Mechanical Puzzle Classification Mapping

The purpose of this section is to provide a mapping among different classification schemes for mechanical puzzles.

Over a century ago, Professor Hoffmann commented on the difficulty of devising and adhering to a rigid scheme for the classification of puzzles - many mechanical puzzles could be classified in multiple equally valid ways. There are two main schemes which have been promoted by major puzzle collectors: Jerry Slocum uses a scheme based on Hoffmann's, and which is now employed by the Lilly Library to catalogue his donated collection of over 30,000 puzzles; and James Dalgety uses a more detailed scheme (see in particular the illustrated summary) to catalogue his enormous Hordern-Dalgety collection (sample catalogue here). The evolution of Dalgety's collection is described in an article he wrote for the CCF newsletter, issue 54 Feb. 2001.

Dalgety's scheme encompasses fourteen main classes, with several sub-classes within each main class, while Slocum makes due with 10 main classes and few subclasses. There is considerable overlap and good correspondence between the two systems. The Wikipedia entry for mechanical puzzles also pretty much agrees with the top level classes.

The classification scheme I have employed on Rob's Puzzle Page is closer to Dalgety's since I prefer finer granularity. I have seen various other schemes around the web, for instance, based on the material from which the puzzle is made - e.g. plastic, wood, glass - but I don't think they're very useful for finding a puzzle or identifying isomorphic or related puzzles. I do think each classification scheme reveals something about the preferences, biases, experience, expertise, and focus of the classifier.

The table below compares and attempts to align the different schemes. I have also found it instructive to include the categories described by van Delft and Botermans in their 1978 classic Creative Puzzles of the World, and the ten sections in Hoffmann's 1893 book, since they help show how the universe of puzzles has evolved over time.

Where I have found expert advice in further classifying particular categories of puzzle, I have highlighted the experts like this.

Recent years have seen a surge in the popularity and visibility (via e.g. social media, videos, Discord) of mechanical puzzles and the number of people who enjoy, collect, create, make, promote, and sell them. New puzzle types and subtypes have come to the fore (e.g. Graduated Challenge, "N-ary," Turning Interlocking Cubes, Sequential Discovery, Restricted Opening Sequential Packing with Rotations, and on) that while perhaps in general encompassed by the existing schemes, are poorly distinguished within them. So it seems as if our taxonomies are destined to evolve if they are to remain relevant. Yet every puzzlist or taxonomist must strike a balance between useful specificity and cumbersome complexity.

Note that a different and perhaps more productive approach to classifying puzzles would be tag based. For example, a puzzle might have attributes of both assembly as well as pattern. Its assignment to one traditional category or the other would be based on a weighting of all of its attributes as determined by an expert authority or by mass consensus.

Anyway, below you will see how the traditional classification schemes for mechanical puzzles compare with my own. I hope you find this entertaining and useful.


10 Main Classes

14 Main Classes

11 Sections

10 Sections
Rob's Puzzle Page
1. Put-Together
  • 1.1) 2D Assembly
  • 1.2) 3D Assembly, non-interlocking
  • 1.3) Misc. Put-Together
  • 1.4) Matchstick
II. Jigsaw
  • JIG-STD - standard
  • JIG-IDEN - identically shaped pieces
  • JIG-SLOP - sloping cuts
  • JIG-LAYR - multiple layer
  • JIG-OTH - other
Supposedly the jigsaw was invented in 1760 by John Spilsbury of London, but dissected maps were being used as teaching aids in the mid 1700s. Jigsaws for amusement appeared as early as 1785 and were available in America by the early 1800s. Hoffmann's section III includes the Chinese Zig Zag, a 3D jigsaw, but no other jigsaw puzzles. Most jigsaw puzzles made in the 19th century had juvenile pictures, fewer than 75 pieces, and were too simple to hold an adult's attention. The first jigsaw craze in the U.S. did not occur until 1908. For these reasons it is not surprising that Hoffmann omits the category. (Some of the above factoids I learned from Anne Williams' excellent book.) Jigsaws

Geert Bekkering, Anne Williams, Bob Armstrong - see Bob's section about jigsaw cutting styles

III. Assembly (non-interlocking)
  • ASS-CART - cartesian parts
  • ASS-STRA - straight edge or face, non-cartesian - includes Tangrams
  • ASS-POLY - polydehdra and spheres - e.g. ball pyramids
  • ASS-OTH - other - e.g. "Pack the Plums", gears
1. Geometrical Problems

1a. "Moving Piece Puzzles" - Tangram

1b. Dissection Puzzles - cut up one shape and make another; includes Letter Dissections and "Disappearance Puzzles"

1c. Polyforms - Hexiamonds, Pentominoes, Solid Pentominoes, Soma

III. Dissected or Combination - includes: Anchor/Tangram, Octogon, Latin Cross, Greek Cross, Checkerboard, Spots (dissected Die), Endless Chain (La Chaine sans Fin), classic 6-piece burr, Diabolical Cube, Les Quatres Vagabonds

In chapter X, Hoffmann describes #48 The Packer's Secret (Le Secret d'un Emballeur).

Tangrams and Richter's Anchor Stone Puzzles

IV. Pattern
  • PAT-EDGE - matching edges or corners
  • PAT-STIX - sticks, incl. matchsticks
  • PAT-NUMB - numbers, incl. magic squares
  • PAT-SIMI - arrange similar pieces - e.g. 8 queens, Instant Insanity, MacMahon Cubes
  • PAT-DISS - dissimilar pieces - e.g. Testa
  • PAT-STAK - stacking and weave
  • PAT-OTH - other
2. Matchstick

3. Domino Puzzles

5. Magic Squares

VII. Puzzles with Lucifer Matches

The Englishman John Walker invented and sold the first friction matches in 1827. In 1830, Samuel Jones begain making and selling them using the name "lucifers." By 1880 match manufacturing was a huge business.

Hoffmann indicates that even in his day there were many matchstick puzzles. He includes only "a brief selection" of 19.

As for other types of pattern puzzle, he covers the 8 Queens puzzle in his chapter VI, #24. Chapter X, #18 Treasure at Medinet is an 8-Queens variant like Jeu des Manifestants. He includes several magic squares in chapter IV. The Thurston edge matching puzzle used by Calumet, and the MacMahon/Journet Mayblox were both first patented in 1892. Hoffmann might not yet have seen them - the only edge-matching type puzzles he mentions are "The Royal Aquarium Thirteen Puzzle" (equivalent to the French Le Nombre Treize) #72 in chapter IV, and "The Endless Chain" (equivalent to the French La Chaine sans Fin) #18 in chapter III. The Instant Insanity family wasn't invented until 1900.


2. Take-Apart
  • 2.1) Trick or Secret Opening
  • 2.2) Secret Compartment
  • 2.3) Trick Locks and Keys
  • 2.4) Trick Matchboxes
  • 2.5) Trick Knives
V. Opening
  • OPN-BOX - containers
  • OPN-LOCK - locks
  • OPN-HIDD - find hidden compartments
  • OPN-OTH - other
II. Mechanical Puzzles Dependent on Some Trick or Secret

Chapter II is where Hoffmann really shines for a mechanical puzzle collector. He lumps some tanglements in as well, and it makes a kind of sense since one has to take them apart, but today we would classify them separately.


3. Interlocking Solid
  • 3.1) Figural
  • 3.2) Geometric Objects
  • 3.3) 3-D Jigsaw
  • 3.4) Burrs
  • 3.5) Keychain
  • 3.6) Misc.
I. Interlocking
  • INT-BOX - boxes that disassemble
  • INT-CART - cartesian; 3 mutually perpendicular axes
  • INT-POLY - polyhedral and non-cartesian
  • INT-OTH - other
4. Construction and Packing - includes: Kumiki, OCC, Burrs, Pagoda Burr, Diagonal Burr, O'Beirne's Melting Block, Conway's Packing, Haslegrove Box, Chinese Cube, 13/14 Hoffmann didn't spike out Interlocking puzzles - he included a 6-piece burr in his "Combination" chapter III, #36. Slocum has traced the 6-piece burr back to Germany in 1698. Figural/representational Kumiki puzzles were invented in Japan in the 1890s by Tsunetaro Yamanaka, but the world had to await the invention of many of the best geometric interlocking puzzle designs by Stewart Coffin in the 1970s. The keychain puzzle originated at the 1939 New York World's Fair. Interlocking

Keychain Puzzles


4. Dis-
  • 4.1) Cast Iron and Sheet Metal Puzzles
  • 4.2) Wire Puzzles
  • 4.3) String Puzzles
  • 4.4) Misc.
VI. Tanglement
  • TNG-RIGI - rigid and semi-rigid parts
  • TNG-R&F - rigid and flexible parts
  • TNG-FLEX - all flexible parts
  • TNG-RING - finger rings
6. Ring-
- including Crown, Patience, Chinese Ladder, Ox Yoke, Victoria, Imperial Scale

9. Wire Puzzles

VIII. Wire Puzzles Tanglement

(Dr. Richard Hess)

Vintage French Boxed Tanglement Puzzles


5. Sequential Movement
  • 5.1) Solitaire
  • 5.2) Counter
  • 5.3) Sliding Piece
  • 5.4) Rotating Piece
  • 5.5) Maze & Route
  • 5.6) Misc.
  • 5.7) Mazes and Labyrinths for People
VII. Route-Finding
  • RTF-CPLX - changing path or complex traveler
  • RTF-STEP - plate-and-ring, step mazes e.g. Pike's Peak
  • RTF-UNIC - unicursal
  • RTF-SHOR - shortest
  • RTF-ANY - traditional/any path
  • RTF-OTH - other
8. Mazes and Labyrinths Hoffmann includes a ball-in-maze puzzle in chapter X, #3 "Hide and Seek." Also in chapter X are the ring-in-plate mazes #42 The Conjurer's Medal and #43 The Maze Medal. Route-Finding/Maze

VIII. Sequential Movement
  • SEQ-PLAC - placement
  • SEQ-RIVR - river crossing
  • SEQ-HOPP - hopping & jumping - peg solitaire, counters
  • SEQ-SIMP - simple sliding/shunting - no group moves
  • SEQ-GRP - sliding/shunting where group moves needed
  • SEQ-ROLL - rolling block
  • SEQ-OTH - other - e.g. Hexadecimal, The Brain, SpinOut
11. Positioning Puzzles

11a. Crossing the Water

11b. Peg Solitaire (and Tower of Brahma/Hanoi)

11c. Shunting Problems

11d. Puzzles with Checkers

11e. Sliding Block Puzzles - e.g. The Flying Puzzle, Ma's Puzzle, George Washington

VI. Puzzles with Counters

e.g. #13 8-Point, #14 Okto, #17 Right and Left (Hop-Over), #19 Four and Four, #24 No Two in a Row (8 Queens)

X. Miscellaneous

Hoffmann includes in chapter X the classic Gray-code puzzles #4 The Brahmin's Puzzle (i.e. Towers of Hanoi) and #5 Cardan's Rings (Chinese Patience). #11 is peg solitaire.

Sequential Movement

Sliding Piece



6. Dexterity
  • 6.1) Throw and Catch
  • 6.2) Rolling Ball
  • 6.3) Maze Dexterity
  • 6.4) Misc.
X. Dexterity
  • DEX-UNCA - uncased
  • DEX-BALL - plain balls into holes
  • DEX-OBST - sundry obstacles
  • DEX-LQOB - liquid (mercury) balls
  • DEX-INLQ - liquid medium
  • DEX-MIRR - mirrors
  • DEX-MECH - mechanized
  • DEX-TOOL - uses tool(s)
  • DEX-RTFL - route following
  • DEX-HIDD - concealed objects
  • DEX-ELEC - electronic
  • DEX-PINB - pinball
  • DEX-OTH - other
I. Puzzles Dependent on Dexterity and Perseverance

In chapter X, Hoffmann describes #38 La Question de la Marmite, #39 Le Pont du Diable, and #40 The Two Corks, which I would categorize as "Tricky Arrangement" dexterity puzzles.


7. Puzzle Vessels XI. Jugs and Vessels
  • JUG-STD - standard - built in tubes to suck
  • JUG-CPLX - complex requiring special manipulation
  • JUG-BASE - pour from the base
  • JUG-NLID - lidless (fill from the base)
  • JUG-OTH - other e.g. Royale's patent, spoutless winepots (hydraulic seal)
Trick Vessels

According to Slocum and Botermans (1994), this class contains the oldest surviving mechanical puzzles - a puzzle jug made in the south of France circa 1400 is in the Exeter Museum. However, Dalgety believes the oldest puzzle may be a dexterity puzzle found in the Indus Valley dating to circa 2500 B.C. Another contender for the title of Oldest Mechanical Puzzle is Archimedes' Stomachion, dating back about 2200 years. (Read about the Stomachion palimpsest.)

Regardless of its antiquity, this is an interesting but potentially messy (and vaguely cruel) category. While I do own one trick cup, I have not focused here.

9. Folding Puzzles IX. Folding and Hinged
  • FOL-SPRI - springy wire and strips
  • FOL-HGOP - hinged parts in open chain - e.g. cube snakes
  • FOL-HGCL - hinged parts in closed chain - e.g. flexagons, Rubik's Magic
  • FOL-SHEE - sheets and strips

8. Vanish Puzzles

10. Impossible Puzzles

XIII. Ambiguous Pictures and Puzzling Objects
  • AMB-POBJ - paradoxical (impossible) - e.g. arrow through bottle
  • AMB-VANI - vanish
  • AMB-DIST - distortions - anamorphic pictures
  • AMB-ARCH - Archimboldesque objects
  • AMB-HIDD - hidden image, no manipulation required
  • AMB-HMAN - hidden image, manip. required
  • AMB-TURN - turn picture to show different images
  • AMB-ILLU - perception illusions
In chapter X, Hoffmann describes #32 The Two Dogs puzzle, which is a variant of the "seat the riders" puzzle popularized by Sam Loyd. Impossible Objects

Vanish Puzzles

Paper and Card Picture Puzzles

Find It/Crowded Field - e.g. I Spy, Where's Waldo, Animalia (usually in books, some in transparent canisters)

XII. Other Types
  • OTH-ELEC - electronic
  • OTH-BAL - balancing non-dexterity e.g. 1892 Columbus Egg
  • OTH-MEAS - measuring and weighing
  • OTH-CUT - cutting
  • OTH-WORD - word - incl. rebus, anagrams, riddles, crosswords
  • OTH-RIDD - riddles
  • OTH-GAME - puzzle-related games - e.g. Rubik's Challenge
  • OTH-MATH - math
  • OTH-LOGI - logic
  • OTH-TRIK - trick or catch
  • OTH-MAGI - magic tricks
  • OTH-MYST - objects whose function is a mystery
  • OTH-VIRT - virtual puzzles - e.g 4D
  • OTH-SET - compendiums
  • OTH-PEND - catchall for puzzles awaiting classification
7. String Puzzles - rope tricks

10. Number and Logic Puzzles

IV. Arithmetical - by far the largest chapter with 112 puzzles

V. Word and Letter

IX. Quibble or Catch

XIV. Related Ephemera (EPH)
  • EPH-SHAD - shadow effects
  • EPH-HTL - hold to light
  • EPH-MICR - microscopic printing
  • EPH-MOIR - moire
  • EPH-HOLO - holographic
  • EPH-ANAG - anaglyphs - require red/blue 3D glasses
  • EPH-STRP - strip - different views from different angles
  • EPH-OTH - other - e.g. non-rebus heiroglyphics

The classification scheme used by the U.S. Patent Office devotes a class and several subclasses to puzzles. For mechanical puzzles, you'll probably want Class 273. Go to the Advanced Search Page to enter a query, select the year range to include in your search, and execute your search.
(The count column shows a range from what the count used to be years ago when I created this table, versus the count on 3/20/21 and gives an idea of which categories have grown.)

Class NameCCL/273/...Count
Puzzles 153R 626 - 686
Pyramid building 153P 23 - 25
Shifting movement 153S 548 - 592
Jumping movement 153J 57 - 59
Balancing Ovoids 154 23
Folding and relatively
movable strips and disks
155 327 - 339
Take-aparts and
156 347 - 383
Transparent overlay 157A 65 - 69
Geometrical figures,
pictures, and maps
157R 989 - 1061
Bent Wire 158 114 - 117
Flexible cord or strip 159 91 - 95
Mortised blocks 160 222 - 228

The European Patent Office describes their classification scheme and offers a way to browse their classification scheme. The relevant top-level class is A63 - Human Necessities/Sports;Games;Amusements, with A63F9 containing many subclasses of interest.