Panex variants and unlike the original Panex, this one can be played from both sides, with or without visible hints for the stair structure of the channels (but still the number indicators). This puzzle was developed in a discussion about CR231
References

CR262 NameZigguchain

[1]
[2] [3] [3] [4]
Designer Manufacturer Year
Bram Cohen, Oskar van Deventer Oskar van Deventer 2024
Arity No of pieces Piece type Solution length function Number of moves
4 6 chain link ring 2m+2m—7 243
RemarksGoal: Disassemble and re-assemble again. This is a chain version in the Ziggurat line of puzzles. Moves are linking/unlinking rings via the notches, and rotational moves of a ring (rotating until the move is blocked). The puzzle consists of 6 identical ring pieces which are only different in colours as shown in the second picture. Each ring has a little knob to run in the maze of the neighbour ring. The rings are held in place and the knob inside the groove by the available space of each ring being filled by the two neighbour rings. The third picture shows the initial arrangement for the assembly, after each ring has been inserted and rotated by 180°, and during the solution to be rotated until the 270° mark. Note how the notches in the rings all point into the same direction (towards the purple end in the picture). While each ring can be added in two orientations to the existing chain, only one will work, which allows the knob to run into the groove. All rings will now need to be rotated until their notches point to the sides, in a helix like pattern, as shown in the first picture. The fourth picture shows an intermediate configuration somewhere in the solution sequence. The whole puzzle is quite wobbly initially (as to be expected from a chain), but in the fully assembled state it is quite stable and the puzzle can be picked up on any of the rings and will retain the shape. Of course, this only holds for arrangements with more than 2 rings, as 2 rings don't have the stabilizing mechanism via the available space inside rings. During the solve, a configuration with a notch pointing towards the neighbor ring will be a bit unstable as the little knob can now exit the groove and slide into the notch a bit, but with proper handling solving works fine. The fourth picture and reference [2] below show a 12 piece version, for which the formula provides a count of 16365 moves.
References

CR256 NameZigguflat

[1]
[2] [3] [4]
Designer Manufacturer Year
Bram Cohen, Oskar van Deventer Oskar van Deventer 2023
Arity No of pieces Piece type Solution length function Number of moves
4 6 board 2m+1—2·m—3 113
RemarksGoal: Disassemble and re-assemble again. Flat version of CR234 with one basical piece shape only (except for the borders). The puzzle consists of 6 pieces, but can be assembled in different ways with the same pieces: Removing green and yellow, a square version of 4 pieces (21 moves for full disassembly). By removing green or yellow, and turning purpple and blue over, in a rectangular version of 5 pieces (51 moves), and also a 3 piece version with red, orange, and yellow (ignoring the closed borders, 7 moves). With multiple copies of the puzzle, more inner pieces (yellow, green) can be added for higher move count, like an 8 piece version at 493 moves or a 10 piece version at 2025 moves. This is the first n-ary interlocking puzzle that is flat without a frame. This puzzle was used as DCD42 welcome gift in October 2023. The other two pictures show versions with 4 and 8 pieces as examples what can be built with the pieces as well. The fourth picture shows the mass produced version by Recent Toys.
References

CR264 NameZigguhooked

[1]
[2] [3]
Designer Manufacturer Year
Oskar van Deventer Oskar van Deventer 2024
Arity No of pieces Piece type Solution length function Number of moves
4 6 disks 2m+2—3·m—3 235
RemarksGoal: Rotate the discs so that they end up in the furthest anti-clockwise orientation, which unhooks the purple one from the tray blocker protusion and the board with the discs can be slid out from the tray. This is a 2D modification of the puzzle CR261 where the two functional layers of the discs have been replaced by a mechanism of two hooks per disc, which hook into gaps of the next disc. Here, an obvious similarity with the structure of CR256. Unlike the Ziggutwist, the movements in this puzzle are only subtle moves by a slight turn each, and they are shown in the second picture. An alternate version with the discs arranged in a stair shape can be seen in the video linked below.
References

CR234 NameZiggurat

[1]
[2] [3]
Designer Manufacturer Year
Bram Cohen, Eitan Cher Bram Cohen, Eitan Cher 2021
Arity No of pieces Piece type Solution length function Number of moves
4 8 board 2m+1—2·m—3 493
RemarksThis puzzle comes is a 3D printed stack of boards with pins running in grooves in the next two lower boards and a stand. Goal is to disassemble and re-assemble the puzzle. The boards come in two chiral variants, and the stack of boards alternates between left and right handed boards. Each board has a pin that runs through the next two boards and it is assumed that this the minimum number of boards for creating a meaningful recursive move pattern in the solution sequence. The first picture shows the whole puzzle on a stand, the second the puzzle in its initial configuration with only 6 of the 8 boards used, and the third picture from the bottom of the boards in mid solution somewhere. The puzzle was 3D printed in different colour schemes, and the Design Competition version clearly distinguished between the two chiralities by two different board colours. Reference 3 below is a Burr-Tools file created for the analysis of this puzzle. It shows two main aspects: The n-ary nature allowing to add more and more pieces, and the move counts appearing, and then also a left handed and right handed version of the puzzle. This is one of the few puzzles allowing such two different assemblies. Mazes with more grooves leading to a 4-ary or 6-ary puzzle (etc.) can also be created, so both the arity and the number of pieces can be changed.
References

CR269 NameZiggustretch / Screwy-Louie

[1]
[2] [3] [4]
Designer Manufacturer Year
Oskar van Deventer, Zachary Zieper Oskar van Deventer 2024
Arity No of pieces Piece type Solution length function Number of moves
4 [8] 6 tubes 2m+1+3·m—8 138
RemarksGoal: disassemble and then reassemble. This is a variation of the other Ziggu puzzles, and in this case the maze allows 4 different positions of each piece in the fully assembled state, where positions are indicated by the width of the gaps. In the second picture, both the internal mazes for the small pegs running in them can be seen, one S shaped maze, and a straight groove. The two pegs of each piece run in the straight groove of the next tube, and in the S shaped maze of the next piece after that, hence directly interacting with the two next pieces. Rotational moves will translate to a screwing motion, extending or shortening the gaps. When the puzzle is fully extended, it can be disassembled starting at the purple end, and each piece will then traverse the S shaped maze of the neighbor once more, so each piece has 8 positions in reality. Those last steps can be skipped by tilting the piece, but have been included in the solution length formula and total move count. As shown in the picture, there are two main flavors of pieces: Left handed and right handed pieces. These occur in an alternating fashion in the puzzle and additionally there are two modified end pieces (red and purple) without pegs or maze respectively. As the others are identical pairs, these could be used to build arbitrary large puzzles from these pieces. Pictures 3 and 4 show the Screwy-Louie puzzle, the smaller IPP41 Exchange puzzle version. The end pieces have front and back of a dachshund attached as 3D print, based on a 3D scan of Zachary's dog Louie. The goal is to dissassemble and reassemble, and also assemble into a 2 and a 4 piece dog. These shorter assemblies automatically line up the four legs on the same side as they should be.
References

CR265 NameZiggutrees

[1]
[2] [3] [4]
Designer Manufacturer Year
Oskar van Deventer Oskar van Deventer 2024
Arity No of pieces Piece type Solution length function Number of moves
4 6 round trees    
RemarksGoal: Rotate all trees so that the arrows are pointing to the opposite direction from the starting configuration, and then slide the board with the trees (screwed on) out from the tray. Similarly to CR263, this is achieved by an interaction by the bottom part of the purple piece (only in this case) and a cut-out in the frame. Here, the arrangement of the pieces has been changed into two lines that occur in a zig-zag pattern. The order of the piece to rotate is still the same, shown by the colours, but in this case each piece interacts with two neighbors in each direction, e.g. the yellow piece interacts with red and orange on one side, and on the other side it interacts with green and blue. For each piece, both earlier neighbors need to be arranged correctly to allow the current piece to rotate. The pieces come in two sets of 3 identical tree pieces, 3 left-handed, and 3 (mirror imaged) right-handed ones. While the other trees all make use of all 4 possible orientations during the solution, the red and orange trees only make use of their two extreme orientations. However, it is possible to rotate them to the other positions as well and then lock them with their neighbors, leading to dead end configurations.
References

CR261 NameZiggutwist

[1]
[2] [3]
Designer Manufacturer Year
Oskar van Deventer Oskar van Deventer 2024
Arity No of pieces Piece type Solution length function Number of moves
4 6 disks 2m+2—3·m—4 234
RemarksGoal: Rotate all disks so that the arrows are pointing in a 135° angle away from the initial position along the main axis of the puzzle (shown in second picture). While the puzzle has some resemblance with Spin-Out or Crazy Elephant Dance, this one does not feature a sliding frame to synchronize the disks. Instead only a local interaction between neighboring pieces is achieved here, which is similar to the other Ziggu* puzzles, and also the ternary puzzle inside CR195. However, the mechanism in the Ziggutwist puzzle is based on indentations in the disks, a bit similar to Spin-Out. Here, the disks have two layers with a different indentation arrangement (identical except for the first and last one). The third picture shows the possible orientation of the disks in an example configuration, and the interaction between neighbors is also visible in some places, as are some of the indentations on the lower layer as well. The longer indentations allow the respective disk to rotate between two orientations, while the shorter ones are used to enable a neigbor disk's rotation. Not all possible configurations occur in an optimal solution sequence. The discs are mounted to the board using screws and a second set of screws restrict the rotation of the disks to 135°.
References

CR263 NameZiggutwist Too

[1]
[2] [3]
Designer Manufacturer Year
Oskar van Deventer Oskar van Deventer 2024
Arity No of pieces Piece type Solution length function Number of moves
4 6 disks 2m+2—2·m—4 240
RemarksGoal: Rotate all disks so that the arrows are pointing in a 135° angle away from the initial position along the main axis of the puzzle (shown in second picture) and then slide them out from the puzzle. This is a minor modification of the puzzle CR261 where the discs still have the same two functional layers, but the pieces have now been extended so that they lock into a tray provided, instead of screwing to a board. They can be slid in the 135° position and are locked in the others. As all pieces are identical, all possible permuations of colours can be set up here.
References

3 Definitions, Examples and More

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.

3.1 Definition of CR Recursive Puzzle

A CR recursive puzzle is a puzzle that contains m special similar pieces (with m ≥ 1) and
  1. the puzzle can be generalized to other values of m ≥ 1 and
  2. each special piece has n different positions (e.g. 0,...,n—1, with n ≥ 2) and
  3. there is a uniform condition stating that a special piece can only move between some positions if the other special pieces are in certain positions.

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. Also note, that one of the different positions each piece could have is the "removed" state, when it is extracted from the puzzle. This state is only counted in this definition if it occurs within the n-ary sequence and occurs regularly, not when at the end all pieces are extracted from the puzzle one after the other.

This is a short and formal definition related to the structure of the puzzle. Some examples might be useful.

3.2 Examples

3.2.1 Classic CR puzzle

Chinese Rings

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:

and the uniform condition for moving a ring is: The k-th ring can be moved between 1 and 0, if and only if ring (k—1) is in position 1 and all rings to the left of (k—1) are in position 0.

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.

3.2.2 SpinOut

SpinOut SpinOut

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).

3.2.3 Crazy Elephants Dance

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.

3.2.4 Kugellager

Kugellager

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.

3.2.5 Tower of Hanoi

Tower of Hanoi

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.

3.3 What does "uniform" mean in the definition?

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:

3.4 Where does the term "recursive" come from?

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:

  1. Only one disc may be moved at a time
  2. Never place a bigger disc on top of a smaller one

Tower of Hanoi

A typical Algorithm to solve this problem can be described informally as follows:

Move Tower of n discs from startTower to endTower:

  1. 6 - startTower - endTower → auxiliaryTower // the tower that is not one of the two above
  2. if n>1 then
  3. Move Tower of n—1 discs from startTower to auxiliaryTower
  4. Move one disc from startTower to endTower
  5. if n>1 then
  6. Move Tower of n—1 discs from auxiliaryTower 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.

Chinese Rings

This can be established by a recursive algorithm with the following ideas:

  • move i-th ring off the loop:
    1. Move ring i—1 (to the left of ring i) onto the loop
    2. move all rings left of i—1 off the loop
    3. then perform the movement of i-th ring

  • move i-th ring onto the loop:
    1. Move ring i—1 (to the left of ring i) onto the loop
    2. move all rings left of i—1 off the loop
    3. then perform the movement of i-th ring
Here we see that for the movement of the i-th ring, preparation moves must be performed, and for these the algorithm can invoke itself recursively. More details can be found in the book [3] and a more mathematical observations in the book [6].

3.5 Tuple Representation and a Different Notation: n-ary Puzzles

Before the formalization of the recursive puzzles as above, a different notation was used in prior discussions: "n-ary 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 2m. 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 2m, which is a justification for our structural definition. Why ternary puzzles can have 2m as solution length function is discussed below.

A mathematical argument for calling these puzzles "n-ary" is that their current state can be represented by an m-tuple 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:

(0,0,0,0,0,0,0) → (0,0,0,0,0,0,1) → (0,0,0,0,0,0,1,1) → ... → (1,1,1,1,1,1,0) → (1,1,1,1,1,1,1)

A ternary example is the Crazy Elephant Dance, with the following encoding:

(0,0,0,0,0) → (0,0,0,0,2) → (0,0,0,1,2) → (0,0,0,1,0) → (0,0,0,2,0) → (0,0,0,2,2) → (0,0,1,2,2) → ... → (2,2,2,2,2)

3.6 Puzzle Parameter and Different View: Number of Moves

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
2m+m+3 Θ( 2m ) Linear and constant summands neglectable
2 · 5n Θ( 5n ) Constant factor neglectable
2(m—1) Θ( 2m ) 2(m—1)= (1/2)·2m, constant factor neglectable
3 · (2m—1) — 2·m Θ( 2m ) Combination of examples above

The Θ notation is taken from Computer Science and Mathematics, the formal definition and details are explained in [5].

3.7 CR recursive puzzles with solution length only ~2m

Why do some CR recursive puzzles with n>2 have a solution with only ~2m moves, not ~nm? CR recursive puzzles with solution length ~nm obviously use all different combinations of piece positions in their solution. To see this, just recall that the number of m-tuples over a set with n different values is exactly nm 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 ~2m 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.

Crazy Elephants Dance

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:

  1. Condition for moves: Puzzles with all configurations (and hence solution length nm) have conditions that involve both lower and higher pieces. For an example see the Kugellager above. Others do only involve a part of the other pieces. The examples in this paragraph are of such nature. For Ternary Burr and Crazy Elephant Dance, it only matters which positions the lower pieces have. Pieces may be moved no matter in which positions the higher pieces currently are. This allows to bring a piece from position 0 to n—1 without touching the higher pieces at all. When solving Kugellager, you will notice that when moving the lowest piece later in the solution, you will have to move higher pieces before.
  2. The second observation deals with Tower of Hanoi and Rudenko Clips. Both have the same general structure (3 positions) and equivalent rule: However, the first one has a solution length ~2m, while the Clips need ~3m moves. Here, the condition is the same, but there is an additional condition in Rudenko Clips: The three positions 0, 1, and 2 are in a row and a clip may only move between positions 0 and 1, if the stack of smaller clips is on 2, and a clip may only move between positions 1 and 2, if the stack of smaller clips is on 0. No direct move from 0 to 2 is possible for all clips except the biggest one. For Towers of Hanoi, we may use positions freely (only obeying the "bigger disc" rule). In the picture below, the red clip is not able to move from position 0 to 2 over the green one, while this would be the canonical next step in Tower of Hanoi. For a discussion on graph representations also leading to 2m and 3m as solution lengths, please see [4].
Rudenko Clips

3.8 Tower of Hanoi - binary or ternary?

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.

3.9 A different definition for n-ary puzzles based on number of moves

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 n-ary 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 nm, it is classified as n-ary (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 2m, 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.

4 References

[1] Goetz Schwandtner. Kugellager.pdf.

[2] Goetz Schwandtner. n-ary 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 N-ary Mechanical Puzzles. CFF95. Rijswijk, 2014. The next entry [12] is the most recent updated version

[12] Goh Pit Khiam. Design of N-ary Mechanical Puzzles. (extended version, latest update 2014-12-15; 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] CFF 100 (Cubism For Fun 100). Rik van Grol (Ed.). Rijswijk, 2016.

[16] Analysis of Ring Puzzles. Chinese Rings, Pagodas, Zig Zags. For IPP13. Richard I. Hess. Amsterdam, 1993.

[17] CFF67. Rik van Grol (Ed.). Rijswijk, 2005.

[18] Homage to a Pied Puzzler. Alan Schoen, Tom Rodgers, Ed Pegg Jr. CRC Press. 2009. ISBN: 1138115010

[19] The Puzzler.One Man's Quest to Solve the Most Baffling Puzzles Ever, from Crosswords to Jigsaws to the Meaning of Life. A.J. Jacobs. Crown. New York, 2022. ISBN: 9780593136713

[20] Puzzling Aspects of Binary Disk, CFF122. Goetz Schwandtner (Auth.), Rik van Grol (Ed.), Brunssum, 2023.

5 Acknowledgements

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, Fredrik Stridsman, and Oskar van Deventer. 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)

6 Feedback

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.