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

Image(s) of puzzle. Click on image or links for bigger image versions. 
Designer  Manufacturer  Year  
Name of creator of puzzle design  Name/Company name of manufacturer  Year of first release  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
# of Levels (n) or n' [n], see note below  special pieces only  of special pieces (m)  exact or asymptotic (Θ) function of n and m  counted/calculated  
Remarks  Remarks about special features, similar puzzles.  
References  Links to patents, Extremely Puzzling page, other web pages on this puzzle  
Symbols:  ^{§}=counting moves of special pieces only; ^{‡}=counting moves until first piece comes out 
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 nary 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 3^{m}), 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 nary 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 CtrlF or F3).
Hint: For previews of secondary images or the variants (entries with IDs), please hover the mouse pointer over the corresponding link (without clicking). In the top right corner of the browser window, a preview will appear. Unfortunately, this does not work on all browsers; in particular some Internet Explorer versions do not show these previews.
Beside this introduction and the list of puzzles there are also a page with a formal definition of the structure of puzzles that belong into this compendium, including some properties and examples. The compendium is concluded by a page to contribute to this compendium by adding puzzles or new information. Please have a look at the navigation bar on top of all pages or the table of contents below.
PuzzleID  Name  (example entry for explanation of fields)  

Image(s) of puzzle. Click on image or links for bigger image versions. 
Designer  Manufacturer  Year  
Name of creator of puzzle design  Name/Company name of manufacturer  Year of first release  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
# of Levels (n) 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  
Remarks  Remarks about special features, similar puzzles.  
References  Links to patents, Extremely Puzzling page, other web pages on this puzzle  
Symbols:  ^{§}=counting moves of special pieces only; ^{‡}=counting moves until first piece comes out  
CR226  Name  4L 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  Lblock  2^{m+1}—2  30  
Remarks  Variant: CR237. Goal is to pack all the Lblocks 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  [1]  
CR237  Name  5L 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  Lblock  2^{m+1}—2  62  
Remarks  Variant: CR226. Goal is to pack all the Lblocks 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  [1]  
CR214  Name  5 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  
Remarks  Variant: CR212. This box has one compartment and follows the basic move scheme of CR172.  
References  [1]  
CR091  Name  Algorithme 9  
Designer  Manufacturer  Year  
Patrick Farvacque  Patrick Farvacque  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  9  discs  
Remarks  The Algorithme series features different puzzles with different number of discs, different disc heights and post heights. They are all some variation of Tower of Hanoi, which can also be seen in the rules: move one disc at a time, which is on top of its pile; no bigger disc may be put on a smaller one (equal size is OK); piles may only go up to post end, not higher.  
References  CFF79 contains an article by Dick Hess about Algorithme 6  
CR174  Name  Alken/Kenal  
[1] [2] [3] 
Designer  Manufacturer  Year  
Alfons Eyckmans, Ken Johnson  Alfons Eyckmans  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2 [4]  6  panel  321  
Remarks  Variant of CR160, but not coming apart and only with 5 binary pieces, and one lid piece to be removed by the solution sequence. The lid piece has a different structure, and leads to four puzzles: Alken has lid piece which is binary (135 moves) in one orientation and 6ary (321 moves) in the other. Kenal has a binary (135 moves) and 4ary (257 moves) lid piece. The 135 move configurations also allow the solution sequence to run over the point branching into the last few moves before lid removal, and then leading to a dead end. These dead ends can also be reached when reinserting the lid and trying to close the box. Also at the beginning of the 135 move sequences (box closed) there are some dead ends possible. Second pictures shows the box open and details of the lid pieces, the third piece shows the lid to be slid open without removal, possible for the Kenal 135 configuration just before the end of the sequence.  
References  [1]  
CR127  Name  Alles Schiebung  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  slider  42  
Remarks  Additional locking mechanism; AKA: Sternary  
References  [1]  
CR212  Name  Aquarius 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  
Remarks  Variant: 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  [1], [2]  
CR172  Name  Aquarius Drawer (5 devices)  
Designer  Manufacturer  Year  
Hiroshi Iwahara  Hiroshi Iwahara  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  block  61  
Remarks  Five blocks form a ternary chain of pieces, with two small drawers at the ends. First drawer can be opened after 5 device moves, the other requires 61 moves.  
References  [1], [2]  
CR061  Name  A Slidely Tricky Tower  
[1] [2] [3] [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( 3^{m} )  485  
Remarks  Different 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 2·3^{m—1}—1 moves. Other cases have just Θ(2^{m}) 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 onetower Panex.  
References  [1]  
CR046  Name  Apricot  
Designer  Manufacturer  Year  
Akio Kamei  Akio Kamei  2002  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  panel  
Remarks  
References  [1]  
CR023  Name  Auf dem Holzweg  
Designer  Manufacturer  Year  
Juergen Reiche  Siebenstein  2011  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  slider  
Remarks  Two arity 3 puzzles in one  
References  [1]  
CR177  Name  Bald Eagle  
Designer  Manufacturer  Year  
DDK, Aaron (Yulong) Wang  Aaron (Yulong) Wang  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
1 [2]  5  ring+connector  Θ( m )  
Remarks  Goal is to remove the big foldable circle piece, which starts in the middle. It can traverse to the left or right end, both consisting of 5 ring+connector pairs. While there are two states for the big circle and each ring+connector pair (i.e. binary), the overall solution is linear. Each pair is traversed only once. The zigzag chain of rings on the main loop looks like the structures used in others of Aaaron's nary puzzles.  
References  [1]  
CR039  Name  Barcode Burr  
[1] [2] [3] 
Designer  Manufacturer  Year  
Lee Krasnow  Lee Krasnow  2004  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  burr piece  2^{m+1}—4  124  
Remarks  Variants: CR137, CR199; some shortcuts exist  
References  [1]  
CR137  Name  Barcode 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  2^{m+1}—4  124  
Remarks  3D 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  [1]  
CR199  Name  Barcode 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(4^{m})  1233  
Remarks  3D 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 addon 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 nary sequences. This set can be seen in the fourth picture and third reference.  
References  [1], [2], [3]  
CR257  Name  BBar  
Designer  Manufacturer  Year  
Felix Davis  FADplus  2023  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  slider  2^{m}  256  
Remarks  Goal 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  [1]  
CR160  Name  BBox  
[1] [2] 
Designer  Manufacturer  Year  
Goh Pit Khiam  Eric Fuller  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2 [4]  6  panel  135  
Remarks  This is a combination of puzzle box and burr. Not only the panels can be opened and removed, but also the frame can be taken apart completely. Inside the box is a second puzzle, the Reactor by Eric Fuller, a small puzzle box.  
References  [1]  
CR115  Name  Bicomplementary Formation b/b:1/2  
[1] [2] [3] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  11  bars, sticks  70^{‡}  
Remarks  V1, N01; Two interlocking binary sequences (one of bars, one a bit hidden of the sticks). Beside the binary moves, this puzzle also contains burr moves without an nary scheme and with halfnotches. The number of moves contains the binary sequences and some of the burr like moves.  
References  [1]  
CR134  Name  BiNary  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  sliderpair+ball  259  
Remarks  This puzzle combines the mechanisms of CR064 and CR087. The pictures shows second and first edition. The second is more stable and removes a solution issue of the first.  
References  [1], [2]  
CR247  Name  Binary 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  
Remarks  There 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  [1], [2], [3], reference section [20]  
CR006  Name  Bin Laden  
Designer  Manufacturer  Year  
Rik van Grol  Rik van Grol  2006  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  drawer  21  
Remarks  Partially ternary and modified sequence  
References  [1]  
CR150  Name  Bin Laden Too  
Designer  Manufacturer  Year  
Rik van Grol  Rik van Grol  2015  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  drawer  
Remarks  Additional mechanisms, modified sequence, combination of several binary sequences. The objective to remove the dice modifies the sequence even further, as a die can only be taken out when a drawer is fully extended and the drawer above in its starting position inside the box.  
References  [1]  
CR073  Name  Binary Bud  
[1] [2] [3] [4] [5] [6] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  leaf  Θ( 2^{m} )  
Remarks  Goal: 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  [1], [2]  
CR169  Name  Binary Ladder Disentanglement  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  ring  
Remarks  Name unknown; this version is of early 1990s or shortly before.  
References  [1]  
CR063  Name  Binary Key II  
Designer  Manufacturer  Year  
Goh Pit Khiam  Cubicdissection  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  switch  ^{1}⁄_{6} [—7·(—1)^{m}+2^{m+4}—9]  85  
Remarks  Variation of CR058  
References  [1]  
CR207  Name  Black BowTie  
[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  2·9^{m}  13122  
Remarks  Variant: 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 9ary 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  [1]  
CR163  Name  BNary  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  slider  Θ( 3^{m} )  220  
Remarks  The mechanism is hidden and seems to consist of the four sliders, several ball bearings, and sliding pieces. There is also one additional ball bearing that has to travel from start to goal, from where it can be put into the start position via a reset feature. During this time, the ternary sequence is executed twice (forwards, then backwards) with 54 slider moves each. The total number of moves includes these slider moves (2·54), the corresponding tilting moves to move ball bearings/sliding pieces (2·54), tilting moves to move the extra ball bearing inside the puzzle and out (3+1). Once the extra ball bearing has reached the half way position, it can go inside the sliders and cause some lockups that have to be undone by reversed moves before the regular sequence can continue.  
References  [1]  
CR182  Name  Buggin  
Designer  Manufacturer  Year  
Stuart Gee  Stuart Gee  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  loop  
Remarks  Variant of: CR031 by linking two of these (with 3 loops) together at the end of the sequence. Sequences can mainly be traversed one after the other.  
References  [1]  
CR248  Name  Caged 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  
Remarks  Goal 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  Name  Cast Infinity  
Designer  Manufacturer  Year  
Vesa Timonen  Hanayama  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
6  2  disc  
Remarks  Two interlocking discs which can rotate between six positions and can move up and down. Objective is to remove the discs.  
References  [1]  
CR059  Name  Chinese Rings 5  
[1] [2] [3] 
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  ring  [2^{m+1}/3]  21  
Remarks  Variants: CR042, CR208. The pictures 2 and 3 show other versions with 5 rings. Reference [14] shows a 7 ring variant including solution.  
References  [1], [2], [3], Reference Section [9] and [14] (pp. 100102)  
CR042  Name  Chinese Rings 9  
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  ring  [2^{m+1}/3]  341  
Remarks  Variants: CR059, CR208  
References  [1], Reference Section [9]  
CR208  Name  Catacombs / Chinese Rings 12  
Designer  Manufacturer  Year  
Puzzlemaster.ca  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  12  ring  [2^{m+1}/3]  2730  
Remarks  Variants: CR042, CR059  
References  [1], Reference Section [9]  
CR202  Name  Chinese 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( 2^{m} )  
Remarks  Version 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 online, 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  [1], [2], [3]  
CR236  Name  Coherent 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( 2^{m} )  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  [1], [2]  
CR123  Name  Complementary parity  
[1] [2] [3] [4] [5] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  14  bars, loops  102^{‡}  
Remarks  Complimentary combination of several different sequences: Top 5 bars run in a 3ary sequence, together with the 5 bottom bars, who run (slower) in a 2ary sequence. These interact with the 4 looppieces, which run accross in a 3ary sequence. First challenge of the puzzle is to understand these sequences, then the second is to disassemble and correctly reassemble the puzzle, with many other parts, alltogether 29 pieces.  
References  [1], [2]  
CR054  Name  Computer Loops  
Designer  Manufacturer  Year  
MagNif  1975  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  ring  [2^{m+1}/3]  170  
Remarks  
References  [1]  
CR031  Name  Computer Puzzler No 2  
[1] [2] 
Designer  Manufacturer  Year  
Tenyo  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  loop  Θ( 2^{m} )  
Remarks  
References  [1], [2] (US Patent 1091709), [3]  
CR034  Name  Computer Puzzler No 5  
[1] [2] 
Designer  Manufacturer  Year  
Tenyo  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  loop  
Remarks  was No 3 earlier; Variants: CR003, CR013, CR024, CR045, CR081, CR122  
References  [1], [2]  
CR010  Name  Crazy Elephant Dance  
[1] [2] [3] 
Designer  Manufacturer  Year  
Markus Goetz  Peter Knoppers  2005  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  elephant  3·(2^{m}—1)—2·m  83  
Remarks  The second and third pictures show the original prototype of the puzzle.  
References  [1], reference section [17], [18]  
CR219  Name  Crazy 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·(2^{m}—1)—2·m  367  
Remarks  3D 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  [1]  
CR175  Name  Corn on the Cob I  
Designer  Manufacturer  Year  
Aaron (Yulong) Wang  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2 [4]  9  ring pairs  Θ( 2^{m} )  
Remarks  This is mainly a (binary) Chinese Rings puzzle with single rings. The second ring of each pair is dropped from the main bar when the corresponding ring get's off the bar. It will then stay unhooked, while the primary ring follows the usual Chinese Rings sequence. For each pair there are four states (on/off loop for each ring), so this puzzle can also be considered quarternary. However, the main sequences and interactions are only binary, with touching every secondary ring only once, hence classified as binary here.  
References  [1]  
CR178  Name  Corn on the Cob II  
Designer  Manufacturer  Year  
Jianjiang Wu  Aaron (Yulong) Wang  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2 [4]  9  ring pairs  Θ( 2^{m} )  
Remarks  This is mainly a (binary) Chinese Rings puzzle with single rings in a chinese rings chain (CRC) and then an additional chain, a zig zag chain (ZZC) through the connector piece ends. When the last ring from the CRC on the handle bar is dropped, a sequence through the ZZC follows. As this is a ZZC, half of the rings are wrongly oriented for the usual sequence, and at those points parts of the CRC are traversed to the beginning of the CRC, to allow access to the ZZC rings in the other orientation. These interruptions in the ZZC sequence by CRC sequences will then happen until the completion of the solution. The main scheme is that the rings of the CRC come off one after another like in a Chines Rings puzzle. Consequently, the reassemlby follows this scheme: Run through the CRC to put on the last free ring of the CRC, then put the lasts free ring of the ZZC on the handle bar. This automatically adds two rings of the ZZC, so one will need to be released to allow to put on the next CRC ring. For this some ZZC sequences are required, with some CRC sequences performed up to the correct entry point of the ZZC. The scheme can be learned with a few ring pairs (up to 4) initially, but only with 7 or 9 ring pairs, all required moves become apparent.  
References  [1]  
CR188  Name  Corn on the Cob III  
Designer  Manufacturer  Year  
Jianjiang Wu  Aaron (Yulong) Wang  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2 [4]  9  ring pairs  Θ( 2^{m} )  
Remarks  Like the first two puzzles in the series, the CotC III is mainly a binary chinese rings puzzle. Each ring is part of a pair with a free ring (only one end caught in a connector) and a ring part of the main zigzag back bone. After analysis, the puzzle can be solved with some simple rules: Each ring has only one correct orientation on the handlebar piece. The free rings form a binary chinese rings puzzle that needs to be solved, and when the bar needs to go through one ring of a pair, it should always go through the free ring. The last rule is about reassembly (entanglement): When the handlebar is at the rightmost free/zigzag ring pair, it should break the rule before and go through the zigzag ring.  
References  [1]  
CR203  Name  Corn 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( 2^{m} )  
Remarks  This 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 zigzag backbone, while the other ring is only attached to one connector and can be on the main handle or off. The zigzag 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  [1]  
CR204  Name  Corn 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( 2^{m} )  
Remarks  This 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  [1]  
CR206  Name  Corn 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( 2^{m} )  
Remarks  This 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  [1]  
CR047  Name  Cross and Crown  
[1] [2] 
Designer  Manufacturer  Year  
Louis S. Burbank  1913  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  rivet  2·5^{m}  1250  
Remarks  Variants: CR120, CR121, CR158  
References  [1] (US Patent 1071874), [2]  
CR120  Name  Cross and Crown 2013  
Designer  Manufacturer  Year  
Louis S. Burbank  Robrecht Louage  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  rivet  2·5^{m}  1250  
Remarks  Reproduction based on the original patent; Variants: CR047, CR121, CR158  
References  [1], [2] (US Patent 1071874)  
CR121  Name  Cross and Crown 7  
Designer  Manufacturer  Year  
Louis S. Burbank, Michel van Ipenburg  Robrecht Louage  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  rivet  2·7^{m}  4802  
Remarks  Variants: CR047, CR120, CR158  
References  [1]  
CR140  Name  Crossing  
[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  
Remarks  Goal: slide the pieces so that the left black L shape ends up in the bottom left corner  
References  [1], reference section [12]  
CR056  Name  CUBI  
Designer  Manufacturer  Year  
Akio Kamei  Akio Kamei  1985  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  2^{m—1}  32  
Remarks  Variant: CR048, CR162  
References  
CR092  Name  Delirium  
[1] [2] [3] [4] 
Designer  Manufacturer  Year  
Stéphane Chomine  Claus Wenicker  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  28  burr pieces  (2^{m+2}—1 — (m mod 2))/3  357913941  
Remarks  Simplified version of: CR012, CR076, pictures show versions with 28, 5, 6, and 38 special pieces. Reference 1 shows form for arbitrary many special pieces. Variant: CR154  
References  [1]  
CR154  Name  Delirium 13  
Designer  Manufacturer  Year  
Stéphane Chomine  Johan Heyns  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  12  burr pieces  (2^{m+2}—1 — (m mod 2))/3  5461  
Remarks  Simplified version of: CR012, CR076. Reference 1 shows form for arbitrary many special pieces. Variant: CR092  
References  [1], [2]  
CR250  Name  Devil  
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  
Remarks  Goal 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 mixedbase 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 nary 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  [1]  
CR075  Name  Devil's Cradle  
Designer  Manufacturer  Year  
Rick Irby  2000  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  pair of loops  
Remarks  Variants: CR014, CR030, CR067, CR068, CR069, CR070  
References  
CR060  Name  Die Welle  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  3  ball  5^{m}—1  124  
Remarks  
References  [1]  
CR124  Name  Digi Fork Lock  
[1] [2] [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  
Remarks  Enhancement 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  [1], [2]  
CR159  Name  Digits' Compressor  
[1] [2] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  disc  49  
Remarks  Goal is to compress the digit stack to minimal height by rotating discs and moving them verticalle, and additionally to line up the red markings with the four red markings on top and bottom parts. There are several differentlength dead end sequences. The five gray discs move in a binary symmetric Gray code sequence, unlike the black ones. Each disc has an orange pin, which can interock with two different holes in the disc below, i.e. two differet positions for each disc.  
References  [1], [2]  
CR158  Name  Disc & Crown CFF 100 Jubilee Edition Puzzle  
[1] [2] 
Designer  Manufacturer  Year  
Robrecht Louage, Michel van Ipenburg  Robrecht Louage  1916  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  rivet  2·3^{m}  54  
Remarks  Limited edition of 500 that was a gift with CFF issue 100. Variants: CR047, CR120, CR121  
References  [1], Reference Section [15]  
CR192  Name  Disordered Chinese Rings  
Designer  Manufacturer  Year  
Yuandong Jiang, Aaron (Yulong) Wang  Aaron (Yulong) Wang  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  rings  
Remarks  While the rings in the classic Chinese Rings puzzle are linking their connector with the next connector each, in this one, the regular scheme is broken and some rings go over the next two or three connectors. Some of them lead to irregularly stacked rings on some connectors, while for others the rings over the next one and two connectors are aligned in parallel over one connector. When solving, one has to ensure to choose the right ring for the sequence and which ring to skip, while the overall solution sequence is aligned to the general Chinese Rings sequence.  
References  [1]  
CR074  Name  Dispersed GC Lock  
[1] [2] [3] [4] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  switch  184  
Remarks  Code corresponds to setting 1100 of CR020  
References  [1], [2]  
CR143  Name  DITWIBIN  
[1] [2] [3] [4] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  slider  Θ( 2^{m} )  
Remarks  One of the simplest designs of a whole puzzle family, with different number of sliders, disks, and arities. This design was devised fist for higher order variants in August 2014, about a month before this puzzle. One of the higher order variants is CR149.  
References  [1]  
CR170  Name  Double Helix  
Designer  Manufacturer  Year  
Goh Pit Khiam  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  pairs of burr sticks  73  
Remarks  This puzzle consists of 20 pieces, of which 8 are the special pieces (middle layers). A pair of pieces makes up one level, as outlined in the article referenced below.  
References  reference section [12]  
CR194  Name  Double Image  
Designer  Manufacturer  Year  
DDK  Aaron (Yulong) Wang  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  ring+connector  
Remarks  The main chain of this is a classic 9 ring Chinese Rings puzzle. Attached to rings 3, 5, 7, and 9 are a small ring and connected to that two regular sized rings. Those rings are linked with the previous and next connector. During the solution, only at most one ring of each additional ring pairs will be on the handle. The main solution sequence is still binary, but one has to determine when to pick up the forward / backward secondary ring. At some points in the solution, both the primary ring and the secondary ring are on the main bar, at other points in the solution, also only the secondary ring might be on the main bar (but this only holds for the forward rings, the secondary backwards rings are never on the handle alone). Therefore, the puzzle could also be classed as a ternary puzzle, or even quarternary, but the main structure is still binary.  
References  [1]  
CR135  Name  Double Loop  
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  2  loop pairs  
Remarks  Variant: CR067 (other variants see there)  
References  [1], [2]  
CR101  Name  Dragonfly  
[1] [2] 
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  rings  23  
Remarks  extra rings for symmetry; second picture shows Airplane puzzle  
References  [1]; Reference Section [7] and [8]  
CR146  Name  Drunter & Drueber  
Designer  Manufacturer  Year  
Juergen Reiche  Siebenstein  2015  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  loop  Θ( 2^{m} )  
Remarks  
References  [1]  
CR014  Name  Electro 1  
[1] [2] [3] 
Designer  Manufacturer  Year  
Tenyo  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  pair of loops  26  
Remarks  The second picture shows an unknown variant. Variants: CR030, CR067, CR068, CR069, CR070, CR075  
References  [1], [2]  
CR015  Name  Electro 2  
[1] [2] 
Designer  Manufacturer  Year  
Gabor Vizelyi  Tenyo  1981  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  loop  25  
Remarks  
References  [1] , [2] US Patent 4391445, [3]  
CR153  Name  Elephant Wire Puzzle  
Designer  Manufacturer  Year  
Beijing Oriental Top Science Trading Ltd  2003  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  loop  
Remarks  Variant of: CR031 with a more irregular shape. The instructions lists 11 different starting positions as challenges.  
References  [1]  
CR198  Name  Entwined Loop Lattice  
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
7  4  loop  Θ( 3^{m} )  80  
Remarks  This is actually a section of an infinite puzzle: The puzzle could be extended infinitely to the right or left. If this structure is closed as a loop, this will lead to something like CR197. Therefore, the arity is hard to determine. There are six loops and the configuration off the loop for each pole/sector, so 7ary might be a good description. However, the solution only makes use of 4 of the poles (and the rope off the puzzle), so it is more 5ary, and the actual solution length is 3ary. For the solution the two bends of the rope start in the compartments denoted by red triangles, and each bend will be maneuvered off the puzzle separately, with 40 moves each. In the IPP38 Design Competition it participated as part of "Loopy Lattice Puzzles"; other puzzles from the same series: CR196, CR197  
References  [1], [2]  
CR245  Name  Eurofalle 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  
Remarks  Variant of: CR023, Two arity 3 puzzles in one. Goal is to remove the top slider and extract the coin.  
References  [1]  
CR071  Name  Expansion V  
[1] [2] 
Designer  Manufacturer  Year  
Akio Kamei  Akio Kamei  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  2^{m—1}+3  35  
Remarks  Simpler variant of: CR094  
References  [1], [2]  
CR094  Name  Expansion VI  
[1] [2] [3] 
Designer  Manufacturer  Year  
Akio Kamei  Akio Kamei  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  Θ( 2^{m} )  83  
Remarks  More complicated variant of: CR071  
References  [1], [2]  
CR157  Name  Extended Chinese Rings  
Designer  Manufacturer  Year  
Ruan Liuqi  Bob Easter  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  rings  Θ( 2^{m} )  
Remarks  Various extended Chinese Rings, based on the designs from the book given in the references section. These designs are e.g.: CR108, CR110, CR111  
References  Reference Section [7] and [8]  
CR228  Name  Faraday Cage  
Designer  Manufacturer  Year  
Heping Gao  Heping Gao  2021  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  loop  
Remarks  Goal is to remove the rope with the wooden ball. The sequence is similar to some classic loop and rope based nary puzzles.  
References  [1]  
CR072  Name  Ferris Wheel  
Designer  Manufacturer  Year  
Jean Carle  Eureka 3D Puzzles  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  loop  
Remarks  Variant: CR144  
References  [1], [2]  
CR147  Name  Fibula Puzzle  
Designer  Manufacturer  Year  
Lord Minimal  Monkeys Cage  2015  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  loop  
Remarks  
References  [1], [2]  
CR052  Name  Fidgety Rabbits  
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2012  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  rabbit disc  Θ( 2^{m} )  170  
Remarks  Variant: CR018  
References  [1], [2]  
CR018  Name  Fidgety Rabbits ternary  
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2012  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  rabbit disc  Θ( 3^{m} )  230  
Remarks  Variant: CR052  
References  [1]  
CR129  Name  Find my Hole  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  discs  
Remarks  This puzzle contains three disks, but from a mathematical view, the top and bottom disc act as one and have to be moved simultaneously in different directions. Additional locking mechanism.  
References  [1]  
CR098  Name  Fish  
[1] [2] 
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  rings  27  
Remarks  The first picture shows the "Wicked Wire" version by Professorpuzzle.  
References  [1]; Reference Section [7], [8], and [14] (p.153)  
CR161  Name  Fishing Hook Chain 9Ring  
Designer  Manufacturer  Year  
DDK  Aaron (Yulong) Wang  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  9  rings+loops  
Remarks  The three states of each ring+loop pair are: main bar through the loop (or "fishing hook", initial configuration), through the ring, and off both. When reassembling the puzzle, an additional challenge arises: it may easily happen that some hooks end up on the main loop in wrong orientation. As this can only be seen after many (up to 1000s) of moves, careful planning is advised and analaysis of smallers problem of the first few hooks only. One feasible approach is to arrange the loops in an alternating pattern above and below the the backbone while running through the sequence.  
References  [1]  
CR114  Name  Football  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  21  
Remarks  
References  Reference Section [7] and [8]  
CR110  Name  Fortune  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  12  rings  993  
Remarks  
References  Reference Section [7] and [8]  
CR081  Name  Frame & Loop Octet  
[1] [2] 
Designer  Manufacturer  Year  
Abraham Jacob  Abraham Jacob  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  loop  
Remarks  Variants: CR003, CR013, CR024, CR034, CR045, CR122  
References  [1]  
CR024  Name  Frame & Loop Quartet  
Designer  Manufacturer  Year  
Abraham Jacob  Abraham Jacob  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  loop  
Remarks  Variant of Computer Puzzler No 5; Variants: CR003, CR013, CR034, CR045, CR081, CR122  
References  [1]  
CR003  Name  Frame & Loop Quintet  
Designer  Manufacturer  Year  
Abraham Jacob  Abraham Jacob  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  loop  
Remarks  Variants: CR013, CR024, CR034, CR045, CR081 , CR122  
References  [1]  
CR122  Name  Frame & Loop Septet  
Designer  Manufacturer  Year  
Abraham Jacob  Abraham Jacob  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  loop  
Remarks  Variants: CR003, CR013, CR024, CR034, CR045, CR081  
References  [1]  
CR045  Name  Frame & Loop Sextet  
Designer  Manufacturer  Year  
Abraham Jacob  Abraham Jacob  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  loop  
Remarks  Rereleased for IPP34 Exchange; Variants: CR003, CR013, CR024, CR034, CR081, CR122  
References  [1]  
CR013  Name  Frame & Loop Trio  
Designer  Manufacturer  Year  
Abraham Jacob  Abraham Jacob  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  loop  
Remarks  Variants: CR003, CR024, CR034, CR045, CR081, CR122  
References  [1]  
CR079  Name  Frequency Doubler 1  
[1] [2] 
Designer  Manufacturer  Year  
Oskar van Deventer  Tom Lensch  2012  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  slider  4·(m^{2}+2·m—1)  28  
Remarks  Variants: CR080, CR090 older design, but first made in this version in 2012  
References  [1]  
CR080  Name  Frequency Doubler 2  
[1] [2] 
Designer  Manufacturer  Year  
Oskar van Deventer  Tom Lensch  2012  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  6  slider  4·(m^{2}+2·m—1)  56  
Remarks  Variants: CR079, CR090 older design, but first made in this version in 2012  
References  [1]  
CR090  Name  Frequency Doubler 3  
[1] [2] 
Designer  Manufacturer  Year  
Oskar van Deventer  Tom Lensch  2012  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  8  slider  4·(m^{2}+2·m—1)  92  
Remarks  Variants: CR079, CR080, second picture shows solved state, older design, but first made in this version in 2012  
References  
CR229  Name  Gears Box  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2021  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  7  sliders and gear rows  
Remarks  Goal is to open the box. For this, first the additional cover needs to be removed and then the nary 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  [1]  
CR089  Name  GC machine ternary  
[1] [2] [3] [4] [5] [6] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  switch  141  
Remarks  Goal is to move all switches to the "far out" position  
References  [1]  
CR065  Name  Generation Lock  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
15  8  slider  2·15^{m—1}  341718750  
Remarks  second picture shows comparison with CR037; Variant: CR037  
References  [1] [2]  
CR067  Name  Gordian Knot  
Designer  Manufacturer  Year  
Eureka 3D Puzzles  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  2  pair of loops  
Remarks  Variants: CR014, CR030, CR068, CR069, CR070, CR075, CR135; alternative version named "Gekkenwerk" was devised by Jack Botermans, see reference section [13] pp. 76 and 77, including a solution  
References  [1], [2], reference section [13]  
CR068  Name  Gordian Knot 2  
[1] [2] 
Designer  Manufacturer  Year  
Huso Taso  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  1  pair of loops  
Remarks  The second picture shows a variant built by Jan Sturm (new in 2014). Variants: CR014, CR030, CR067, CR069, CR070, CR075  
References  [1], [2]  
CR069  Name  Gordian Knot 4  
Designer  Manufacturer  Year  
Huso Taso  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  2  pair of loops  
Remarks  Variants: CR014, CR030, CR067, CR068, CR070, CR075  
References  [1]  
CR070  Name  Gordian Knot 6  
Designer  Manufacturer  Year  
Huso Taso  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  pair of loops  
Remarks  Variants: CR014, CR030, CR067, CR068, CR069, CR075  
References  [1]  
CR112  Name  Gourd  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  rings  5  
Remarks  
References  Reference Section [7] and [8]  
CR118  Name  Grydlock  
[1] [2] 
Designer  Manufacturer  Year  
Robert Hilchie  Robert Hilchie  1993  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  10  slider  3^{m/2}—1  242  
Remarks  The puzzle can be built with various slider shapes, leading to different mazes. Most of them are not nary, like the one shown in the pictures. Several puzzles have been implemented as online version (see reference [2]), an nary one has also has been implemented — please see reference [3], and for this the solution length and other details are provided here.  
References  [1] (US Patent 5470065), [2], [3]  
CR108  Name  Happiness  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  13  rings  364  
Remarks  
References  Reference Section [7] and [8]  
CR043  Name  Hanui  
Designer  Manufacturer  Year  
Yoshiyuki Kotani  1994  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  U piece  3^{m—1}·2^{i—1}  242  
Remarks  Piece i not allowed on middle position; 242 moves for i=biggest piece  
References  
CR020  Name  Hexadecimal Puzzle  
Designer  Manufacturer  Year  
William Keister  Binary Arts  1970  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  switch  Θ( 2^{m} )  170^{§}  
Remarks  Binary and 170 move sequence for setting 1110; Variants: CR040, CR066  
References  [1] (US Patent 3637216), [2], [3]  
CR040  Name  Hexadecimal Puzzle Reproduction  
Designer  Manufacturer  Year  
William Keister  Bill Wylie  2011  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  switch  Θ( 2^{m} )  170^{§}  
Remarks  Binary and 170 move sequence for setting 1110; Variants: CR020, CR066  
References  [1] (US Patent 3637216), [2], [3], [4]  
CR066  Name  Hexadecimal Puzzle 2013  
Designer  Manufacturer  Year  
William Keister  Creative Crafthouse  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  switch  Θ( 2^{m} )  170^{§}  
Remarks  Binary and 170 move sequence for setting 1110; Variants: CR020, CR040  
References  [1] (US Patent 3637216), [2], [3], [4]  
CR195  Name  JackintheBox  
[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  
Remarks  From 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 anticlockwise as possible to unlock a panel.  
References  [1]  
CR216  Name  Jack'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  
Remarks  Goal 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 (zigzag part, handlebar loop).  
References  [1]  
CR235  Name  Jacob'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  4^{m}—1  1298074214633706907132624082305023  
Remarks  Goal 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 10^{33} moves in the solution, and which was presented at MoMath event in February 2022. The second picture shows a closeup 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  [1], [2], reference section [19]  
CR259  Name  Jellyfish  
[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  
Remarks  Goal 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 nary structure, but also some more irregular structure as well which can be seen in the second picture. The overall solution is still the nary 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 nary 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 4^{th} 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  [1]  
CR164  Name  JUNC  
[1] [2] [3] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  slider pair  
Remarks  Goal is to move all light sliders down and all dark sliders left. By unlocking and removing the transparent lid, all little square pieces can be reoriented, allowing for 4^{25}≅10^{15} different challenges. Not all of these are possible as can be seen from the second picture, where a partial configuration is shown with the two topleft slider pairs blocking each other, unable to move. While the first picture shows the simple standard configuration of the puzzle, the third one shows one adapted from the N522 puzzle (CR087), with nontrivial solution and exponential solution length. The letters of the name depict the various configurations of the small squares.  
References  [1]  
CR049  Name  Junk's Hanoi  
[1] [2] 
Designer  Manufacturer  Year  
Junk Kato  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  block  Θ( 3^{m} )  161  
Remarks  Variation: Israelogi by ThinkinGames / Ili Kaufmann. The image shows a different version created by Dirk Weber.  
References  [1], [2]  
CR053  Name  K323  
[1] [2] 
Designer  Manufacturer  Year  
Kim Klobucher  Kim Klobucher  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  block  323  
Remarks  Variants: CR016, CR038  
References  [1], [2]  
CR038  Name  K419  
Designer  Manufacturer  Year  
Kim Klobucher  Kim Klobucher  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  6  block  419  
Remarks  Variants: CR016, CR053  
References  [1], [2]  
CR017  Name  KingCUBI  
Designer  Manufacturer  Year  
Hiroshi Iwahara  Hiroshi Iwahara  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  6  panel  1536  
Remarks  
References  [1]  
CR051  Name  Kugellager  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  ball  2·5^{m}  1250  
Remarks  Variants: CR027, CR028  
References  [1]  
CR028  Name  Kugellager 7  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
7  4  rivet  2·7^{m}  4802  
Remarks  Variants: CR027, CR051  
References  [1]  
CR027  Name  Kugellager 8  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  ball  2·5^{m}  1250  
Remarks  Smaller Version and upsidedown to original Kugellager; AKA: Kugellager 2; Variants: CR028, CR051  
References  [1]  
CR088  Name  Labynary  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  slider pair+switches  
Remarks  Beside the 8 main sliders, the puzzle contains several other smaller sliders for the interaction between the 8 main sliders. Additionally, there is a small ball and a ball maze in this puzzle, and the goal is to get the ball out at one of the three maze exits. The maze is also part of the sliders (see second image) and therefore the binary character only holds for the basic puzzle, without the ball.  
References  [1]  
CR240  Name  Lager Lock  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2022  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  ball  2·5^{m}  1250  
Remarks  Based 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  [1]  
CR029  Name  LeftRight Chinese Rings  
Designer  Manufacturer  Year  
Jan Sturm  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  ring  
Remarks  
References  [1]  
CR078  Name  Lego Ternary Gray Code Puzzle  
[1] [2] 
Designer  Manufacturer  Year  
Adin Townsend  Adin Townsend  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  lever  3·(2^{m}—1)—2·m  177  
Remarks  Lego variant/implementation of CR010. Second picture shows the three different piece states, with one moved out to the right already. Second reference links to building instructions created by Jeremy Rayner; the puzzle can be built with the pieces of a Mindstorms NXT set, but slight modifications might be necessary depending on the actual piece set.  
References  [1], [2]  
CR100  Name  Lock  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  23  
Remarks  extra ring for symmetry  
References  Reference Section [7] and [8]  
CR130  Name  Lock 14  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  slider+ball  
Remarks  First shackle part has ternary sequence, second part additional trick. Mechanism is like in CR064; AKA: Alphalock  
References  [1]  
CR037  Name  Lock 250+  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
6  4  slider  Θ( 5^{m—1} )  310  
Remarks  Lowest (4th) ring piece has only 2 position and acts as slider, AKA: Big Sliding Lock, Schloss 250+; Variant: CR065  
References  [1]  
CR102  Name  Longevity  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  rings  37  
Remarks  extra rings for symmetry  
References  Reference Section [7] and [8]  
CR030  Name  Loony Loop  
Designer  Manufacturer  Year  
Trolbourne Ltd  1975  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  2  pair of loops  
Remarks  Variants: CR014, CR067, CR068, CR069, CR070, CR075  
References  [1] (US Patent 2091191), [2] (US Patent D0172310), [3], [4]  
CR196  Name  Loopary Branch  
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  loop  Θ( 2^{m} )  127  
Remarks  The linear structure is bent into U shape. In the IPP38 Design Competition it participated as part of "Loopy Lattice Puzzles"; other puzzles from the same series: CR197, CR198  
References  [1], [2]  
CR243  Name  Magestic 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  
Remarks  Variation of CR125 with reduced piece counts and slight modification of the pieces leading to a slighly less regular sequence.  
References  [1]  
CR008  Name  Magnetic Tower of Hanoi  
Designer  Manufacturer  Year  
Uri Levy  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  disc  Θ( 3^{m} )  83  
Remarks  
References  [1], [2]  
CR111  Name  Mandarin Duck  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  15  rings  3287  
Remarks  
References  Reference Section [7] and [8]  
CR099  Name  Maze  
[1] [2] 
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  24  
Remarks  The first picture shows "Rat Race" by Puzzlemaster  
References  [1]; Reference Section [7] and [8]  
CR162  Name  Mechanic CUBI  
Designer  Manufacturer  Year  
Akio Kamei  Akio Kamei  2005  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  2^{m—1}  32  
Remarks  Variants: CR048, CR056. Mechanism is completely made out of wood, no metal (pins) used. Kamei also included a second alternate solution with a shortcut, which will only work at the beginning of the usual sequence, and is a couple of moves only.  
References  [1], [2]  
CR077  Name  Meiro Maze Variant  
Designer  Manufacturer  Year  
Fujita  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  pair of loops  
Remarks  First goal is to remove the coin, second the whole thread from the metal part. Both challenges are the same ternary puzzle repeated, but for releasing the coin additional restrictions exist. This seems to be a variant of the Meiro Maze shown in reference 2.  
References  [1], [2]  
CR167  Name  Merrygoround  
[1] [2] [3] [4] 
Designer  Manufacturer  Year  
Jack Krijnen, Goh Pit Khiam  Jack Krijnen  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
6 [8]  6  burr sticks  13432  
Remarks  Variants: CR126, CR136; This puzzle is a further developed variant of the original Power Tower, and as such it also comes as a whole set of pieces. With these pieces coming as 2ary, 3ary, 4ary, 5ary, and 6ary (in the version shown in the pictures), different configurations can be created. There is a special binary piece as a key piece that is part of all configurations as top piece. Therefore, there are 6 slots and 5 of each piece arity (only 2 for 6ary). Reducing the massive block to a slim tower allows pieces of different length and theoretically in arbitary arity without changing the central tower or other pieces. In the pictures, different examples are shown: 3 binary pieces (solved), 6 binary pieces (solved), one of each kind (midsolution). While the Power Tower has pairs of mirrorsymmetric pieces, here all pieces of same arity are the same and have to be entered in a helical pattern. While the sequences for even and odd arity pieces differ especially at the beginning, they are the same in this puzzle. Goal is to choose a configuration, enter the pieces into the tower, and slide them until they are all flush with the tower side on one end. The maximum number of moves for the puzzle in the picture is 13432, with pieces: (2*, 5, 5, 5, 6, 6).  
References  [1]  
CR260  Name  MiBinity 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  
Remarks  Goal 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 mixedbase 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  [1]  
CR139  Name  Mini Num Lock (binary)  
[1] [2] 
Designer  Manufacturer  Year  
Goh Pit Khiam  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  slider  
Remarks  Variants: CR125 and CR176; the second picture shows three different even and odd base variants: bases 2, 3, and 4. The ternary one is the cross referenced Num Lock in this puzzle list.  
References  reference section [12]  
CR180  Name  MiSenary Puzzle Box  
[1] [2] 
Designer  Manufacturer  Year  
Michel van Ipenburg  Michel van Ipenburg  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
7  2  slider  Θ( 7^{m} )  
Remarks  The object is to open the box, by tilting it to the left and right, while pulling/pushing the lid. The puzzle was entered into the 2017 IPP Nob Yoshigahara Puzzle Design Competition.  
References  [1], [2]  
CR149  Name  MixTerMaxTer  
[1] [2] [3] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2015  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  8  slider  Θ( 3^{m} )  342  
Remarks  One of a whole puzzle family, with different number of sliders, disks, and arities. CR143 is a simpler variant. The goal of MinTerMaxTer is to move the sliders from the outer discs with two slots to the outer disc with 8 slots and collect them there.  
References  [1], [2]  
CR016  Name  MMMDXLVI  
Designer  Manufacturer  Year  
Kim Klobucher  Kim Klobucher  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  9  block  3546  
Remarks  Variants: CR038, CR053  
References  [1], [2], [3]  
CR171  Name  Mountain Trail  
Designer  Manufacturer  Year  
DDK, Aaron (Yulong) Wang  Aaron (Yulong) Wang  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  rings+connectors  
Remarks  Main binary chinese rings chain, with three additional binary chains of 2 rings each, attached to rings 5, 7, and 9. These are interwoven with the main chain, leading to ternay subsequences, with some quaternary positions, where two subchains meet. Of each of those additional sequences, there is always only one of the two rings on the main loop. This is one of six puzzles in the Chinese 99ring series.  
References  [1]  
CR193  Name  Mountain Trail II  
Designer  Manufacturer  Year  
DDK, Aaron (Yulong) Wang  Aaron (Yulong) Wang  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  rings+connectors  
Remarks  This one is based on a main binary chinese rings chain, with an additional chain of 3 rings starting under the 5th and 8th ring. Unlike CR171, these additional chains are not rings linked directly with each other, but each ring is connected to one of the vertical bars via a smaller ring. In the starting position, these look like linked chains, during the solve, the chains act like secondary chinese rings chains, and therefore also multiple rings of the same secondary chain will be on the main bar at the same time, especially when one of them is put on/off the main bar. While the overall structure of the chains is binary, each of the four possibilities for each ring pair of ring on/off the handle (on/on, on/off, off/on, off/off) occurs and this puzzle could also partially be classified as a quarternary puzzle. For each pair of primary and secondary ring, putting on/off each of the rings of the pair requires a traversal of the lower rings sequence, making it a quite long solution sequence, adding up all these binary sequences. From the solution standpoint it might therefore also be classified as being partially ternary, and probably this is the main influence on the solution length. This is a later puzzle of the Chinese 99ring series.  
References  [1]  
CR033  Name  Mysterians  
Designer  Manufacturer  Year  
Oskar van Deventer  George Miller  2002  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  3  plate  5^{m}—1  124  
Remarks  
References  [1], [2], [3]  
CR232  Name  N3Box  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2021  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  sliderdisc pair  
Remarks  Box with a round variant of the series: CR131, CR132, CR087, CR133; The box has a lid with an nary 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  [1]  
CR131  Name  N5  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  2  sliderpair  20  
Remarks  Variants: CR087, CR132,CR133; Beside ternary sliders in two orientations, there is a simple ball maze built into the left end of the sliders and the ball is to move from bottom to top as goal, while the moving sliders obstruct and open some of the maze parts. The second picture shows the position in which the maze is usable; only the first slider has to be moved up and down while the ball traverses the maze. The number of moves is for putting all sliders up/to the right (calculcated with BurrTools, see second reference), with one additional move of the left slider to remove the ball, totalling 21.  
References  [1], [2]  
CR132  Name  N52  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  sliderpair  68  
Remarks  Variants: CR087, CR131,CR133; Beside ternary sliders in two orientations, there is a simple ball maze built into the left end of the sliders and the ball is to move from bottom to top as goal, while the moving sliders obstruct and open some of the maze parts. The second picture shows the position in which the maze is usable; only the first slider has to be moved up and down while the ball traverses the maze. The number of moves is for putting all sliders up/to the right (calculcated with BurrTools, see second reference), with three additional moves of the left slider to remove the ball, totalling 71.  
References  [1], [2]  
CR087  Name  N522  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  sliderpair  212  
Remarks  AKA: "522"; Variants: CR131, CR132,CR133; Beside ternary sliders in two orientations, there is a simple ball maze built into the left end of the sliders and the ball is to move from bottom to top as goal, while the moving sliders obstruct and open some of the maze parts. The second picture shows the position in which the maze is usable; only the first slider has to be moved up and down while the ball traverses the maze. The number of moves is for putting all sliders up/to the right (calculcated with BurrTools, see second reference), with five additional moves of the left slider to remove the ball, totalling 217. This is the first model of the series. Physically built have been all versions from 2+2 to 10+10 sliders, and some are presented on this page.  
References  [1], [2]  
CR133  Name  N522222222  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  10  sliderpair  
Remarks  Variants: CR087, CR131,CR133; Beside ternary sliders in two orientations, there is a simple ball maze built into the left end of the sliders and the ball is to move from bottom to top as goal, while the moving sliders obstruct and open some of the maze parts. The second picture shows the position in which the maze is usable; only the first slider has to be moved up and down while the ball traverses the maze. Number of moves yet to be determined. This is the biggest of the series actually built.  
References  [1]  
CR223  Name  NAiry 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( 3^{m} )  85  
Remarks  This 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  Name  New Puzzle Rings 3  
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  ring  
Remarks  Variant: CR117  
References  [1]  
CR117  Name  New Puzzle Rings 5  
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  ring  
Remarks  Variant: CR116  
References  [1]  
CR187  Name  New Secret Box IV  
Designer  Manufacturer  Year  
Akio Kamei  Karakuri Creation Group  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  2^{m—1}  32  
Remarks  Variants: CR048, CR056, CR162. Mechanism is completely made out of wood, no metal (pins) used.  
References  [1], [2]  
CR106  Name  Nine Twists  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  
Remarks  
References  Reference Section [7] and [8]  
CR179  Name  No Full Pirouette!  
[1] [2] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  6  module  61  
Remarks  Starting position is with all green arrows pointing to the green rectangle (right). Goal is to turn all the elements on the modules with the blue arrows pointing right. There are dead ends and it is not always immediately obvious which move should be the next one. The modules have arities (left to right): 4,3,3,2,3,2. The puzzle won a Jury First Prize in the 2017 IPP Nob Yoshigahara Puzzle Design Competition. The name is based on the following little anecdote relating to the movement of the pieces: The teacherchoreographer of ballet school gathered the students of various classes near the bar and tried to arrange a new divertissement with pirouette as the main element of group dance in a limited area. He ordered to make pirouette one by one to avoid collisions. But it was impossible in limited space to do that. The lesson failed. Somebody suggested asking the math teacher to help. Luckily the mathematics was passing near and was interested in assigned task. After some measuring, he proposed a scenario and exclaimed: One by one spin back and forth and no full pirouette!  
References  [1], [2]  
CR125  Name  Num Lock  
[1] [2] 
Designer  Manufacturer  Year  
Goh Pit Khiam  Tom Lensch  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  sliders  16 (3^{m—2}) —1 ^{‡}  143^{‡}  
Remarks  Variants: CR139 and CR176  
References  [1], [2], reference section [12]  
CR176  Name  Num Lock (mixed bases)  
[1] [2] [3] 
Designer  Manufacturer  Year  
Goh Pit Khiam  Johan Heyns  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
9  9  sliders  4 n_{0}··· n_{m—1}(n_{m}+1) —1 ^{‡}  50009399^{‡}  
Remarks  Variants: CR125 and CR139. The first piece shows the puzzle on the stand with 9 sliders entered and one of each arity 3, 5, 7, and 9 coming with the set, and some sheets listing number of moves for certain configurations. Those sheets are based on above formula involving the base/arity n_{m} of the leftmost piece and the product n_{0}··· n_{m—1} of the arities of the other pieces, regardless of their order. The second picture shows the puzzle with 9 sliders and all 16 knobs in two rows. The third picture shows all pieces of the set, including the leftmost pieces (called "starting block") for each arity, and the common piece. There are following piece counts: 3ary: 7+1 (1 block attached), 5ary: 4+1 (2 blocks), 7ary: 3+1 (3 blocks), 9ary: 3+1 (1 blocks), 1 common piece, 16 knobs. The reset and piece number selection mechanism has not been shown in the pictures, as finding this is an extra puzzle posed by Johan.  
References  [1], reference section [12]  
CR151  Name  Oh Sh*t! Puzzle  
Designer  Manufacturer  Year  
Woodenworks  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  loop  Θ( 2^{m} )  
Remarks  Variants: CR032, CR145  
References  
CR258  Name  O.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  
Remarks  Goal 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 zigzagshape. 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 2^{nd} and 3^{rd} panels. After the removal of the 1^{st} panel, the 3^{rd} 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  [1]  
CR107  Name  Pagoda  
[1] [2] [3] 
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  rings  397  
Remarks  The third picture shows the simpler variant "Tree Puzzle" by Puzzlemaster  
References  [1]; Reference Section [7] and [8]  
CR009  Name  Panex Gold  
Designer  Manufacturer  Year  
Toshio Akanuma  TRICKS  1983  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  20  slider  31537  
Remarks  Variant: CR035. Goal is to slide the pieces (without turning) to exchange the left and right stacks.  
References  [1], [2], [3]  
CR231  Name  Panex 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  
Remarks  Variant: 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  [1], [2]  
CR230  Name  Panex 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  
Remarks  Variant: 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  [1]  
CR035  Name  Panex Silver  
Designer  Manufacturer  Year  
Toshio Akanuma  TRICKS  1983  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  20  slider  31537  
Remarks  Variant: CR009. Goal is to slide the pieces (without turning) to exchange the left and right stacks.  
References  [1], [2]  
CR128  Name  Panex Squared  
Designer  Manufacturer  Year  
John Haché  John Haché  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  12  slider  68  
Remarks  Variant of CR035 which includes overlapping and interacting Panex instances. As the original design was not solvable (as discovered by Bob Hearn), this puzzle has to be modified by removing the blocking mechanism in the center. Goals are: 1) to swap pieces horizontally (e.g. A and B), and 2) swap pieces vertically (e.g. A and C), obeying the Panex rules, i.e.: in the vertical grooves, no smaller piece can be below (i.e. closer to the center) than a larger piece, same for the horizontal grooves (no larger piece closer to the center, but for both sides of the groove). This modification was proposed by Diniar Namdarian in 2015. The solutions provided have 46 moves for swapping A and B, and 68 moves for swapping A and C.  
References  [1]  
CR113  Name  Pear  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  rings  62  
Remarks  
References  Reference Section [7] and [8]  
CR036  Name  Pharaoh's Dilemma  
Designer  Manufacturer  Year  
Mag Nif  1970  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  disc  
Remarks  Tower of Hanoi variant  
References  [1]  
CR109  Name  Phoenix  
[1] [2] 
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  16  rings  502  
Remarks  
References  Reference Section [7] and [8]  
CR217  Name  Piano  
Designer  Manufacturer  Year  
DDK  Aaron (Yulong) Wang  2020  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2[4]  10  rings  
Remarks  Goal 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  [1]  
CR119  Name  Pin Burr 2  
[1] [2] [3] [4] 
Designer  Manufacturer  Year  
Jerry McFarland  Jerry McFarland  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  burr pieces  Θ( 2^{m} )  38^{§}^{‡}  
Remarks  Binary sequence, which is nonGC based and uses a pinmazemechanism, a little trick was added corrupting the sequence and making it more interesting for the solver. The third picture shows the prototype, which has a simpler frame but same sequence, the last picture shows both puzzles.  
References  [1]  
CR186  Name  Planex  
Designer  Manufacturer  Year  
Goh Pit Khiam  JL Puzzles (Jerry Loo)  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  sliding block  42  
Remarks  Variant: CR035, CR009. This puzzle is basically a Panex puzzle with only 3 levels (6 pieces) instead of the 10 levels (20 pieces) of the Panex puzzles. Goal is to slide the pieces (without turning) to exchange the yellow and blue stacks.  
References  [1]  
CR126  Name  Power Tower  
[1] [2] [3] 
Designer  Manufacturer  Year  
Jack Krijnen, Goh Pit Khiam  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3 [5]  4  burr sticks  3^{m}—m—1 ^{‡}  76^{‡}  
Remarks  Variants: CR136, CR167  
References  [1], reference section [12]  
CR136  Name  Power Tower (mixed base — variable stage)  
[1] [2] 
Designer  Manufacturer  Year  
Jack Krijnen, Goh Pit Khiam  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5 [7]  6  burr sticks  2·(n^{m}—1)/(n—1)—m  7806  
Remarks  Variants: CR126, CR167; This Power Tower is a whole set with a block hosting up to 6 stages, a blocker piece to set the number of stages (between 3 and 5, 6 stages without blocker), and a set of pieces for each of the two orientations (two different woods). The pieces come in binary, ternary, and quaternary shape and can be combined arbitrarily, leading to mixed (or uniform) base sequences, which can be quite confusing. There are 1080 different possibilities, with the level varying from 11 to 2724. The solution length is for a uniform nary configuration with m pieces. Addition: This now includes an extension set of quinary pieces. The overall entry now contains these pieces and there are now solutions possible up to level 7806.The second picture shows this extension set.  
References  [1], reference section [12]  
CR141  Name  Power Box  
[1] [2] 
Designer  Manufacturer  Year  
Goh Pit Khiam  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2 [4]  6  panels  
Remarks  
References  reference section [12]  
CR032  Name  Puzzle H  
Designer  Manufacturer  Year  
Eureka 3D Puzzles  1997  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  loop  Θ( 2^{m} )  
Remarks  Variant: CR145  
References  [1]  
CR004  Name  PyraCircle  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2008  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  10  block  116  
Remarks  Variation of Panex, a nondisjoint union of several such puzzles; 116 is minimum number of moves  
References  [1]  
CR197  Name  Quadrupled Quadlooplet  
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  loop  3^{m}  81  
Remarks  This puzzle contains 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  [1], [2]  
CR082  Name  Quatro  
Designer  Manufacturer  Year  
Eric Johansson  Eureka 3D Puzzles  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  loop  Θ( 2^{m} )  7  
Remarks  One of the solutions (reference 2) acts like Chinese Rings, please see reference 3. There are also other solutions.  
References  [1], [2], [3], [4]  
CR148  Name  Racktangle  
Designer  Manufacturer  Year  
Goh Pit Khiam  Tom Lensch  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3 [5]  4  plate  
Remarks  Variable number of stages (1 to 4, box is built modular) and plates of base 2 and 3 included, which together with the solid plate for the lowest position, can be used to create all mixed base 2 and 3 puzzles for up to 4 stages.  
References  [1], [2], reference section [12]  
CR241  Name  Railings  
Designer  Manufacturer  Year  
DDK  Heping Gao  2022  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  10  ring  Θ( 2^{m} )  
Remarks  Goal 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  [1]  
CR093  Name  Railing with Draining ternary  
[1] [2] [3] [4] [5] 
Designer  Manufacturer  Year  
Namick Salakhov  Namick Salakhov  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  slider  
Remarks  Quaternary version is: CR124  
References  [1]  
CR218  Name  Rainbow  
Designer  Manufacturer  Year  
DDK  Aaron (Yulong) Wang  2020  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2 [8]  11  rings  
Remarks  Goal 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 8ary puzzle with four special elements.  
References  [1]  
CR254  Name  Ratchet  
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( 2^{m} )  
Remarks  Goal 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  [1] [2]  
CR173  Name  Reflection  
Designer  Manufacturer  Year  
DDK  Aaron (Yulong) Wang  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  9  pairs of rings  
Remarks  Variation directly created from Chinese Rings by attaching a small connector ring and a second bigger ring to each ring, below the first and around the same vertical rod. There are four states for each ring pair: main bar through lower ring (initial position), through upper ring, through both rings ("double ring"), and off the rings. All those appear in the solution, and the double ring configuration is used to mimic the classic binary chinese rings. The configurations with one ring on the loop appear exactly once in the solution sequence, and their transitions interrupt the binary sequence in a regular pattern and increase the number of moves considerably. This is one of six puzzles in the Chinese 99ring series.  
References  [1]  
CR155  Name  ReTern Key  
Designer  Manufacturer  Year  
Goh Pit Khiam  Charlie Rayner  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  slider  8 · 3^{m—1}—8·m+1  185  
Remarks  The full name is "The Return of Tern Key" and demonstrates a variant of CR125 without a long synchronizing slider piece. Variants: CR168, CR223, CR224.  
References  reference section [12], [1]  
CR168  Name  ReTern Key with circular pieces  
Designer  Manufacturer  Year  
Fredrik Stridsman  Fredrik Stridsman  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  slider  Θ( 3^{m} )  
Remarks  The ReTern Key was the base for this puzzle, and the designer replaced the groups of small pieces running on the sides of the puzzle for synchronization by circular pieces. Variants: CR155, CR223, CR224.  
References  
CR224  Name  ReTern 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( 3^{m} )  313  
Remarks  The ReTern Key was the base for this puzzle, and the designer replaced the groups of small pieces running on the sides of the puzzle for synchronization by circular pieces. 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  Name  Reverse Chinese Rings  
Designer  Manufacturer  Year  
Aaron (Yulong) Wang  Aaron (Yulong) Wang  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  ring pair+connector  Θ(m·2^{m})  
Remarks  This puzzle looks like a chinese rings with all the rings put on the main handle backwards. At a closer look, each ring has a second ring attached at the bottom. To solve this puzzle, the bottom chain has to be solved like a standard chinese rings puzzle, and at the end of each run, one more ring from the reversed top chain comes off. While there are more than two states for each ring pair (4 states, each ring can be on or off the handle), the main sequence is binary, which is why it is classed binary here, and considered as chinese rings puzzle with some extensions.  
References  [1]  
CR021  Name  Rings Bottle  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2012  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  ring  
Remarks  
References  [1], [2]  
CR041  Name  Row to Row  
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  8  disc  Θ( 2^{m} )  
Remarks  
References  [1]  
CR007  Name  Rudenko Clips  
Designer  Manufacturer  Year  
Valery Rudenko  Roscreative  2011  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  7  clip  ( 3^{m}—1 )/2  1093  
Remarks  Tower of Hanoi with move restriction  
References  [1], [2], [3]  
CR019  Name  Rudenko Disc  
Designer  Manufacturer  Year  
Valery Rudenko  Roscreative  2011  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  7  disc  Θ( 2^{m} )  
Remarks  Tower of Hanoi with simplification  
References  [1], [2], [3]  
CR044  Name  Rudenko Matryoshka  
Designer  Manufacturer  Year  
Valery Rudenko  Roscreative  2011  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  7  slider  Θ( 2^{m} )  
Remarks  Tower of Hanoi equivalent with restriction of moves between the outer two rows  
References  [1], [2], [3]  
CR252  Name  Salva  
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  
Remarks  Goal is to free the Salva dog coin from the cage. The puzzle is a combination of a 6ary maze puzzle and a sequential discovery puzzle that offers an additional prize. The 6ary sequence occurs in two stages, and the two thin sliders interact with two different areas of the large maze board.  
References  [1]  
CR227  Name  Sea 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  
Remarks  Goal is to remove rope. Nicely made variant of CR031  
References  [1]  
CR086  Name  Seestern  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
11  3  Layers  11^{m}—1  1330  
Remarks  
References  [1]  
CR190  Name  Second Order Chinese Rings  
Designer  Manufacturer  Year  
Aaron (Yulong) Wang  Aaron (Yulong) Wang  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  11  rings  
Remarks  While the rings in the classic Chinese Rings puzzle are linking their connector with the next connector each, in this one, each ring links its connector with the next two adjacent connectors. The solution is based on the Chinese Rings solution, and is in fact the same sequence like for the Dispersed GC lock CR074  
References  [1]  
CR255  Name  Sensi 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  
Remarks  This is a combination of puzzle box and burr. Not only the panels can be opened and removed, but also the frame can be taken apart completely. Inside the box is a second puzzle, the 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 6ary  
References  [1]  
CR209  Name  Septenary 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^{§}^{‡}  
Remarks  Objective 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  [1]  
CR201  Name  Sequence 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  2^{m+1}—2  8190  
Remarks  The 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  [1], [2]  
CR253  Name  Shoulder 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  
Remarks  Goal is to free the rope (withtout using the quickreset 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  [1]  
CR251  Name  Shuttle 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  
Remarks  Goal is to free the rope (withtout using the quickreset 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  [1]  
CR064  Name  Six Bottles  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  slider+ball  4·(2^{m}—1)  252  
Remarks  Each metal ball can be in a topleft, bottomleft, or a bottomright position, and there are corresponding slider positions middle and top. The bottom slider position occurs only during transition of ball between left and right. A newer circular version replacing balls by switches is: CR083  
References  [1]  
CR211  Name  Six Keys Box  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2019  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  key slider+ball slider pair  ^{4}⁄_{3} ·3^{m}—3  969  
Remarks  Move 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  [1]  
CR011  Name  SlidingBlock Chinese Ringsstyle Puzzle  
[1] [2] [3] 
Designer  Manufacturer  Year  
Bob Hearn  2008  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  3  pair of yellow blocks  
Remarks  The second picture shows the different position of the special pieces, the pairs of yellow blocks in positions 0, 1, and 2. There are other positions not part of the solution. Recently, we found a shorter, nonternary solution that was not intended, with goal configuration in third picture; under investigation.  
References  [1], [2]  
CR249  Name  Slidebox  
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  
Remarks  Goal 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 mixedbase 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  [1]  
CR142  Name  Slots and Pins (mixed base)  
Designer  Manufacturer  Year  
Goh Pit Khiam  Jack Krijnen  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  slider  
Remarks  This version has mixed bases, i.e. binary and ternary pieces/piece parts.  
References  reference section [12]  
CR210  Name  Sluice 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  
Remarks  The 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  [1]  
CR048  Name  Small CUBI  
Designer  Manufacturer  Year  
Akio Kamei  Akio Kamei  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  panel  2^{m—1}  32  
Remarks  Variants: CR056, CR162. Mechanism is completely made out of wood, no metal (pins) used.  
References  [1], [2]  
CR022  Name  SpinOut  
Designer  Manufacturer  Year  
William Keister  Binary Arts  1970 / 2006  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  disc  [2^{m+1}/3] ^{§}  85 ^{§}  
Remarks  Version with elephants and reset shortcut, green/red/orange. There exists an unintended shortcut solution with 49 moves (see Jaaps's page below). Variants: CR026, CR050  
References  Variation on [1] (US Patent 3637215), [2], [3], [4], [5]  
CR050  Name  SpinOut  
[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  [2^{m+1}/3] ^{§}  85 ^{§}  
Remarks  There 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  [1] (US Patent 3637215), [2], [3], [4], [5]  
CR026  Name  SpinOut  
Designer  Manufacturer  Year  
William Keister  ThinkFun  1970 / 2001  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  7  disc  [2^{m+1}/3] ^{§}  85 ^{§}  
Remarks  reset shortcut. There exists an unintended shortcut solution with 49 moves (see Jaaps's page below); Variants: CR022, CR050  
References  [1] (US Patent 3637215), [2], [3], [4]  
CR084  Name  Spiralschloss  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  shacklelayer  2·(n^{m}—1)  160  
Remarks  Mechanism similar to CR085. Goal: Open all shacklelayers completely.  
References  [1]  
CR233  Name  Square Tower of Hanoi  
Designer  Manufacturer  Year  
Junichi Miyoshi, Mineyuki Uyematsu, Hajime Katsumoto  MINE/DYLANKobo  2020  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  10  disc  108  
Remarks  Goal 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  [1]  
CR222  Name  Stacker  
Designer  Manufacturer  Year  
Jared Petersen  CoreMods  2021  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  5  ball bearing  
Remarks  Goal 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  [1]  
CR246  Name  SternBox/Star Box/Sun Box  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2022  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  sliderpair  
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  [1]  
CR083  Name  Steuerrad  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  8  slider+switch  3·2^{m}  768  
Remarks  Round variant of CR064. Goal: Move all handles to the outer position and reveal hidden message "Nicht durchdrehen", German for "do not get mad" and also referring to turning the steering wheel (German: Steuerrad). 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  [1], [2]  
CR025  Name  SuperCUBI  
[1] [2] [3] 
Designer  Manufacturer  Year  
Hiroshi Iwahara  Hiroshi Iwahara  2000  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  panel  324  
Remarks  First image shows newer version (opposite panels following in solution), second and third the older version (panels following in 90° turn order); Variant: CR165  
References  [1]  
CR165  Name  SuperCUBI (small)  
[1] [2] 
Designer  Manufacturer  Year  
Hiroshi Iwahara  Hiroshi Iwahara  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  panel  324  
Remarks  Smaller version of original SuperCUBI with adjacent panels moving on opposite sites. Comes with a solution leaflet showing all 324 moves, and additionally some instructions on how to calculate and identify the current configuration. Varaiant: CR025  
References  [1], [2]  
CR239  Name  Switched 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  
Remarks  AKA: 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 nary 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  [1], [2]  
CR104  Name  Teapot  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  22  
Remarks  
References  Reference Section [7] and [8]  
CR242  Name  Telefon Box  
Â´  Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2022  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  sliderdisc pair  
Remarks  Box with a round variant of the series: CR131, CR132, CR087, CR133; The box has a lid with an nary 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 3ary 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  [1]  
CR002  Name  Tern Key  
Designer  Manufacturer  Year  
Goh Pit Khiam  Cubicdissection  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  switch  12·(2^{m})—12·m—10  134  
Remarks  
References  [1], [2], [3]  
CR005  Name  Ternary Burr  
Designer  Manufacturer  Year  
Goh Pit Khiam  Jack Krijnen  2010  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  burr pieces  6·2^{m}—4·m—5 ^{§}^{‡}  75^{§}^{‡}  
Remarks  Move count includes control bar; Variant with only two frame pieces; Variants: CR055, CR095  
References  [1]  
CR055  Name  Ternary Burr  
Designer  Manufacturer  Year  
Goh Pit Khiam  Mr. Puzzle  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  burr pieces  6·2^{m}—4·m—5 ^{§}^{‡}  75^{§}^{‡}  
Remarks  Move count includes control bar; 95 moves for complete disassembly; Variants: CR005, CR095  
References  [1], [2], [3], [4], [5]  
CR095  Name  Ternary Burr  
Designer  Manufacturer  Year  
Goh Pit Khiam  Eric Fuller  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  burr pieces  6·2^{m}—4·m—5 ^{§}^{‡}  75^{§}^{‡}  
Remarks  Move count includes control bar; 95 moves for complete disassembly; Variants: CR005, CR055  
References  [1], [2]  
CR205  Name  Ternary / 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^{§}^{‡}  
Remarks  Objective 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  [1]  
CR220  Name  Ternary 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  2·3^{m} ^{§}^{‡}  162^{§}^{‡}  
Remarks  Objective 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  [1], [2]  
CR181  Name  The Bell  
Designer  Manufacturer  Year  
Juergen Reiche  Siebenstein  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  12  slider  881  
Remarks  Variant: CR035, CR009. This puzzle is basically a Panex puzzle with only 6 levels (12 pieces) instead of the 10 levels (20 pieces) of the Panex puzzles.  
References  [1]  
CR012  Name  The Binary Burr  
[1] [2] 
Designer  Manufacturer  Year  
Bill Cutler  Jerry McFarland  2003  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  burr pieces  ( (1)^{m+1} + 2^{m+2} ) / 3 ^{§}^{‡}  85^{§}^{‡}  
Remarks  Move count includes control bar; There is also a very rare 10 ring piece version, which is shown in the pictures; Variants: CR076, CR156  
References  [1]  
CR076  Name  The Binary Burr  
Designer  Manufacturer  Year  
Bill Cutler  Eric Fuller  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  burr pieces  ( (1)^{m+1} + 2^{m+2} ) / 3 ^{§}^{‡}  85^{§}^{‡}  
Remarks  Move count includes control bar; Variants: CR012, CR156  
References  [1], [2]  
CR156  Name  The Binary Burr (small)  
[1] [2] [3] [4] [5] [6] [7] [8] [9] 
Designer  Manufacturer  Year  
Bill Cutler  Maurice Vigouroux  2016  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  10  burr pieces  ( (1)^{m+1} + 2^{m+2} ) / 3 ^{§}^{‡}  1385^{§}^{‡}  
Remarks  Move count includes control bar; the first picture shows the whole group of the Binary Burrs (small) with 3 to 10 special pieces, all with solid cage, the other pictures show the individual puzzles; Variants: CR076, CR012  
References  [1], [2], [3], [4], [5], [6], [7], [8]  
CR057  Name  The Brain  
[1] [2] [3] [4] 
Designer  Manufacturer  Year  
Marvin H. Allison, Jr.  MagNif  1973  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  8  switch  [2^{m+1}/3]  170  
Remarks  Pictures 2, 3, and 4, and reference 2 show the newer version  
References  [1], [2], [3], [4]  
CR096  Name  The Cat  
Designer  Manufacturer  Year  
William Keister  Binary Arts  1985  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  2  rings  
Remarks  
References  [1]  
CR097  Name  The Horse  
Designer  Manufacturer  Year  
William Keister  Binary Arts  1985  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  rings  
Remarks  
References  [1]  
CR058  Name  The Key  
[1] [2] [3] 
Designer  Manufacturer  Year  
Goh Pit Khiam  Walt Hoppe  2004  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  switch  40  
Remarks  Variant: CR063  
References  [1], [2]  
CR225  Name  The 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  
Remarks  From the description: It is sequential (puzzle) discovery, it is riddle solving, it is nary, 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  [1]  
CR191  Name  Third Order Chinese Rings  
Designer  Manufacturer  Year  
Aaron (Yulong) Wang  Aaron (Yulong) Wang  2018  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  13  rings  
Remarks  While the rings in the classic Chinese Rings puzzle are linking their connector with the next connector each, in this one, each ring links its connector with the next three adjacent connectors. This is a logical extension of CR190.  
References  [1]  
CR062  Name  Tower of Hanoi  
Designer  Manufacturer  Year  
Edouard Lucas  Philos (and others)  1883  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  9  disc  Θ( 2^{m} )  
Remarks  
References  [1], [2]  
CR105  Name  Trapeze  
[1] [2] [3] 
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  61  
Remarks  extra rings for symmetry; third picture shows puzzle Dingo Trap, a variant with the rings separated and held by smaller loops; reference [14] shows this variant including building instructions and solution  
References  [1], [2]; [3] (US Patent 4497489) Reference Section [7], [8], and [14] (p.109)  
CR144  Name  Tricky Frame  
Designer  Manufacturer  Year  
Philos  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  loop  Θ( 2^{m} )  
Remarks  Variant: CR072  
References  [1]  
CR145  Name  Tricky Mouse  
Designer  Manufacturer  Year  
Philos  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  4  loop  Θ( 2^{m} )  
Remarks  Variant: CR032  
References  [1]  
CR244  Name  Tvnary  
[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  
Remarks  Goal is to disassemble this interlocking puzzle. The puzzle is a combination of an nary puzzle and a maze puzzle, in which the nary 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 5ary, 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  [1]  
CR085  Name  Uhrwerk  
[1] [2] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2013  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  ball/gear  2·(n^{m}—1)  160  
Remarks  Mechanism similar to CR084. Goal: Move the one ball with the special starting position to its third hole and remove (only) this ball from puzzle. The two pictures show second (more stable) and first edition.  
References  [1], [2]  
CR138  Name  Unknown Disentanglement  
Designer  Manufacturer  Year  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  3  loops  
Remarks  Choosing one of the sides, the consecutive loops on that side will act like a Chinese Rings puzzle. All other loops are not part of the solution.  
References  [1]  
CR213  Name  Vertical  
[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 (5^{m—2}) —1 ^{‡}  14999^{‡}  
Remarks  Variants: 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  [1]  
CR152  Name  Viking Box  
Designer  Manufacturer  Year  
Sven Baeck, JeanClaude Constantin  JeanClaude Constantin  2014  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  4  switches  
Remarks  The basic mechanism of the box is a ternary mechanism consisting of discs with the switches attached and visible to the puzzler, and some ball bearings. These will move into some cutouts of the discs and block them in various positions, same general concept as in CR064. Additionally, there are two mechanisms interacting with several discs each: One visible as the bottom horizontal slider, the other hidden, but with its state visible through a small hole below the left disc. This mechanism and the ball bearings have to be manipulated via tilting. The lid contains the mechanism and is firmly closed. However, a second variant was released with a transparent top, allowing the puzzler to see most of the mechanism.  
References  [1]  
CR200  Name  Visible 5Ary 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 · 5^{m—1}+1  51  
Remarks  A 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  [1]  
CR221  Name  Void Box  
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2020  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  3  slider  2·5^{m}  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  [1]  
CR001  Name  Void Lock  
[1] [2] [3] 
Designer  Manufacturer  Year  
JeanClaude Constantin  JeanClaude Constantin  2009  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  3  slider  2·5^{m}  250  
Remarks  AKA: Kleines dickes Schloss; the second variant shown in picture and references is a metal version released in 2018 by Constantin  
References  [1], [2]  
CR103  Name  Wheel  
Designer  Manufacturer  Year  
Ruan Liuqi  Ingenious Rings  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  5  rings  24  
Remarks  
References  Reference Section [7] and [8]  
CR215  Name  White BowTie  
Designer  Manufacturer  Year  
Aleksandr Leontev  Aleksandr Leontev  2019  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
5  4  blocks  2·5^{m}  1250  
Remarks  Variant: CR207. This puzzle is a 2in1 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 5ary 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 3ary and 5ary mazes does not seem to work, as the 3ary mazes are not wide enough to allow for the 5ary transitions.  
References  [1]  
CR183  Name  xBrain binary  
[1] [2] [3] 
Designer  Manufacturer  Year  
David Guo  David Guo  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
2  6  switch  [2^{m+1}/3]  42  
Remarks  This puzzle is based on: CR057. Variants: CR184 and CR185. The second picure shows the goal configuration (all sliders moved to the border), and the third picture a different colour variant in a configuration during the solution.  
References  [1]  
CR184  Name  xBrain ternary  
[1] [2] [3] 
Designer  Manufacturer  Year  
David Guo  David Guo  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
3  6  switch  2·3^{m — 1} — 1  485  
Remarks  This puzzle is based on: CR057. Variants: CR183 and CR185. The second picure shows the goal configuration (all sliders moved to the border), and the third picture a different colour variant in a configuration during the solution.  
References  [1]  
CR185  Name  xBrain quarternary  
[1] [2] [3] 
Designer  Manufacturer  Year  
David Guo  David Guo  2017  
Arity  No of pieces  Piece type  Solution length function  Number of moves  
4  6  switch  0.1 · (—1)^{m} + 0.4 · 4^{m} — 0.5  1638  
Remarks  This puzzle is based on: CR057. Variants: CR183 and CR184. The second picure shows the goal configuration (all sliders moved to the border), and the third picture a different colour variant in a configuration during the solution. The solution length function for the number of moves f(m) is a solution of the recursion f(m) = 3f(m—1) + 4f(m—2) +3 with f(0)=0 and f(1)=1 derived from solving the puzzle with m pieces.  
References  [1]  
CR238  Name  YPANEX  
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  
Remarks  Variant: 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  [1]  
CR262  Name  Zigguchain  
[1] [2] [3] [3] 
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  2^{m+2}—m—7  243  
Remarks  Goal: Disassemble and reassemble 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.  
References  [1]  
CR256  Name  Zigguflat  
[1] [2] [3] 
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  2^{m+1}—2·m—3  113  
Remarks  Goal: Disassemble and reassemble 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 nary 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.  
References  [1], [2], [3], [4], [5]  
CR234  Name  Ziggurat  
[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  2^{m+1}—2·m—3  493  
Remarks  This 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 reassemble 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 BurrTools file created for the analysis of this puzzle. It shows two main aspects: The nary 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 4ary or 6ary puzzle (etc.) can also be created, so both the arity and the number of pieces can be changed.  
References  [1], [2], [3]  
CR261  Name  Ziggutwist  
[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  2^{m+1}—3·m—4  234  
Remarks  Goal: 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 SpinOut 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 SpinOut. 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  [1]  
This compendium contains a special collection of puzzles which are somehow related to the famous Chinese Rings puzzle. For a definition which puzzles are included in this compendium and for a clear understanding why they are included, we will provide a structural definition of the class of puzzles in this compendium, the CR recursive puzzles. We will provide a definition, with some examples, and with some interesting properties of these puzzles.
A CR recursive puzzle is a puzzle that contains m special similar pieces (with m ≥ 1) and

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

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

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

2^{m}+m+3  Θ( 2^{m} )  Linear and constant summands neglectable 
2 · 5^{n}  Θ( 5^{n} )  Constant factor neglectable 
2^{(m—1)}  Θ( 2^{m} )  2^{(m—1)}= (1/2)·2^{m}, constant factor neglectable 
3 · (2^{m}—1) — 2·m  Θ( 2^{m} )  Combination of examples above 
The Θ notation is taken from Computer Science and Mathematics, the formal definition and details are explained in [5].
Why do some CR recursive puzzles with n>2 have a solution with only ~2^{m} moves, not ~n^{m}? CR recursive puzzles with solution length ~n^{m} obviously use all different combinations of piece positions in their solution. To see this, just recall that the number of mtuples over a set with n different values is exactly n^{m} and so all these tuples occur in the description of the solution (see tuple representation above). So the puzzles in question that have solution length ~2^{m} will not use all these tuples in their solution, but leave some out. For example, on the (shortest) solution path for the Ternary Burr, you will never find a configuration corresponding to tuple (1,0,0,0)  this configuration is not needed. If you have this puzzle or the equivalent Crazy Elephant Dance, just try it out (with the lowest 4 elephants)! When you try the solution for on of these puzzles, you will find that directly before reaching this position, you will have the configuration (1,0,0,1)  which is not part of the shortest solution either  and this will be the only successor configuration after (1,0,0,1). Shortly said: only from (1,0,0,1) you reach (1,0,0,0), and your only option is going back to (1,0,0,0), and this is a detour way back from the solution from (0,0,0,0) to (2,0,0,0). Please see picture for these solution steps in the actual puzzle.
This effect occurs in several different puzzles, but what are the reasons for some puzzles to use all possible configurations, and for some others to omit configurations in their solution? Several reasons have been observed so far:
In the paragraphs above the relation between binary and ternary regarding the solution length has been discussed. There is also a binary representation that can be used for describing the solution of Tower of Hanoi, for details, please see [4].
Recently Goh Pit Khiam created a nice illustrated example of a variant of Tower of Hanoi: Linear Tower of Hanoi. In this variant, the three poles are in a line and a disc may only move from a pole to an adjacent pole. The obvious implications are that there are no direct moves between pole 0 and 2, and that a bigger disc may not move between poles 0 and 2, whenever there is a smaller one on pole 1. This makes it very similar to a Rudenko Clips (see previous section above). The less obvious implication is that the puzzle follows a ternary gray code. Please see [10] for the illustrated example of this puzzle, which also shows a nice ternary representation of Tower of Hanoi.
Our definition of CR recursive puzzle is based on the structure of the puzzle, which makes it (relatively) easy to spot if a puzzle belongs to this class. However, there is another different and commonly used definition of nary puzzles that first requires the puzzle to be analyzed and solved fully before it can be classified. Once one has determined that there are m special pieces and the solution length function is asymptotically equal to n^{m}, it is classified as nary (in this solution length based notation). We are using the structural definition provided above (as it seems easier to apply it in most cases), but there might be some confusion. Some ternary puzzles (our definition) may have a solution with (asymptotic) length 2^{m}, while the solution length function based definition would call them "binary" for this reason. One prominent example is the Ternary Burr by Pit Khiam Goh. This ternary (sic!) variation of the Binary Burr by Bill Cutler would be classified as binary following the solution length based definition.
[1] Goetz Schwandtner. Kugellager.pdf.
[2] Goetz Schwandtner. nary Puzzle Group.
[3] Ring of Linked Rings. Sydney N. Afriat. Gerald Duckworth & Co Ltd (November 1982). ISBN 0715616862
[4] Tower of Hanoi (Wikipedia).
[5] Theta Notation (Wikipedia).
[6] The Tower of Hanoi — Myths and Maths Andreas M. Hinz, Sandi Klavzar, Uros Milutinovic, Ciril Petr. Springer Basel 2013.
[7] Ingenious Rings. Yu Chong En and Zhang Wei. Beijing, 1999. The diagrams shown in the puzzle list of this Compendium for the Ingenious Rings Puzzles are taken from this book and were created by Wei Zhang.
[8] ChinesePuzzles.org: Ingenious Rings Wire puzzles
[9] ChinesePuzzle.org: Nine Linked Rings
[10] Goh Pit Khiam. The Linear Tower of Hanoi and the Ternary Gray Code.
[11] Goh Pit Khiam. Design of Nary Mechanical Puzzles. CFF95. Rijswijk, 2014. The next entry [12] is the most recent updated version
[12] Goh Pit Khiam. Design of Nary Mechanical Puzzles. (extended version, latest update 20141215; main updates are from page 28 on: The Power Box, Racktangle, Mixed Base Power Tower illustrated overview and simplification)
[13] New Book of Puzzles. Jerry Slocum and Jack Botermans. New York, 1992.
[14] Denkspiele der Welt. Pieter van Delft and Jack Botermans. München, 1977.
[15] 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.
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)
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.