The goal is to arrange the pieces in some simple configuration such that their features respect a given rule (or rules)  form a pattern  occasionally but not typically enforced by mechanical means. For example, "piece features at specific points (e.g. edges or corners) match (or complement, or dismatch) those at corresponding points on abutting pieces" or "the heights (or numeric values) of aligned pieces total a specific constant" or "defined sets of faces have all distinct (or equal) features." Sometimes, as in the case of matchstick puzzles or the "Eight Queens" puzzle, the individual pieces are indistinguishable, but their arrangement in a particular pattern is paramount.
Unlike with Assembly puzzles, laying the pieces out or into a tray, or stacking them together to form a particular shape, is not the primary focus, though it might contribute to the difficulty  it is the pattern rule which provides the chief challenge. Success is usually determined by careful inspection, checking to see that the given rule has been everywhere satisfied.
You might see some puzzles in this section that remind you of jigsaw puzzles  but the key difference here is that the edge features are compatible with several other potential mates and there are usually several other pieces that match any given piece. The individual pieces can be easily arranged in many different ways that partially satisfy the rule  but overall there is usually only one total arrangement (or a relatively small number among all possible arrangements) that will completely meet the goal. Finding a solution within a huge range of possibilities can be very hard, and this class is often attacked using computers  but beware, the class of edgematching puzzles is NPComplete . You can read more on this topic in Erik and Martin Demaine's 2007 paper Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity ( download a PDF here ).
Jacques Haubrich published his definitive Compendium of Card Matching Puzzles in three volumes, in which he describes over 1000 puzzles, and a companion volume called About, Beyond, and Behind Card Matching Puzzles in which he provides interesting theoretical and historical analyses. According to Haubrich, and to Slocum and Botermans in their 1986 book Puzzles Old and New, the first edgematching puzzle patent was applied for in 1880 by Edwin Lajette Thurston of Cleveland, Ohio (b.1857 in MA, d.1921) and granted in 1892  see 487797 and 487798; also see 1893's 490689. Thurston was, of all things, a patent attorney! For a precursor to the edgematching puzzle, using triangular tiles like "Triominoes," see U.S. Patent 331652  Richards 1885. Richards doesn't claim the triangular form of the dominoes, but rather the ways to make and mark them. He never uses the word "puzzle"  he describes a number of games but none come close to being a puzzle.
In Hoffmann's 1893 Puzzles Old and New, the only edgematching type puzzles mentioned are #72 in chapter IV "The Royal Aquarium Thirteen Puzzle" (equivalent to the French Le Nombre Treize), and #18 in chapter III "The Endless Chain" (equivalent to the French La Chaine sans Fin).
Major Percy Alexander MacMahon and his friend Major Julian R. Jocelyn applied for a patent in Great Britian in 1892 (#3297  I could not find a copy online  it is reproduced in Haubrich's About,...) in which they describe several triangular tile games and puzzles. In his 1921 book New Mathematical Pastimes, MacMahon published some of the first material to treat edgematching puzzles with mathematical rigor. That work also discusses his 3D puzzle Colored Cubes, first introduced in a lecture he gave in 1893.
Tilelaying puzzles (in German, "Legespiel") of both the edgematching and polyform varieties have been explored and produced by Kate Jones at Kadon, and you can read a lot of interesting material at the Kadon site  see Edgematching Colors and Shapes, and More About Edgematching. You can see Erich Freidmann's collection here. You can see some original designs by Yukio Hirose here. Take a look at George Hart's article "A ColorMatching Dissection of the Rhombic Enneacontahedron." Also see Peter Esser's page. And Toby Gottfried's site.
Jacques suggests the following seven categories:



Jacques also defines a classification scheme by which one can identify the puzzles abstractly and find isomorphisms (i.e. equivalent puzzles).
Jacques' conclusions, based on computer analysis, regarding the best approach to solving these puzzles agree with my empirical findings  in general, fix the tile in the middle and work around it. A good tile to choose for this middle position is the tile with the most possible matches.
As discussed in my polyforms section, the only regular polygons which can be used to completely tile the plane are the equilateral triangle, the square, and the hexagon. It is evident in Haubrich's Compendium that these shapes comprise the majority of tile shapes used in existing edgematching puzzles. Rectangles have also been used, as have octagons (allowing empty areas). I've organized my example puzzles by tile shape:
[Square Tiles]  [Hexagonal Tiles]  [Triangular Tiles]  [Other Tiles] 
Some puzzles have tiled surfaces other than a plane  e.g. the platonic solids, or a cylinder. I would file such things under 3D edgematching puzzles.
The Thurston design was used by Calumet ca. 1930 as advertising for their products. In the Calumet Puzzle, one must match not just the proper color edges, but also the corresponding top and bottom halves of the baking powder cans. I solved the Calumet puzzle using a variant of my Drive Ya Nuts technique. 
The Grandpa's Wonder Soap Puzzle was patented (U.S. Patent 1006878) in 1911 by A.K. Rankin. It is described on page 36 of Slocum and Botermans' "Puzzles Old & New." The goal is to form a 3x3 grid such that at the points where the quartercircles on the corners of the tiles meet (either four or two), there are always different colors on each of the meeting quartercircles. Grandpa's head must always be upright on every card, so the cards cannot be rotated. Jacques says this is the first example of a corner dismatching puzzle. There are different versions. 
The Besco Soap Puzzle  from the Beaver Soap Company of Dayton Ohio. Form a 3x3 grid such that there are four different colors in each circle at the corners, and two different colors in each halfcircle. There must also be a different color at each of the four corners of the grid. The pieces must all remain oriented with the words "Besco Soap" upright. JH Vol.2 p163 2 solns 
Le Berger Malin  The Lazy Shepherd (N.K. Atlas Paris circa 1910). NOTE: "malin" can also be translated as "ingenious." There are nine tiles, each of which is divided into four quadrants by two diagonals. There is a number in each quadrant, and the corresponding number of sheep are depicted. Arrange the tiles in a 3x3 grid such that the total in each square formed where edges meet totals 10. According to Jacques, this is the first known example of a Heads/Tails puzzle (the two numbers which must add to ten comprising the head and tail). 
Le Fermier Avise  The Wise Farmer The same principle as the Lazy Shepherd, except with chickens and now it's a wise farmer. 
This is a French puzzle (CasseTete) called "Le Nombre Treize"  The Number Thirteen. Arrange the tiles in a 3x3 square such that the red figures align vertically and the blue figures align horizontally, and such that the three figures in each of the six rows and six columns add to 13. 
The Vess Cola Nine Piece Puzzle is an advertising giveaway, promoting Vess Cola; its pieces are equivalent to the Calumet Puzzle. 
The Vess Mystery Puzzle two versions 
Here is a 3x3 heads/tails that Norman Sandfield found on a visit to the remote Easter Island (Rapa Nui). He bought all he could find, and I got one from him at the 2006 New York Puzzle Party. 
Pepsi edgematching puzzle (Spanish) 
La Canadienne  an advertising promotion edgematching puzzle 

The "33 to 1" Puzzle, advertising Pabst beer. Copyright 1940. One version shows bottles, the other cans. 
Pabst 33  arrange the cards in a 3x3 grid so that the numbers total 33 horizontally, vertically, and along the main diagonals. 
PelFreeze JH Vol.1 p93  two solns 
ATreat Mystery Puzzle  ATreat Bottling Co. PA Three versions. 
Jacques' Compendium, Volume 1, pp724, indicates that the following 9square puzzles are isomorphic and have only one solution:

Nestle NineSquare 
Lionstone Whisky, Kentucky 1973 
Camel  an advertising promo from a cigarette manufacturer. 
Bits and Pieces  match the color dots on the squares' edges 
Nitty Gritty  Arrange the colored tiles in the tray so that the edge patterns on all adjacent tiles match. 
In Mattel's Mangle Quadrangle one also has to arrange the colored tiles in the tray so that the edge patterns on all adjacent tiles match. One in a series of Brain Drain puzzles. 
Loncraine Broxton/Lagoon Games offers a set of four Professor McBrainy's Zany optical illusion puzzles: Fusion, Cosmos, Vortex, and Kaleidoscope. The patterns are psychedelic. 
Ovals  Nob  OPico/Color Match Puzzland Hikimi JH Vol.1 p151  6 solns 
Chelona Pocket Puzzle  Cats A ninesquare edge matching puzzle from Chelona in Greece. Cute, colorful graphics on thin plywood. Novel packaging  an extra backing tile has an attached elastic cord to enclose the stacked tiles. A solution diagram is on the bottom. Available from Padilly. 
Crafty Butterfly 
IZZI  Binary Arts Geo Matrix made by Binary Arts for The Museum Company is the same. (I don't have Geomatrix.) JH Vol.2 p303 
Zoki See U.S. Patent 5524898  Pavlovic 1996 
At the January 2007 Toy Fair, Tomy launched the Eternity II puzzle (Wikipedia entry here) and a contest prize of $2M USD. Eternity II employs 256 square tiles to be arranged in a 16x16 grid, which must have a gray border and a particular tile at a given "starting" position. The "final scrutiny date" passed without a winner, so the prize went unclaimed. 
Scramble Squares Tropical Fish Sea Shells There are many different versions of Scramble Squares, and most of them are in fact distinct puzzles (not just the same puzzle with different pictures). 
12 Ladies, from the Dr. Wood Mind Challenge series. 
A Tens Edgematching puzzle from the Plantecs at PuzzleMePlease.com. Same idea as Le Berger Malin. 
One Tough Puzzle is a 3x3 heads/tails edgematching puzzle. I solved it using an extension of the technique I describe for the Drive Ya Nuts. JH Vol.1 p107 
Another Tough Puzzle is a 7piece hexagonal heads/tails edgematching puzzle. (I have listed it here with the original One Tough Puzzle.) JH Vol.1 p35  1 soln 
Another Tough Puzzle (Triangles)  Great American Puzzle Factory 
The Ultimate Puzzle (4x4 square tiles)
The Ultimate Puzzle Two (3x3 right triangle tiles) Both designed by Lee Willcott of Estonia. The original version has square tiles  each side has a cutout or tab, in one of four shapes: an "in" arrow, an "out" arrow, a cross, or an oval. There are four challenges: build a 2x2; build a 3x3 (find 9 tiles that work); build a 4x4 with no sideup constraint; build a 4x4 with either all smooth sides or all rough sides up. The Ultimate Puzzle Two has 18 righttriangular tiles, pairs of which form squares. Nine squares must be arranged in a 3x3 grid (so I have listed it here in the square tiles section with the original version). Each tile has a cutout on each side  the cutouts form halves of four symbols: crown, heart, spade, and star. On one pair of tiles, a heart on the diagonal is offset  the bumps half is lower and the v half is deeper. Where tiles touch the halves must form a whole symbol, so this is a "heads and tails" type edgematching puzzle. 

DaMert 3D Squares Cars 
4D Metapuzzle 
4D Metapuzzle No. 4 
Instant Insanity  Hexagon Puzzles 1986 JH Vol.1 p151  2 solns 
A fourpiece glass edgematching puzzle made by Brett. 
The Great Canadian Puzzle 
Setko Match Heads 
Peterson Uptight Spider JH Vol.1 p149  1316 solns 
The Wobbly Web Create a rectangle from the 15 square tiles such that web strands join (edgematching). JH Vol.2 p210 (See the Waddington's series, below.) 
PeekaBoo Snakes 
EyeCue 
Pin Pin Kan 
New Departure Puzzle  advertising New Departure coaster brakes for bicycles. An uncut card. Copyright 1953. 
Celtic Knotwork 
Lagoon Group Safari series  Tiger Puzzle 
Warning  Lagoon 
Jungle Mega Puzzle  Lagoon 
Vintage Chevrolet advertising edgematch. 
"Ladybugs," a "3D Magna Puzzle" by Caeco, purchased from New England Hobby. 16 magnetic square tiles. A holographic image that is 3D when viewed from two orientations, and flat from two others. This is more of a jigsaw since each edge really has only one mate. 
A British Petroleum (BP) advertising edgematching puzzle from Australia. 
The Crazy Cheese Puzzle, from Blue Orange Games. A nice wooden 3x3 edgematching puzzle with two levels of challenge. Purchased at The Games People Play. 
Holland America Edgematching puzzle 
Suits Edgematch I found this at Der Verrückte Laden, a puzzle shop in Berlin. 
Perfect 10 from Creative Crafthouse 
A vintage advertising cardboard edgematching challenge, the Snyder Standard Nine Piece Puzzle.
According to the package, "Par is tweleve minutes."


This vintage sixpiece, squaretile edgematching puzzle from Germany is called the Matador DominoesPuzzle.


Fish Frenzy  arrange the eight cards to form a picture, then move the cards about to form other pictures. 
Colour Rings Puzzlefriend Colin James kindly sent me a copy of this ninesquare edgematching (or dismatching) puzzle. Thanks, Colin! 
The Daily Mail World Record Net Sale puzzle was published in 1920 and has only one solution. See British Patent No. 173588  Hydes and Whitehouse 1921. It was printed and published for Associated Newspapers, Ltd. by the Chad Valley Co. Ltd of Harborne, England. It consists of 19 hexagonal tiles which must be arranged in a large hexagonal grid 3 tiles on a side, while matching the color and the word on adjacent tile sides. The newspaper ran a contest and offered various prizes, and my copy came with a yellowed newspaper clipping showing the winner  one Mr. C. Lewis of Dalston  and the solution. JH Vol.2 p246 
The Nestle's puzzle, published around 19301940, was the first 7tile hexagonal edgematching puzzle. I found one from Malaysia, and one printed in Spanish. There have been many variants, including the modern "Drive Ya Nuts." JH Vol.1 p30  1 soln 

To me, the edgematching puzzle is exemplified by the more recent but nonetheless venerable Drive Ya Nuts. I developed a tabular solution, shown below. There was also a version with red nuts in a silver case  it has the same numbering. 
The Circus Seven by Masudaya is fairly wellknown. In principle it is the same as Drive Ya Nuts, but with tents and colors instead of nuts and numbers. I solved mine easily using my tabular technique. 
The Circus Puzzler is a clone  many variations exist. 
Dunlop Hexagons 
Lyons' Tea 
Match the Colors  Adams ca. 1953 
Gemstone  Nordevco 
Pressman's ThinkOminos 
Melissa & Doug make a similar puzzle called the "Space Edge Matching" brainteaser 
Spider Puzzle  Toysmith 
Hexamania From The Long Point Toy Co. of Ingersoll, Ontario. 19 singlesided hexagonal tiles numbered 1 through 19, each having the edges differently numbered 2 through 7. Arrange the pieces in an edge3 hexagonal grid (i.e. 5 rows  3/4/5/4/3) such that all adjacent edges total 9. A heads/tails type of edgematching puzzle. 
Another Tough Puzzle is a 7piece hexagonal heads/tails edgematching puzzle. (I have also listed it with the original One Tough Puzzle.) JH Vol.1 p35  1 soln 
Pair It  made by Steve Kelsey Arrange the seven hexagonal pieces such that edges match. 
The OXO Triangle puzzle. This was published in 1922 by the OXO Company for a contest. There are 25 equilateraltriangular cards/tiles, numbered 1 through 25. The tiles must be arranged into a side5 large triangle such that at each point where the corners of different tiles meet, the colors are different, and such that at each point where three tiles meet they spell "OXO" and where six tiles meet they spell "OXOXOX." There are 104,920 solutions but finding even one by hand is very difficult. JH Vol.2 p271 
TriPuzzle  Lagoon 
Contack A game (not really a puzzle), played with 36 triangular pieces. The 3 sides of each triangle are different in colour, and each side has a number from 1 to 10 printed at its edge. Players try, by matching color and number, or matching color and making certain score totals, to play all the triangles from their hand and to make as large a score as possible. Listed at Boardgamegeek. 
Butterflies Mini 
Travel Triazzle 
12 Triangles  Majak 
Playtime Flower Puzzle General Toys No. 210 Hong Kong 
BrainArt Level 4  Ekos Designed by Klaus Schröer Arrange the 24 equilateral triangular tiles into a hexagon with one lizard in each cube, then solve four riddles. 
BrainArt Infinity  Ekos Designed by Klaus Schröer Arrange the 24 equilateral triangular tiles into a hexagon so that only one continuous snake is formed, then solve a hidden mystery. 
Jinxed, a vintage edgematching puzzle by Tryne. There are 24 triangular tiles, the edges of which are colored with a dot in one of four colors (red, yellow, white, and green). The tiles are to be arranged into a hexagon such that all touching edges match and the border is all red. (It is possible to solve the puzzle with other border constraints, too.) Puzzles using triangular tiles are discussed by MacMahon in New Mathematical Pastimes on pages 222. MacMahon shows the possible tile sets for 1, 2, and 4 colors in Figure 2, and gives a solution for the 4color set. Kadon's Multimatch III is essentially the same puzzle. 

Another Tough Puzzle (Triangles)  Great American Puzzle Factory (Also listed with the original One Tough Puzzle that has square tiles.) 
Triazzle  Alice in Wonderland 
This is L'Arc en Ciel (The Arc in the Sky  i.e. the Rainbow). There are nine discs on pegs, arranged in a 3x3 grid of holes in a baseboard. Each disc has four diamonds arranged pointing north, south, east, and west. Each diamond is one of eight colors: red, green, yellow, orange, gray, white, pink, and blue. The discs must be arranged such that no color appears more than once in each of the three rows and three columns of six diamonds. In this case, not every color appears in every row or column. There is a second constraint  when a pair of colors is placed adjacent horizontally, then that same pair cannot be placed adjacent again in that direction  likewise for the vertical. JH Vol.1 p162  236,326 solns 

Here is a new favorite, an RGB Roundup from Elverson. The basic puzzle is to build a circle in the provided tray, such that adjoining colored dots match. Additional objectives include building various shapes like in Tangrams. The pieces are made of very nice weight plastic material like MahJong tiles. 
Vintage Set of Four Colorful Circular Torture Puzzles by Shackman 
IZZI 2  Binary Arts Color Matrix made by Binary Arts for The Museum Company is the same. JH Vol.2 p198 
Domino Match 
Double Half  Interkemia 1981 
Block Shock 
Ed Pegg, Jr. developed the game Chaos Tiles based on a nonperiodic tiling. I've read that Ed has yet to determine if the shapes can in fact completely tile the plane. 
Around the Barn 
Concentra Atlantis Dan Gilbert 1994 A circular edgematching puzzle with pentagonal pieces. Not too difficult since the die cuts give clues. 
In this group of puzzles, several rods have been cut into fragments of different lengths 
these must be fit into a base containing sockets drilled to different depths, such that the completed stacks all achieve the same height. 

In Kohner's Even Steven, match pegs to sleeves such that all pegs align at the same height. U.S. Patent 3375009  Stubbmann 1968 
Here is another version of Even Steven, with blue plastic rod pieces to be inserted into a clear base. 

In Reiss' Flat Top, arrange the eight pegs in the four holes so that each stack ends up at the same height. 
Tekozuru Z2 from Hikimi  purchased from Torito 
Adele and Peter Plantec at Puzzle Me Please sent me a selection of their beautiful puzzles crafted from exotic woods. This one is called Double Dowel. Thanks! 
These three puzzles, Nice Cubes, Mental Blocks, and Double Disaster, each comprise a set of
transparent cubes with colored markings.
Their goals, respectively, are: to line up four cubes so all four long sides each show all four colors;
to create a cube so that embedded colored rods match where the pieces touch; and
to create a cube such that each side shows all four colors, then such that each side shows a solid color.
Double Disaster was offered by Scientific Games Division of KMS Industries Inc. of Ann Arbor Michigan, and its
insert mentions the other two. Mental Blocks was offered by Creative Playthings.
The Nice Cubes in their original package say Copyright 1968 Funtastic, Div. of KMS Industries, Inc., Alexandria, VA.


This is Aquarium designed by Kohfuh Satoh. I bought it at Torito.
Three challenges  no incomplete fish ever allowed to show, but unless otherwise noted fish may span edges/turn corners:
1. Use 3 pieces and build a 1x2x3 showing 7 fish. 2. Use all 4 pieces and build a 2x2x2 showing 9 fish. It is also possible to show only 8 or 7. 3. Use all 4 pieces and build a 2x2x2 showing only 6 fish with none turning any corner. 
The Dodeca Nona puzzle comprises a dodecahedral magnetic body, and 12 2sided pentagonal tiles. The tiles are numbered 15 at their vertices in all possible orderings. The objective is to arrange the tiles around the dodecahedron so that the 3 numbers that meet at each vertex add up to nine. JH Vol.2 p202 
Integr8, from the Dr. Wood Mind Challenge series. Arrange the 8 cubes into a larger cube such that only complete circles show on the sides  no semicircles or lines can be visible. 
Here is a solution for Integr8:


This puzzle, called Crux, was made (in Hong Kong) back in 1972 by the Hubley Division of Gabriel Industries  it's marked "Copyright 1972 Gabriel Ind. Inc." It is a version of the Piet Hein design Triple Cross (that I do not own). It consists of six plastic pieces, each with four color spots on the sides. Twist the blocks to ensure that at each intersection, there are three different (or same) colored spots. Pieces are paired by elastic cords threaded through the narrow end and anchored inside on hooks molded on the back plates. The elastic cords had long since worn out, but you can easily pop out the back plate by poking an unbent paper clip through the hole. I replaced the cords with rubber bands. If any of the internal plastic hooks are broken, just anchor the band with a paper clip. 

Mental Misery (aka Double Trouble)  Lakeside A transparent box, a frame which fits inside the box and will hold four cards vertically against the box sides, and five cards each colored with four colors front and back. The four colors are red, yellow, green, and blue. Arrange the cards on five sides of the cube so that edges match inside and outside the cube. The instructions are marked: Made in Hong Kong, Lakeside Industries, a division of Liesure Dynamics, Inc. Minneapolis Minnesota. Copyright 1970 Leisure Dynamics, Inc. The box is marked: Copyright 1969 L.I.I. Made in Hong Kong. The frame is marked: Copyright 1969 Lakeside Toy Division of Lakeside Industries Inc. Made in Hong Kong. 
The Great Pyramid Pocket Puzzle, by Eliot Inventions Wales 1981, is a tetrahedron with 4 equilateral triangular tiles pegged to each side. The triangles are printed on one side only with a series of radiating wedges of different widths. The objective is to arrange the triangles so the edge patterns on all adjacent triangles match. The larger version with 9 triangles per side carried a 25,000 GBP prize for the first solver. I have no idea if it was ever awarded. The small case is a minipuzzle in itself  a 2piece trick box. 

Another oldie but goodie is Onthelevel by Mag Nif. Fit 9 multilevel pieces into a 3x3 grid such that wherever 2 pieces meet along an edge it is at the same level. In addition, the solution must be "toroidal"  i.e. opposite outside edges must all also match. JH Vol.1 p161 
In Contoura, arrange the blocks so that the surface contour is correct. 
Four Cube Impossible Puzzle  Binary Arts 1998 Created by Scott Nelson in 1971  maps the 24 3color MacMahon squares to the faces of four cubes such that all edges match. The puzzle gives 13 arrangements to make and requires that all adjoining edges match. Analyzed by Jaap. 
Chain of Colors  Haubrich IPP26 
EyKoSe Imperial Games Ltd. Southport England Edgematching triangular tiles on the faces of an icosahedron. Alternative challenges include total 15 on every pentagon of five triangular faces, or show a 5letter word on every pentagon. 
Einstein Cube 
DodekDuo Issued by the Dodek Puzzle Company (dead link?) Designed by Jerry LanginHooper 12 magnetic pentagonal pyramid pieces form a dodecahedron. The edges of each pentagonal face have a color (one of five), and a small black shape (one of rectangle, semicircle, triangle). Try to assemble the dodecahedron such that the colors match at face edges (only one solution), then such that the small shapes match (47 solutions, but much more difficult to find). It isn't possible to do both simultaneously. Analyzed by Jaap. 
Dodecahedral edgematching  R.D. Rose Purchased from Norman Sandfield at IPP 29 in SF. 
The Enigma (a dodecahedral edgematching puzzle) by Reiss, 1971 
Colin James sent me a rare Twitchit puzzle, issued in 1972 by the Hubley Division of Gabriel Industries of Lancaster PA, and designed by Piet Hein. This is a dodecahedron whose faces turn. One of three symbols (a circle, square, or triangle) is printed at every vertex of every pentagonal face. The objective of the puzzle is to rotate the faces (in place) so that at all 20 vertices of the dodecahedron, three different symbols show. Although discolored with age, the plastic remains intact and the puzzle is playable. I solved it! Thanks very much, Colin! 
I obtained a copy of the Hubley Toys 1972 Catalog, which features a series of four puzzles designed by Piet Hein. With the acquisition of the Twitchit, I now have an example of each of these vintage Piet Hein puzzles. 
Using this technique I can prove fairly easily that this puzzle has only one distinct solution.
There are seven hexagonal "nuts" that I label A thru G. For each nut, the six sides are numbered 1 through 6 in some order. The numbering scheme of each nut, starting with 1 and proceeding CLOCKWISE, along with the letter ID I arbitrarily assign the nut, is shown below:
All nuts must be used, each once and only once. One nut of seven must be placed in the center. In a solution, each nut except for the center must abut 3 other nuts and at each abutment the numbers assigned to the respective abutting sides must match.
When a central nut is chosen, the remaining nuts must be arranged around it. For any side of the central nut, the orientation of each remaining nut that can abut this side is given by the cell in the apropos row and column of the primary table. The row corresponding to the central nut is eliminated from consideration (indicated by the green line through it). If we rearrange the columns to correspond with the CLOCKWISE side numbering of the central nut (and repeat the "1" column last, for convenience in analysis), we arrive at the 7 diagrams shown below.
Some reflection should convince you that a solution is possible if and only if one can find a set of six cells, such that:
When A is in the center there is no solution possible. Consider nut G. Its 1 cannot be used to abut the central 1 on A, since there can be no nut clockwise from it that matches its 6 while also matching the central 6 required at that position. Hence cell G1 crossed out with line a. G cannot be used to abut the central 6 since there can be no nut counterclockwise from it that matches its 1 while also matching the central 1 required at that position. Hence cell G6 crossed out with line b. Similar arguments apply resulting in the cell in every column of row G being crossed out. This means that G cannot be used, violating rule (1) and proving that nut A cannot be used in the center.
On to nut B in the center. No nut fits counterclockwise of C5, D5, E5 or G5. No nut fits clockwise of A5, or G2. This leaves only nut F possible to abut the central 5, but nothing remains to fit clockwise of it (only another copy of the F nut would fit). This proves that nut B cannot be in the center.
Here, G6 is eliminated  nothing fits counterclockwise of it. This in turn eliminates D4 and G4. Nothing fits clockwise of A4 or E4, or counterclockwise of F4. This leaves only nut B possible to abut the central 4, but nothing remains to fit counterclockwise of it (only another copy of the B nut would fit). This proves that nut C cannot be in the center.
If you logically eliminate all impossible cells from the table when D is in the center, you find a single solution indicated by the six cells circled in blue. This is the only solution to the Drive Ya Nuts puzzle.
When E is in the center, only A can abut the central 1. This then requires C4, but no nut fits counterclockwise from it.
Nothing fits clockwise of G1 (except G again). Nothing fits clockwise of A4, B4 or G4. Since G1 is eliminated, now nothing fits clockwise of D4 or E4. This leaves only C4 but nothing fits counterclockwise of it.
Lastly we tackle G in the center. Nothing fits counterclockwise of B2, A3, C3, D3, or E3. Since B2 is eliminated, nothing fits counterclockwise of F3 either. This leaves only B3 but nothing fits clockwise of it.
Route Building puzzles are a subclass of Edge Matching puzzles ("Continuous Path" or CP Edge Matching puzzles according to Jacques Haubrich's classification scheme). Here, one has to arrange pieces so that connections are made, creating a specific route across the pieces according to some rule.
La Chaine Sans Fin  The Endless Chain A vintage version, and a recent lasercut wooden version by Steve Kelsey. Arrange the pieces in the tray to form a closed loop of chain links. JH Vol.2 p244 
Tantrix is a wellknown modern routebuilding puzzle/game. [Jaap's Tantrix page.] 
PsychePaths (c) 1969 Funtastic, Division of KMS Industries, Inc., Alexandria, VA. A set of 85 hexagonal tiles, each with 3 path segments using up to 3 colors. A solitaire challenge is to build a 9x10 rectangle alternating rows of 9 and 8 tiles. Listed at boardgamegeek.com. Tiles shown here. Play a related game, Kaliko, online here. Here is the included solution to another solitaire challenge:


Rubik's Tangle set of #1 thru #4, and the 9 doublesided plastic tiles version The original sets have 25 onesided cardboard tiles, and come in four versions distinguished by which particular tile is duplicated within the set. JH Vol.2 pp2723 

Chicago L  George Miller 
I believe this is the "IQ Chain" puzzle, by D.P.B. Taiwan 1993 JH Vol.2 p172  1 soln for a single continuous path. 
Krazee Links  Plastrix 1939 JH Vol.2 p207 
The Path  from Family Games 
It's Knot Easy  Milton Bradley JH Vol.2 p240 
Trail Run 
Think Through  Pressman (Equivalent to QED's Set Squares which I don't have.) 
Right Connections  Springbok JH Vol.2 p179 
Fishy  Melissa & Doug 
Snake Pit  Nature's Spaces / Binary Arts 
Octopus  Nature's Spaces / Binary Arts JH Vol.2 p184 

GoGetter 3 Prince and Dragon, and Cat and Mouse  DaMert Designed by Raf Peeters  see his website at www.atelieroker.com 
The Path  Waddington's JH Vol.2 p197 (See the Waddington's series, below.) 
Ant Trails 

The Diamond Dilemma puzzle was Copyright by Price Stern Sloan Limited in 1989, and offered prizes for solutions of various complexity. The instructions tell you to "arrange the playing pieces on the diamond so that a continuous unbroken line is formed." 
This is Dice Dominoes. The box says "Made in U.K." but there's no other provenance. There are twelve cubes, each side of which shows a correctly linked arrangement of two or three dominoes. Paraphrasing from the instructions: Using the box base as the playing area, start with a doublesix in the top left corner. (There are six faces among four of the cubes showing a doublesix.) The box holds a rectangle of 3x4 cubes. Match dice so a continuous pattern is formed, as in regular dominoes. You must use all 28 dominoes and cannot use any domino more than once. Each must line up and doubles must be at right angles. A solution sheet (I haven't looked) is enclosed. 

TSL Maze Assemble the pieces to form a maze. 
Daily Sketch JigSaw Puzzle Fit the pieces into the tray and build a loop. 
Serpentiles  Thinkfun 
Metroville from Smart Games, designed by Raf Peeters  see his website at www.atelieroker.com 
HooDoo Loop by Popular Playthings Build a path using the 14 pieces. Designed by Bill Hanlon and Steve Wagner A gift from the folks at Oy Sloyd Ab. Thanks! 
Cobra Cubes, from SmartZone Games. Designed by Ariel Laden. Purchased at Eureka. Four cubes, each a different color. Each cube's sides have various segments of a snake  a head, tail, or body section. A booklet of challenges, graded A, B, C, or D, requires one to arrange the cubes in order to form a snake that spans all visible faces of the required cubes. 
Anaconda  designed by Raf Peeters A 5x5 grid with one corner filled, seven 2sided pieces, and a 1x1 blank piece. Cover a designated square with the blank, then fill in the rest with the other pieces while building a complete snake. 
Tromino Trails from Pavel Curtis IPP31 Berlin Using subsets of Tromino pieces inscribed with trail segments, make a single closed loop in five differentsized openings in the adjustable tray. 
String Octet Designed by Goh Pit Khiam, made by Walter Hoppe. Purchased from Walter at IPP 29 in SF. 8 1x2 tiles encompassing all the ways a tab and a notch can be arranged, each with a path inscribed connecting the tab and notch. Two 1x1 tiles, one with a notch and one with a tab  the start and end tiles respectively. A 4x5 tray. A sheet with 13 challenges  each specifies positions and orientations for the start and end tiles. The objective is to connect the 1x2 tiles in the tray to create an unbroken path from start to end. I really like this one! 
World Passport, from SmartZone Games. Designed by Tzafrir Kazula. Purchased at Eureka. Fit six polyhex pieces into a hexagonal grid overlaid on a "country" card such that five points are connected in order by a transparent path, with no backtracking. 

Troy Extra Muros from Smart Games, designed by Raf Peeters. I really like this one! A series of challenge cards indicate the placement of up to 4 blue and 4 red soldiers. Place the four wall pieces such that all blue soldiers are completely enclosed and all red soldiers are "outside" the walls ("Extra Muros"). (You are finding the route the walls must take.) Raf gave an interesting talk at IPP31 in Berlin, in which he said that one goal of design is to ensure a customer can apprehend the goal of a puzzle just by looking at it in the package. He achieved that in this case  I could tell what the goal was despite the fact that I found this in Québec City and this box was printed in French! 
Golf Line by Binary Arts 1994 Arrange 20 1x1x2 rectangular cards depicting sections of an 18hole golf course to form a continuous cart path from hole to hole. Hints and solution are included. 

Mall Function, designed and exchanged at IPP32 by Rik van Grol, made by Buttonius 
Network Builder, designed, made, and exchanged at IPP32 by WeiHwa Huang 
Temple Trap  designed by Raf Peeters, issued by Smart Games A 3x3 board with an exit space in one corner. Eight sliding blocks representing walls, hallways, and stairs in various configurations, and a player figure. Set up the blocks and figure per the current challenge, then try to solve it by sliding the blocks and moving the figure from block to block to eventually exit the board. The block where the figure resides cannot be moved, and the figure can only be moved to rest on certain blocks. Temple Trap combines a slidingpiece puzzle with routebuilding challenges and has a great theme reminiscent of Indiana Jones. 

Perplexing Python issued by Pentangle 

Roundabout  invented by Volker Latussek Produced by Popular Playthings Use the 18 pieces of four different shapes to build a closed loop  assemble 50 challenges. 
City Maze  designed by Raf Peeters, produced by SmartGames Thanks, Raf! 
Puzzle Picks, by Kohner (No. 122) 1967. Includes a set of colorful plastic "matchsticks," a booklet of 80 puzzles, and a solution sheet. 
There are lots of matchstick puzzles online...
The book Creative Puzzles of the World by van Delft and Botermans includes a section on matchstick puzzles on pages 49 through 56. 
A set of brightly colored matchsticks, in a matchbox marked "Puzzle" from Japan. 
Allumez les Enigmes, produced by Kikigagne. A set of matches and cards posing 50 matchstick challenges (in French). Thanks, Brett! 

33 Problems  issued by Invicta in 1981 A board containing a set of grooves, arranged so as to provide a playing surface on which to try 33 different matchstick puzzles using a bunch of included red panels in lieu of matchsticks. The panels fit into grooves in the board. An included sheet specifies the setup and objective for 33 puzzles, but does not give solutions. 
This category requires you to arrange the pieces to satisfy some rule or goal relating to a pattern/silhouette the pieces make. There is no physical mechanism to restrict moves  only rules or the goal govern legal combinations. The piece shapes will be fairly abstract but usually it will be easy to abut them and they will interchange positions easily.
Note: I have created a separate page for Tangrams.
This classic threepiece French puzzle is called Bucephale. Arrange the three pieces to form a horse. Described in Slocum and Botermans' New Book of Puzzles on page 23. Sam Loyd called it his Pony Puzzle. 
Demon Dino  William Waite 
Dino Try  William Waite 
Six Australian Animals designed by René Dawir 
Cliko, by Foxmind Comes with a set of blocks and a booklet of problems. Arrange specific blocks to form different silhouettes. With the Tangramino, Equilibrio, and Architecto books from Foxmind, I can use the pieces in the Cliko set I already have, to try many new challenges. 

Copy Device  Hiroshi Yamamoto Place the 3 pieces flat in the tray to create two identical green areas. Winner of a Jury Honorable Mention in the IPP34 Nob Yoshigahara Puzzle Design Competition. 
In this category of puzzle, a set of pieces, often transparent or with cutouts, must be stacked (or folded) over one another in order to achieve some goal.
The Rabbit Silhouette or "Question du Lapin" Layer the five cutouts to form a rabbit Play the rabbit silhouette online. 
Arrange the 5 layers so the cumulative cutout area forms the shape of a pipe. You will then have "This is Not A Pipe"  "Ceci n'est pas une pipe"  as from Rene Magritte's "The Treason of Images." A miniature puzzle in a matchbox. 
Mattel's Virtual Illusion puzzle contains a base and a series of transparencies each containing a portion of a threedimensional image. You need to order the transparencies in the base so that the image appears correctly. 
Two Silhouette Puzzles designed by Diniar Namdarian make a Pigeon, and make a Dog. 
Red All Through 
Animal Land 
Starry Skies 
Transposer 6 
Bonbons 
Genesis 

Kaboozle 
Tiffany 
Tower of London 
Struzzle 
Along the same lines as the Toyo Glass puzzles, combined with the weave concept, Strip Tease requires you to create a 5x5 weave using 10 clear strips having various arrangements of quartersquares so that all solid squares result. 
Trixxy designed by Dror Green  superpose four cards having transparent and opaque colored sections in order to produce a solid column of each of the four colors. 
This is the "2D 3D Burr"  stack the transparencies so that the image of a 3piece burr appears. I bought it at Torito. 
Cover Your Tracks  Thinkfun Four pieces and a set of challenge cards  for each card, pack the four pieces into the tray so that the bootprints on the card are all covered. 
Zoo Panic by Tsugumitsu Noji Purchased at IPP28 in Prague. Four transparent overlays, each with a 6unit enclosure. On each problem background, fence off unlike things. 
Frustables by Gameophiles Unlimited 1973 Six sets of six cards. Each set of six cards has one colored puzzle on the front and another color on the back  twelve puzzles in all. A card has a given color, and may have some black area. The objective given the six cards belonging to a given puzzle is to pile the cards such that all the black areas are covered but no colored area is covered. These are difficult puzzles! 
Ariel Laden's Kookoo Puzzles  Funny Fliers Four sixcard puzzles, and one large puzzle using the backs of all 24 cards. Position and interleave the cards of a set to form a complete picture. This principle is very similar to that of the 1973 puzzle Frustables by Gameophiles Unlimited. 

Four well done puzzle challenges (and two expansion packs) from Smart Games.
Booster packs for North Pole Camouflage and Safari Hide & Seek 
Angry Birds Playground Under Construction  designed by Raf Peeters, issued by Smart Games Using the four pieces (nonflippable F, P, T, and U pentominoes), cover the proper selection of faces on the 5x5 gameboard, per each challenge. I admit I had trouble with the very first problem! 

Mozaniac: Four Painters By Paradoxy Products. Six square cards, each almost cut into quarters and each bearing a portion of four different images. Interlock and overlap the cards to create each image, in turn. 
The Invisible Puzzle, designed by Rich Garner, from Loncraine Broxton  Lagoon Trading Co. Ltd. Make a large hexagon from 18 transparent trapezoidal tiles, while matching edge colors. 
On the Dot  Gamewright 
Get a Clue from Pavel Curtis. A refined version of Pavel's exchange puzzle from IPP30. Nine transparent pieces, and a frame in the shape of a magnifying glass. Arrange the pieces in three layers inside the frame. Find two distinct overall arrangements to determine "two things given to Snow White." I enjoyed this one  it is not too difficult. 

Pathwords invented by Derrick Niederman For each of 40 challenges of graduated difficulty, fit a subset of the supplied transparent pieces to completely cover the field of letters such that each piece covers one word that runs backwards or forwards. 
Cage the Animal, designed by Manabu Satou and Naoyuki Iwase (Osho), made by Woodpecker Hikimi and Lixy, exchanged at IPP32 by Lixy Yamada 
Daily Puzzle  designed by WeiHwa Huang and Oskar van Deventer, produced by Thinkfun Six tiles must be paired and overlaid in variuous ways to form 3latter month abbreviations, and four tiles must be similarly arranged to produce the date. Each tile has either black segments, cutout segments (through which whatever is behind the tile, including the black base) will show, or blank area. 
On the Line  issued by Brainwright A set of graduated overlaypatternassembly challenges. Arrange four identical transparencies to form a given shape. 
This is a vintage WeaveOGram puzzle, copyright 1951 by EdcraftCentury. See US Patent 2439583  awarded to Israel Shamah of London on Apr. 13, 1948.
From the patent description  the WeaveOGram "comprises a framework and a plurality" (patent lawyers love that term) "of flexible bands some extending in one direction and the others at right angles thereto, the various bands being interwoven... and each being capable of relative movement. On each band there is provided a number of sections of a picture... by relative adjustment of the individual bands the various sections of the picture may be juxtaposed so that a complete picture is formed. Each band will be provided with the sections of a number of different pictures so that a number of different complete pictures may be made up."
My copy allows one to make six different circus scenes. The bands move pretty freely, occasionally catching on small rough edges or tears. It is best to use both hands to move a band, slowly, from both edges of the frame simultaneously. As you might expect, WeaveOGram is not too challenging, however the graphics are nice and this is a great implementation of one of those ideas that seems obvious once you've seen it done.
Also see the earlier US Patent 1903226 awarded to Harry Lawson Perry of Jamaica, New York on Mar. 28 1933. Perry's device employs linear strips rather than looped bands.
Then see the later US Patent 3235262  awarded to Ernest Frankl of Middleboro, MA on Feb. 15, 1966. It is pretty much a copy of Shamah's idea  Frankl's improvements are to "effect economies of manufacture and assembly and to provide for ease of manipulation and attractiveness." Frankl assigned his patent to WinthropAtkins Co. Inc. of Middleboro MA, a printing company now owned by Chilcote Co. of Ohio.
From the book Classic Century Powerboats by Frank, Trudi, and Paul Miklos copyright 2002, published by MBI Publishing Company of St. Paul MN. I learned that the company Century (as of March 2012 purchased by Allcraft Marine) makes powerboats, and was founded in Milwaukee in 1926. In 1948, F. L. "Ted" Hewitt Jr. became president. Since boat production orders were seasonal  heavy from March through July and slack during the rest of the year, one of Hewitt's initiatives was to offset the downtimes by producing other, stable products such as toys. Century produced a line of educational toys under the brand Edcraft, including WeaveOGram.
Shamah also patented (in the UK) a locking mechanism for a money box.




The Frustr8tor From my friends at Puzzlemaster.ca  thanks, guys! 28 versions of the 8 Queens to solve. The front side shows an 8x8 grid. The back side has 8 tracks corresponding to the 8 columns of the grid. Along each track, each of the 8 row positions is marked by a number from 1 to 28  some appear three times, some two. One red and one green tab ride in each track  green at the top and red below. To try a puzzle, choose a number and set a red tab at every position marked by that number. Then, using the green tabs in the remaining six columns, fill in the grid according to the usual rules  a dot appears in the grid on the front at the position where a tab is set. 
This vintage French boxed version called "Jeu des Manifestants" uses 8 tiles, and is available in two versions with either triangular or rectangular tiles. Jeu des Manifestants is shown in Slocum and Botermans' "Puzzles Old & New" on page 37. For another version using battleships, see U.S. Patent 1151615  Reibstein 1915. 

Lots O Spots by Peterson  "an L. J. Gordon creation." 16 tiles, each divided into four quadrants, and with 1 or 2 spots on each. When the tile are arranged in a 4x4 grid, the quadrants define 8 rows and 8 columns. The spots come in three colors  red, purple, and green  and are distributed so that there are 8 of each color. In the hardest of four challenges, you must arrange the tiles in a 4x4 grid such that all rows, columns, main diagonals, and all short diagonals contain no more than one spot of each color. This amounts to solving the 8 queens problem simultaneously for 3 colors of queens. 
The Schpotz puzzle by Peterson Games. Arrange the nine tiles in a 3x3 grid such that every row, column, and main diagonal contains exactly three spots. 
This is Out of Line by Crisloid Plastics of Providence RI. The objective is to arrange the eight pegs in the 8x8 grid so that no more than one peg is in any row, column, or diagonal. In addition, at least one peg must be in each of the five differently shaded areas  one of the areas is a single position at the lower right corner. The cover shows a motorcycle gang  I think they're supposed to be "out of line." 

HooDoo from Tryne, circa 1955. An 8x8 board, with inner nested 4x4 and 6x6 areas marked off. 64 pegs, 8 each of 8 different colors, and two extra "neutral" pegs. There seem to have been at least two different sets of instructions issued with this puzzle.
The first two challenges cited on the first instructions, on the 4x4 and 6x6 grids, are easy since you can use more than 4 and 6 colors respectively. However, the 8x8 challenge amounts to superimposing 8 solutions of the 8 queens problem, and is impossible! This puzzle is interesting because it requires superposition, and also because it seems to be one of those rare instances where prize money is offered for an impossible challenge.




The Pin and Dot puzzle  "Insert six pins, each in a separate dot, so that no two pins shall be on the same line." This is equivalent to a sixqueens puzzle. (I don't have this  shown for reference.) 
The sixqueens puzzle has only one unique solution.
Since that solution is 180degree symmetric, it has only four rotations and reflections.

La Strategie des Nippons, Strategie des Boers, and Nouvelle Strategie These vintage French boxed puzzles are all instances of the sixqueens puzzle. (I don't have these  shown for reference.) 

Jeu des Sentinelles "A police chief represented by the red piece, with 7 sentinels represented by the white pieces, must position himself and his sentinels so that no man can see any of the other men along any straight vertical, horizontal, or diagonal line." This vintage French boxed puzzle is an instance of the eightqueens puzzle. (I don't have this  shown for reference.) 
L'Intraitable  "The Intractable" Given a 6x6 grid and 24 tokens  six each of four colors, arrange the tokens on the grid so that no horizontal, vertical, or diagonal line contains more than one token of the same color. This vintage French boxed puzzle is an instance of a superposition of four sixqueens puzzles. (I don't have this  shown for reference.) The four rotations and reflections of the sixqueens solution can be superimposed:

L'Embarras du Brigadier and L'Embarras du Caporal Given a 5x7 grid of points and 12 men, arrange the men on the grid to form six rows with four men in each row. Both of these vintage French boxed puzzles are instances of, using Singmaster's notation, a (12,6,4) configuration problem. (I don't have these  shown for reference.) Singmaster cites several appearances of the (12,6,4) problem, including in The Sociable of 1858 (as Problem 26, The Gardener's Puzzle), The Book of 500 Curious Puzzles of 1859, and Hoffmann (1893) Chapter VI, No. V.
There is a second solution (see The Sociable, or Hoffmann), but it does not fit on the 5x7 grid. Note that some (a,b,c) configuration solutions rely on the trick of stacking more than one token at a given point. 

The FiveQueens puzzle has only two unique solutions.
The asymmetric solution has eight rotations and reflections. The symmetric solution has only two, giving a total of 10. A selection of five can be superimposed.

The SevenQueens puzzle has six unique solutions, and 40 rotations/reflections.

SafeCracker 50  a reproduction of a classic design style, from Dave Janelle at Creative CraftHouse. Thanks very much, Dave! Arrange the five layers so that the five numbers appearing in each of the 16 radial columns total 50. There are many vintage paper/cardboard puzzles using this theme  Dave's is made from lasercut wood and is far sturdier. With the base plate and four additional movable disks, there are 65,536 combinations to try! 
This "SafeCracker" type of puzzle was the subject of U.S. patent 993581, granted to H. Davidson in 1911. But, see below for versions with earlier dates... 
The Davidson patent seems to have been applied to the "Great Burglar Puzzle"
which requires columns to
total 40. You can see the reference to the patent near the center.
(I don't have this.)
Even earlier, the Hegger's Century Puzzle says "Patent applied for, Copyright 1891 by G. A. Bobrick, New York." (I don't have this puzzle.) G. might stand for Gabriel, since he holds other patents from the late 19th century. Unfortunately I could not find a patent pertaining to the puzzle. While the USPTO website does allow searching for applications (as opposed to granted patents), the database only contains records from 2001 onwards. The USPTO allows one to search for granted patents from 1790 through 1975 but only by issue date, patent number, and current U.S. classification.


For reference, here are several more vintage "SafeCracker"type puzzles (I don't have these):
The White Sewing Machine Sixty Puzzle says "Copyrighted by A. L. Vandyke 1890." There doesn't seem to be a date on "The Great '51' Puzzle."
Note the swastikas that appear on the Huntley & Palmers puzzle  the symbol actually means "that which is associated with wellbeing" so this likely predates WWII and the darker usage of the symbol and was probably issued somewhere in the period from 1841 (when Palmers joined Huntley) to 1920 (when the Nazis rose to power). The "Capture UBoat 40" puzzle, however, obviously comes from the WWII period. It was manufactured by the Geiger Bros., Newark N.J. The following photos are from Jerry Slocum's collection, courtesy, The Lilly Library, Indiana University, Bloomington, Indiana. They can be found under classification section 1.3, Miscellaneous PutTogether.
"The Jayne Problem" is Copyright 1906 by George H. Vickers. I don't know what is on the back of the Leinbach puzzle (another sumto40 type) or the "Safe Combination Puzzle" (make all 12 columns sum to 55), but their fronts display no dates.
The Hecker's puzzle says "Pat. applied for" and "Since 1840" so probably dates post 1840, but displays no other info and I don't know what the back might say. The Steinfeld puzzle says "Pat. June 20th, 1882"  with a bit of research I found that the patent in question is US259920 issued to William H. Reiff of Philadelphia on June 20, 1882. That makes this the oldest version as far as I know. 

Dave at
Creative Crafthouse
has brought back the 1882 puzzle and issued
the Word Wheel. Thanks for the copy, Dave!

Leonard Euler (17071783) studied Latin Squares in the late eighteenth century, and research into them has continued, not simply because of their use as puzzles, but more for their application to experimental designs and cryptography.
The enumeration of Latin Squares has not been easy  figures up to order 10 are summarized in the table below. A reduced or standard Latin Square is one where the symbols in the first row and the first column are in lexicographical order. Given the number of reduced squares, R_{n}, the number of distinct squares L_{n} is:
L_{n} = n!(n1)!R_{n}
Order n  Enumerator(s) Year 
# Reduced R_{n}  # Distinct L_{n} 
2  Euler 1782 
1  2 
3  Euler 1782 
1  12 
4  Euler 1782 
4  576 
5  Euler 1782 
56  161,280 
6  Fisher and Yates 1934 
9408  
7  Norton 1939 
16,942,080  
8  Wells 1967 
535,281,401,856  
9  Bammel and Rothstein 1975 
377,597,570,964,258,816  
10  McKay and Rogoyski 1995 
7,580,721,483,160,132,811,489,280 
In 1992, in Discrete Mathematics, J. Shao and W. Wei published a formula for the number of Latin Squares of any order. (It is nontrivial to specify.)
The Safari Puzzle by the German company "Pussy" or "Pussycat." A 7x7 Latin Square puzzle presented as a slidingpiece puzzle. Arrange the pieces (7 each of a Hippo, Lion, Elephant, Rhino, Giraffe, Zebra, and Tree) so that only one of each appears in each row and column. 
More Madness by Parker  The Fun and Game Name. No Date. It comes as a single 5x5 plastic sheet, scored with grooves along which you are to break apart the pieces. Each square is one of five colors  yellow, red, blue, green, or white. The unbroken sheet shows the solution  this is a Latin Square puzzle and in the grid, no color occurs more than once in each row or column. There are nine pieces  two are 1x2, seven are 1x3. 
Bird's Puzzle, by Chad Valley. The Bird's Puzzle is very similar to the More Madness puzzle. There are nine pieces, two 1x2 and seven 1x3, colored with five colors  yellow, red, blue, green, and a Bird's logo  to be arranged into a 5x5 grid such that no color appears more than once in each row and column. 
The Missionary Puzzle and Four Others  Five (5) Old Time Puzzles by The Embossing Company of Albany NY. Includes: Missionaries and Cannibals; Staggered Colors; Change About; Double Up; and Sorting Out. 
A vintage French boxed puzzle called Les 15. An order5 Latin Square. 
Testa Cross Colour Same as Bird's. 
A vintage cardboard advertising puzzle, "Say Cheese Louder."
Nine pieces to be arranged in a square such that only one of the five symbols appears in each horizontal or vertical line.


The "Sudoku 9 Abstract" puzzle from the Plantecs at PuzzleMePlease.com. Form a 9x9 Latin Square using the pieces made from colored woods. 
Utopia issued by Popular Playthings 2009 invented by Sjaak Griffioen Sixteen "buildings"  four each of four different heights. Place on the 4x4 grid according to rules and hints given on 50 challenge cards divided into 25 Phase 1 and 25 Phase 2. I enjoyed Phase 1 but Phase 2 seems overly confusing. (NOTE: this may seem to belong in the GraecoLatin section, but notice that all buildings of the same height are the same color, so height is really the only differentiator.) 
The Thirtysix Officers Problem goes as follows: arrange six regiments of six officers each of six different ranks into a 6x6 square so that no regiment or rank is repeated in any row or column. Note that there are no diagonal restrictions.
It turns out that there are no GraecoLatin squares of order N=6 but this was not proven until 1901 by Gaston Tarry who exhausted all possible arrangements by hand. In 1959 Euler's conjecture was shown to be false for N > 6, by Parker, Bose, and Shrikhande. Rob Beezer shows a nice colorful order 10 square on his web page.
Since in such a superposition, the Latin Squares used cannot both be standard, a GrecoLatin Square in standard form is one where the first Latin Square is standard, and the second has only its first row in lexicographical order.
The maximum number of Latin Squares of order n which can be in a set of MOLS is n1, but some Latin Squares have no mutually orthogonal mates.
In GrecoLatin Square puzzles of order N=4, the pieces are an assortment composed of all the combinations of two features each having four possible values. They must be arranged in a 4x4 grid such that no two with the same feature appear in any row, column, or main diagonal. Sometimes it is prohibited to have a repeated symbol among the four corners of the square, or among the four central cells (see "1000 Play Thinks" #400). There is only one order 4 GraecoLatin Square in reduced form, but it does not meet these additional constraints. But by permuting rows, you can arrive at my solution for an order 4 GraecoLatin Square that meets all those conditions:
Aα  Bβ  Cγ  Dδ 
Cδ  Dγ  Aβ  Bα 
Dβ  Cα  Bδ  Aγ 
Bγ  Aδ  Dα  Cβ 
Bali Buttons Requires you to place the sixteen tokens  all combinations of four different shapes with four different colors  on the 4x4 board so that no row, column, or main diagonal contains more than one token with a given shape or color. This is a GraecoLatin Square puzzle. 
Four Square from the Embossing Company, Albany, NY Combines a GraecoLatin Square puzzle with two sliding piece challenges.
FIRST.
Place the blocks in the box so that no two of the same number nor of the same color
are in any of the 10 horizontal, vertical, or diagonal lines.
SECOND. Remove one of the 4's, then, by sliding them about, arrange them in horizontal rows, each of a different color, and in the order of 1,2,3,4. The fourth or bottom row should be 1,2,3. THIRD. After completing the second, slide them about again to arrange them as in second, but in a vertical position. 
Brain Strain An advertising puzzle consists of sixteen small playing cards  the Jack, Queen, King, and Ace in each suit. As with any GraecoLatin square puzzle, the objective is to arrange the pieces in a square grid so that neither of the two kinds of feature (in this case, face value and suit) appears more than once in each row, column, or main diagonal. This puzzle was first proposed by Jacques Ozanam. 

Quintessence Copyright 1970 by gametime, Inc. of NY, NY A 5x5 GraecoLatin Square  arrange the 25 pieces in a 5x5 grid such that no row, column, or diagonal contains more than one instance of a circle color or tile color. 
A Floral Derangement  Peterson Games 1972 
A vintage advertising GraecoLatin Square puzzle issued by Stephens Motor Works "of the Moline Plow Co., Freeport, Illinois." There are 16 cards: four of each color  orange, purple, green, and yellow; four of each car model  roadster (92), touring (94), touring (96), and sedan (93); and each with a "license number" 1 through 16. The objective is to arrange them in a 4x4 grid such that rows, columns, and main diagonals contain cars of all different models and colors, and the sum of license numbers is 34 in all rows and columns and the four corners, the four centers, and each group of four in a corner! 


4  9  2 
3  5  7 
8  1  6 
Magic Squares exist for all orders except N=2. There is only one distinct Magic Square of order N=3. Supposedly the order 3 magic square was invented in China between 650 and 400B.C. and known as Lo Shu. There are 880 of order 4, and over 275 million of order 5.
In the order 3 normal square, all rows, columns, and the main diagonals total 15. The magic constant for a normal magic square of order n is given by the formula:
M_{n} = n(n^{2}+1)/2
An order 4 Magic Square appears in Albrecht Durer's famous engraving called Melencolia I:
16  3  2  13 
5  10  11  8 
9  6  7  12 
4  15  14  1 
Each row, column, and main diagonal sum to 34, as do the four corners and the four central cells. Note that this is a solution to Skor Mor's Thinking Man's 34, and Reiss' 34 Skidoo of 1971.
Fascinating 15  Crestline Crestline put out this order3 magic square  what could be simpler to manufacture, eh? (I don't have this.) 
Thinking Man's 34  Skor Mor. Also 34 Skidoo by Reiss, 1971. Sixteen wooden tiles printed with the numbers one through sixteen. Arrange them in a 4x4 grid such that every row and column and main diagonal totals 34. Also find an arrangement in each of 12 distinct classes/patterns. 
Mystifying 65  Crestline An order5 magic square from Crestline. (I don't have this.) 
18 17 3 11 1 7 19 9 6 5 2 16 14 8 4 12 15 13 10 
Pinwheel:27 from AreJay Game Company of Ohio 
Catch21 by Gabriel (U.S. Patent 3833222  Castanis 1974) and HiQ Enigma by Ideal are two puzzles where one must fit a group of pieces onto a surface bearing a pattern. Gridlock by Gabriel is a travel version of HiQ Enigma. The pieces match various portions of the pattern, and the proper "covering" must be found so that all the pieces will be accomodated and the surface completely covered. This will work with just patterns although both of these puzzles employ an embossed surface with corresponding holes in the pieces. Of the two, Catch21 is more logically straightforward. It includes a set of dominolike pieces.
Here is my solution "diary" for the 2nd side puzzle of Catch21. Please refer to the diagram at left. This shows the 6x7 board  the number inside each square indicates the pattern on the board. The numbers outside the board label the x (horizontal) and y (vertical) coordinate axes. I will refer to locations on the board via a pair of x and y coordinate pairs. The tiles consist of the 21 "dominoes" representing all ways of pairing the numbers 1 through 6.
Getting started here is not as easy as for the puzzle on the first side, since here there are multiple possible locations for every tile. Begin by considering where the 6/6 tile could be placed  there are only two possibilities: (0,2)/(0,3) or (0,1)/(0,2) shown in red. Choose to place it at the latter location. This forces 2/4 to go at (0,0)/(1,0).
Now review possible locations for the 4/6 tile  there were only two possibilities: (0,2)/(1,2) or (1,0)/(2,0) but the former has been eliminated by our choice of location for 6/6, and the latter has been eliminated by the forced placement of 2/4. Ergo we have made an error and must backtrack.
The only decision point is our choice of placement for 6/6, so we must undo everything back to that point and choose the only available alternative, placing 6/6 at (0,3)/(0,2). This still precludes one location for 4/6 and forces 4/6 to go at (1,0)/(2,0). The 2/6 tile must go at (0,0)/(0,1).
Now consider the 6 at location (5,0). It could be covered by either the 2/6 tile or the 3/6 tile, but 2/6 has been used so 3/6 must go at (5,1)/(5,0). Next consider the 3 at location (0,6). It could be covered by the 3/6 tile or the 3/4 tile, but 3/6 has been used so 3/4 must go at (0,6)/(0,5).
All squares in column 0 have been covered except for (0,4), which now must be covered using the 1/4 tile at (0,4)/(1,4). Now look at the 6 at location (1,6). It could be covered by the 2/6 tile or the 5/6 tile, but 2/6 has been used so the 5/6 tile must go at (1,6)/(2,6). This forces us to place the 2/4 tile at (1,5)/(2,5). Now consider the 6 at location (5,4). It could be covered by 1/6, 3/6, or 5/6, but we have used the latter two so it must be 1/6 at (4,4)/(5,4). Now consider the 4/4 tile. The only remaining possible location for it is at (2,4)/(3,4). Likewise consider the 1/1 tile. It can only go at (3,3)/(3,2).
Next consider the 5 at location (4,3). Either way it must be covered by the 5/5 tile. This implies that the 1/5 tile must be aligned next to it. There are two ways of placing them and either is OK.
Consider the 1 at location (4,1). Either way, it must be covered by the 1/2 tile. This implies that the 2/5 tile must be aligned next to it. There are two ways of placing them and either is OK.
Now look at the 2 at location (2,1). Since the 2/5 tile is used, we must use the 2/3 tile here. Next consider the 4 at (1,2). Either way it must be covered by the 4/5 tile and the 3/5 must be aligned next to it. There are two ways of placing them and either is OK.
There remains only 1 location for 2/2, at (3,6)/(3,5). Lastly, consider the 3 at (5,6). It must be covered by the 3/3 tile and the 1/3 must be aligned next to it. Again, two arrangements are possible and either is OK.
Other good resources for Domino Puzzles:
Instant Insanity was invented by Franz O. (Frank) Armbruster, a California computer programmer, and marketed by Parker Brothers during 196667. It sold about 12 million copies.
I have an original from Parker Brothers, and copies from Winning Moves (found in a shop in Mystic) and Kadon.
There are many puzzles in what I call the "Instant Insanity Family." Typically, the puzzle comprises four colored cubes. Four colors are used, and each of the cubes' faces are colored with one of the four colors. The objective is to find a linear arrangement of the cubes (a rectangular prism) such that all four long sides show each color only once. The faces on the ends and in between cubes don't matter. There are 41,472 distinct ways to line up the four cubes, so exploring them all by hand will take a while!
The number of ways to color a cube, allowing repeated colors, with at most k colors is given by
Polya's Enumeration Formula,
which follows from
Burnside's Lemma.
The formula for a cube is:
This gives the following values for k=2,3,4,... (Sloane's integer sequence A047780):
10, 57, 240, 800, 2226, 5390, 11712, 23355, 43450...
So for fourcolor type puzzles such as Instant Insanity, there are 240 possible cubes to choose from when creating the puzzle. The trick is to find a set that guarantees a solution, and preferably only one solution!
The cubes are typically diagrammed by "unfolding" them and representing them as a cross:
Note that when coloring a cube, once you've colored two pairs of opposing faces, then given colors for the last pair of opposing faces, you define a pair of mirror image cubes by assigning the colors to those two remaining faces in one way or the other. For purposes of this type of puzzle, mirror image cubes are identical and distinctions between them are immaterial to the solution.
Ivars Peterson's MathTrek article of August 9, 1999, "Averting Instant Insanity," is devoted to graphical solution techniques pertaining to this type of puzzle.
I learned from David Singmaster's notes that, according to Thomas O'Beirne, writing in the Mathematical Gazette, Vol. 41, No. 338, Dec. 1957, the graphical technique seems to have first been published in 1947 by Cedric A. B. Smith, writing as "F. de Carteblanche" in Eureka No. 9 (April 1947)  "The Coloured Cubes Problem" pp.911. O'Beirne discusses the puzzle in his 1965 book Puzzles & Paradoxes in chapter 7, though he doesn't reference Carteblanche there. O'Beirne's article on the "Great Tantalizer" from his Puzzles & Paradoxes column in the New Scientist of Aug. 10 1961 is online at Google books.
For the graphical solution technique, the set of cubes is represented as a single undirected pseudograph. The term "graph" usually formally excludes more than one edge connecting any two nodes, and self loops. The term "pseudograph" allows both, and we need both for this type of puzzle. Each of the four colors is a node. Each cube results in three labeled edges on the graph (for twelve edges altogether)  an edge connecting two nodes (or a node with itself) when those two colors appear on opposite faces of the cube, labeled with an identifier for that cube. Given this graph, the solution to the puzzle can be determined, and all puzzles of this type with isomorphic graphs are in essence identical. Note that the Graph Isomorphism Problem is a wellknown area of research.
On the right is the graph for Instant Insanity (I numbered the cubes arbitrarily).
Here is my copy of the solution letter sent out by Parker Brothers on request:
The Schossow / Katzenjammer Puzzle  
The first puzzle in this family was designed and patented in 1900 by Frederick A. Schossow of Detroit. It was marketed as the Katzenjammer Puzzle. An original cardboard container I have is marked "The Katzenjammer Puzzle  B. W. Gottechalk Patentee Chicago, Ill. U.S. Patent No. 646463  Price 10 Cts." The four blocks were marked with the four suits of a deck of playing cards  hearts, clubs, diamonds, and spades. The Katzenjammer puzzle is described on page 38 of Slocum and Botermans' 1986 book "Puzzles Old & New." According to Slocum, this puzzle appeared in the Johnson Smith Catalog of 1919. Slocum's book shows the layout of each of the four cubes, as does the patent, pictured here. In the physical puzzle, each block is a different color  orange, pink, green, and yellow. (I have a complete example and another example with one block missing. I am missing the fourth block from the top in the illustration in the book, which I believe is the yellow one.) "Directions  Mr. Katzenjammer brought this little box of blocks to his wife, and said to her: 'Katerina, you will notice that on the top row of these blocks there is a diamond, a heart, a spade, and a club. Now take the blocks out of the box and place them together so that all four sides will have one spot of each kind in a row. It comes easy, Katerina,' he said. 'If you look at the picture on the box, because that has one spot of each kind on two sides already yet.'" 

Here is a graph of the Katzenjammer puzzle, sidebyside with the graph for Instant Insanity:
It turns out that the Instant Insanity puzzle is isomorphic! I've colored the Schossow nodes to show the correspondence. I numbered the Schossow cubes according to their topdown order in the patent image. I numbered my Instant Insanity cubes arbitrarily  turns out II#1 maps to SK#3 and viceversa. II#2 = SK#2 and II#4 = SK#4. I've analyzed over 20 puzzles in this family, and most of them copy Schossow's design. O'Beirne had already remarked that many versions of this puzzle known to him were isomorphic  including the Katzenjammer, Great Tantalizer, and Symington's. The symbols might be replaced or remapped, but the essential pattern of the set of cubes is isomorphic. For example, see patent 02024541  Silkman 1935. Silkman's cubes are virtually identical  just the symbols have been remapped, and two cubes are mirror images of Schossow's, but this makes no difference to the solution.


So, how does one establish that two such puzzles are in fact isomorphic? Well, I read up on the Graph Isomorphism Problem mentioned previously, and found references to nauty by Brendan McKay, which is evidently the best publicly available software. However, it seems like overkill for my purposes. One also needs a way to represent graphs as data  there seem to be two good standards, DOT and GXL. I've chosen DOT since the graphviz package is handy. I categorize these puzzles by a numeric shorthand: the number of faces per element, the number of elements, and the number of colors/symbols in total. IItype (Instant Insanity  type) puzzles, with 6 faces per cubic element, four cubes, and four colors, are (6,4,4) in my scheme. (6,4,4) puzzles are represented by pseudographs having exactly four nodes and exactly twelve labeled, undirected edges. For now I'll omit puzzles with fewer or more cubes, noncubes, and fewer or more symbols/colors. Many approaches to graph isomorphism entail establishing some way to convert a graph to a canonical form, and showing that two graphs with the same canonical form are in fact isomorphic. Another useful concept is the invariant  some property of a graph, that all graphs isomorphic to it must share  e.g. the number of nodes. Obviously, two invariants that apply here are four nodes and twelve edges. One can also try to define a complete or sufficient invariant which completely decides isomorphism  the number of nodes and edges doesn't meet this need. Yet another useful concept is the signature or certificate of a graph  a way of assigning a coded ID to the graph as a whole, that plays the role of a sufficient invariant. I've come up with what I believe is a good way of assigning certificates to IItype puzzles. First, encode the nodes using four hex digits (0F) based on their connectedness: The rightmost or least significant place counts the number of selfloops on the node. The other three places give the counts of connections to the other three nodes in no particular order, but sorted in increasing value from left to right. For twelveedge graphs, we really only need up to digit 'C' and in practice most counts are only as high as 3. For the II/SK puzzle, the four node codes are: 0221 (the green or heart node), 0230 (the blue or diamond node), 1221 (the red or club node), and 1230 (the white or spade node). This is convenient since each node gets a unique code. Next, encode the cubes themselves, each as a series of six nodecodes derived previously  remember, an edge on the graph was defined by a pair of opposing faces on the cube. So an edge can be encoded with 8 digits by concatenating the codes for the two nodes it connects, sorted in lexicographic order (the edges are undirected, after all). And, a cube can be represented with 24 digits by concatenating the codes for the three edges it contributes to the graph, again sorted. These two sorting steps mean that we lose info to distinguish mirror image cubes, but as previously established, that doesn't matter to the solution! Finally, the whole puzzle's 96digit certificate is the four codes for the cubes, again sorted. And here again, the sorting doesn't matter, since the order of the cubes doesn't matter to the solution. For the both the Instant Insanity puzzle and the Schossow/Katzenjammer design, this certificate is (shown with some punctuation to aid understanding):
02210221023012210230123002211221
My claim is that any (6,4,4) puzzle with this certificate is isomorphic to the original Schossow design. 





An advertising version of the Tantalizer puzzle, from Bass. 
I am not sure what this puzzle is actually called, but on the bottom of the tray it says "Masudaya Made in Hong Kong" so I call them the Masudaya Cubes. This may be the same as Ideal's Face Four puzzle, which I also found.


LogiQubes 
Those Blocks 
Krazi Kubes 

Taktikolor 
Devil's Dice  Pressman 
Devil's Dice  made in Hong Kong No.104A 

Daffy Dots  Reiss 1971 



"Can you solve those Damblocks?" were offered by the Schaper Manufacturing Company, Minneapolis, Minn. in 1968. I have examples in red, white, and black. 
I got Mutando by Logika at Games People Play, and Mutando II from Time Machine Hobby. 



Coloured Cubes Peter Pan Series Regd. 

Color Cubes 
Crazy Blocks Color Puzzle Created for Jak Pak Inc. of Milwaukee Made in British Crown Colony of Hong Kong 
Levenger Cubes 



Idiot's Delight  Field Mfg. Co. Inc. NY Cube set signature 01143639  Isomorphic to SK 
Suits Me  Steve Kelsey Arrange the four cubes in a row such that all four long sides show each suit once. (Eq. to SK) 

There can be more than four cubes and four colors... 

The Allies Flag Puzzle is another very old example of this family. This puzzle has five cubes, and each cube has some arrangement of five flags on its faces. According to Slocum, this puzzle was sold in Britain at Gamage's in 1915. 
Dorobo  Hanayama 
Hlavolam Iribako 

This is Meffert's "Drives You Crazy." It includes six cubes instead of the usual four. 
six cubes 

The pieces aren't always cubic... 

This is the Masudaya Hexagon Mind Exerciser. It has six hexagonal pieces. The objective is to line up the six hexagons so that each of the six rows of six faces shows all six colors. Unlike a set of cubes, where on each cube two faces are not used in a solution, here all six faces of every hexagon will be used. This means that there must be in total six faces of each of the six colors. In my copy of the puzzle, all six hexagons have distinct color arrangements  i.e. there are no duplicate pieces. I have found at least one solution  one can employ the graphical technique, but not in exactly the same way as for cubic puzzles  here, three mutually consistent subgraphs are needed, and they are not independent. 
A vintage Cylinder Ten by Masudaya. Ten rotating disks each with ten color segments. The English instructions say, "Arrange 10 different colors in a line to get all rows correct. The probability of getting the correct order is one in a billion. This puzzle will give the whole family hours of amusement. Note: it is packed in the factory with colors in the correct order (i.e. the solution)" There is no date I can find on any of the material. However, I translated "Cylinder 10" into Japanese and did a search on Google Japan just to see what would turn up, and I found a "FrogPort" blog article from April 2008 talking about the release of this puzzle and how it is in a series with Masudaya's other puzzles Face 4, Hexagon Mind Exerciser, and Circus 7. Here is a link to the blog via google translation to English. The instructions say "10 different colors in a line" but do NOT stipulate that the SAME ten colors must be in every line! This is unlike the traditional Instant Insanity type where one of each color must be present. This allows the rotating disks to have repeated or missing colors. A "line" is a row of stickers across all ten disks. There are ten disks each with ten positions/stickers, so they are accurate in saying one in a billion, since there are 10^9 possible settings (the setting of the first disk is immaterial). 
Go Crazy Embree Manufacturing Co. NJ 1969 Arrange the five disks so that alternate rows have five different colors, then three different colors. The five disks are separate and may be removed from the case and reordered. 

The Buvos Golyok is a clever variant using balls enclosed in a tube. 
Bognar Planets (Bolygok)  brown, white 
Hungarian Tactics 

Stan Isaacs sent me examples of his Doctor Octo and Dr. High Octane puzzles.
These versions use octahedrons rather than cubes,
and a clever mirrored base to allow one to see all faces.
Thanks, Stan!


The cubes are usually labeled with colors, but sometimes numbers are used... 

Twenty Teazer Arrange the cubes so that each side totals 20. 
Crazy Cubes 
Tantalizing Ten  Shackman 



Kathy's Kubes by R. Gee Arrange so dots total 10 on each long side. 
Steiffel Tower 
Totemania 
Match 'Em High  Roads 
Match 'Em High  Pipes 
[59]
I used the graphical technique to solve Nice Cubes:
Below is my solution to the Masudaya Cubes, using the graphical technique. The connectivity of this graph is similar to that of the Nice Cubes, though its edges seem differently labeled. Are the puzzles in fact isomorphic?
Recall that there are 240 ways to color a cube using 4 colors. Given a "stable" of 240 cubes from which to choose four, how many possible 4cube sets are there? To allow repeats but eliminate sets that are identical (since the ordering of the 4 cubes does not matter), we use the formula for a multicombination:
(n+k1)_C_k
In our case, n=240 and k=4, (240+41)_C_4 = 141,722,460. So, we've got over 140 million sets to explore! Also, for a set of 4 cubes, there are 41,472 possible ways to arrange them  that's going to be a lot of work.
But we can reduce this by eliminating from consideration all cubes that do not have at least one face of each color. It's a little arbitrary, and it means my conclusions are not universal over the entire universe of possible puzzles, but I think it's reasonable  most commercial puzzles comply. Of the 240 possible fourcolor cubes, there are 68 that use all four colors at least once each.
Each cube can be represented by a fournode, 3edge pseudograph, where the nodes are the four colors symbolized by the letters ABCD and each edge corresponds to a pair of opposing faces on the cube. The graphs are the same for mirrorimage cubes, since the edges are undirected. The 68 cubes give rise to only 52 unique graphs. Those 52 graphs can be grouped into 6 groups  each group is closed with respect to a permutation of the node/color assignments, of which there are 24 (4!).
Below is a chart I made identifying the 52 graphs/cubes by unique ID number (0051) and a small diagram showing the 3 edges. The colors identify the six groups. It should be easy to construct a cube given its little diagram and the key on the lower right. You just have to decide on your assignment of actual colors to ABCD, and then be sure to remain consistent.
Rick Eason worked on this problem, too, after we talked at NYPP2010.
Rick assigned numbers to these groups as follows, and noted that cubes in a group have the given number of possible effective orientations within a puzzle,
ranging from 10 to 24.
A higher number of possible orientations might contribute to a harder puzzle.


Here is a chart of number of solutions, number of sets that have the given number of solutions, and the first set found that has that number of solutions. I have omitted solution counts where no set had that number of solutions.
A set is represented by its "signature"  an eightdigit number (zeroes on the left, if dropped, should be inferred) that is simply the four cube IDs (0051) from the chart, concatenated, always from lowest numerical ID on the left to highest on the right.
0) 132647 00010203 1) 5160 00010218 2) 21186 00010234 3) 3428 00010329 4) 38466 00010318 5) 2088 00011839 6) 8070 00011631 7) 612 00031631 8) 28626 00010518 9) 702 00032939 10) 3276 00012039 11) 282 00031839 12) 7310 00011639 13) 312 00032637 14) 1380 00032651 15) 144 00033539 
16) 9060 00012750 17) 120 00033139 18) 360 00032039 20) 1980 00032549 22) 111 00052039 23) 12 03082645 24) 2340 00032338 26) 204 00162238 27) 1 00193141 28) 486 00033847 29) 18 00194045 30) 30 00163147 32) 1188 00051639 34) 18 01163246 36) 114 01033839 
40) 420 00163841 44) 156 01030539 48) 94 00274250 52) 12 01164045 53) 3 06184045 54) 6 01283844 56) 96 01063847 60) 6 03113949 64) 120 01030523 72) 51 01032338 80) 3 24274350 96) 12 01233438 128) 6 03052339 140) 3 01163847 160) 6 01052338 
I found 5160 sets that have a single solution. There were many sets  almost half  that had no solution at all. Some sets have more than one solution, and the maximum number of solutions any set can have seems to be 160. Most solvable sets have four solutions. There is only one set that has exactly 27 solutions, and 27 solutions is the only count where only one set has that count. Interestingly, the cubes used for this set are the four from the yellow group in the chart. It is not hard to solve this set by hand.
Based on a cursory check, it appears that none of the cubes in groups 5 (tan) or 6 (blue) are used at all in singlesolution sets!
Rick Eason says that by using Burnside's Lemma to eliminate color permutations, the 270,725 figure can be collapsed to 11,746 sets. If we further eliminate the 12 cubes not used in singlesolution sets (the tan and blue groups), we end up with only 3949 sets. I did not perform this collapsing for my runs, so my totals do not take into account color permutations.
In a brief 1977 paper entitled On "The Tantalizer" and "Instant Insanity" (PDF online here), Frank Harary (19212005), recognized as one of the fathers of modern graph theory, notes that "Using standard methods of graphical enumeration [Harary and Palmer 1973], it is not difficult to develop a formula for the number of different 'Tantalizer' games with four cubes. This can be done by associating a graph with each such game, and then counting graphs." When I first began to research this topic, I checked Harary's book out of the library, but I failed to find a handy formula for enumerating these graphs. If you know of one, please let me know!
01 04 20 40 01 14 36 39 02 03 22 45 02 12 33 44 03 07 17 40 03 14 26 47 03 30 35 38 04 08 16 45 
04 12 28 32 04 29 37 46 06 20 33 47 06 22 32 39 07 10 28 30 07 14 44 48 07 18 39 46 08 10 26 37 
08 12 36 51 08 18 33 38 12 20 25 35 13 17 33 37 13 22 30 51 14 22 25 29 15 16 30 39 15 20 37 48 
The set identified by O'Beirne in his Great Tantalizer article in Figure 1 is the first listed, 01042040.
SK consists of 1 cube from group 2 (green), 1 cube from group 3 (teal), and 2 from group 4 (lavender). Rick suggests that the most difficult puzzles will consist of only cubes from groups 1 (yellow) and 4 (lavender), since those groups offer the most possible orientations (24 each). Rick found the following 13 singlesolution sets using only cubes from groups 1 and 4:
00 03 04 19 00 03 04 20 00 03 04 30 00 03 04 31 
00 03 04 39 00 03 14 19 00 03 14 20 00 03 14 22 00 03 14 37 
00 03 14 39 00 03 14 41 03 04 08 12 03 04 12 20 
Could these be the most difficult puzzles of the Schossow/Katzenjammer/Instant Insanity family?
The certificate with the smallest number of sets having that certificate is shared by only six sets:
02202240022022402240224002202240
02202240224022400220224002202240
22402240022022400220224022402240
is assigned to sets:
00030419, 00071231, 00081441, 19203031, 19223741, and 31333941.
In each set, a given pair of colors appears only once each on adjacent sides on all four cubes, with the other four sides of each cube having the other two colors. The graph of such a cube will have only one edge leading from each of the two colors, which will not share an edge. Four colors, taken two at a time, 4_C_2, gives the 6 possibilities. In signature order, they are: CD, BD, BC, AD, AC, and AB. These sets are easy to solve  identify the special colors. Orient all cubes so that the sides with the special colors are on top and front. Now it is a simple matter to turn three of them so that the solution is found.
At the other end of the scale, there is one certificate that encompasses 144 sets:
11201121112112211221122111201221
11211121122112211120122111211221
12211221112012211121122112211221
The first example having that certificate is 00162936.
According to my analysis, there should be 200 distinct singlesolution puzzles, where every cube uses all four colors, and each set uses four distinct cubes. You can download a text file "singlesolnsigsandcerts.txt" in which my program output cube set signatures and certificates for every singlesolution set. Those sets isomorphic to SK are noted. The tail of the file contains a summary of the 200 unique certificates and the count of sets having a given certificate.
The table below lists, in (mostly) alphabetical order (I tried to keep sequels together), those I know of and shows images where I either have a copy or have been able to find pictures. I don't have them all and I will note the ones I don't have. Those I have are highlighted like this. Those I do not have are highlighted like this.
I would like to acknowledge the following:
Bananas
Bananas 1982 Onsworld Ltd. "Arrange cubes to show four complete bananas each with a label." There are four cubes, and four types of side: a banana tip, stem, middle segment with no label, and middle segment with label. Unlike a standard IItype puzzle, the images have distinct orientations which must be respected to form the complete bananas. The tips, stems, and middle segments must all be aligned properly. A little analysis reveals that the usual fourinarow arrangement of the cubes cannot satisfy the goal  but then, the objective does not stipulate that arrangement, does it? 
Bananas II
Bananas II (I don't have this one.) 
Blue Movie
Blue Movie  1986 Wellingtons I don't have this. 
Body Job
Body Job  Onsworld I don't have this. 
Boob Cube
Boob Cube  Wellingtons I don't have this. 
Booby Trap
Booby Trap  1986 Wellingtons I don't have this. 
Bunkered
Bunkered 1987 Wellingtons "Teeoff by placing the cubes together then rearrange them to show, simultaneously, TWO identical golf courses." 
The Cat Puzzle
The Cat Puzzle  Wellingtons I don't have this. Image from Jim Storer's collection. 
Computer Challenge
Computer Challenge  1984 Wellingtons I don't have this. 
Computer Magic Square Challenge
Computer Magic Square Challenge 1995 Images & Editions 
Computer Word Challenge
Computer Word Challenge  1985 Wellingtons I don't have this. 

Crossword Cubes
Crossword Cubes  1989 Wellingtons I don't have this. Here is a possible alternative package: 
Cubix 3D
I don't have this, but see Rebus in the Pattern Blocks section below. 

Cuss
Cuss 1980 Onsworld Ltd. "Simply arrange the blocks in a row so that each side carries a dictionary four letter word, all reading from left to right. No foreign words or proper names allowed. A clue in case you get stuck and a solution are included." "This is one of a unique range of cube puzzles devised for Onsworld by Stephen Leslie. The series includes Cuss, Diabolical, Footsie, Frantic, Son of Cuss, and Walk Up." 
Son of Cuss
Son of Cuss 1982 Wellingtons Devised by Stephen Leslie "Arrange the cubes to show at least 24 different fourletter (dictionary) words." 
Diabolical
Diabolical (Onsworld) "Arrange the dice in a row so that the four long sides all carry the same total number of spots." Multiple solutions exist  the set of addends doesn't have to be same for each side. 
Double Cross
Double Cross Wellingtons 1991 
Fascinating Felines
Fascinating Felines  1993 Wellingtons 
Footsie
Footsie 1982 Wellingtons "Arrange the four cubes in a square so that wherever the surfaces of two cubes join (top, bottom, and sides) pairs of feet are formed." Devised by Stephen Leslie. 
Frantic
Frantic 1980 Onsworld Ltd. "Place the four cubes in a row and simply rearrange them so that one of each colour shows on each long side." Devised by Stephen Leslie. Isomorphic to SK! 
Frantic (alt.)
An alternative version of Frantic, with solid colors. Colin says it is the same graph.

Frantic II
Frantic II "Place the cubes together in a square so that wherever they meet, top, bottom, and sides, the coloured squares match." Frantic II was invented by Dr. Kenneth Miller. 
Golf
Golf  Wellingtons "Places the cubes together to show the word GOLF four times. The letters must all point the same way. Try it  then baffle them at the 19th." 
Golf Crazy
Golf Crazy  Wellingtons 
Grandstand
I don't have this. 
The Great British Puzzle
The Great British Puzzle  1997 Images & Editions 
The Kitten Puzzle
The Kitten Puzzle  1999 Images & Editions by Dr. Kenneth Miller 
Knickers
Knickers  Wellingtons I don't have this. "Arrange the knickers in a line so that there is one of each colour on each long side  they can be in any order and face any direction." 
Marilyn  The Eternal Puzzle
Marilyn  The Eternal Puzzle  1989 Wellingtons 
Match of the Play
Match of the Play 1989 Wellingtons "Solve the puzzle by placing all six cubes together so that both sides show a player being tackled." 
Monkey Business Spring Fever
Monkey Business Spring Fever  Wellingtons I don't have this. 
Nuts
Nuts 1982 Wellingtons "Place the four cubes in a row and simply rearrange them so that one of each kind of nut shows on each long side." Isomorphic to SK! 
180 Top Dart
180 Top Dart 1990 Wellingtons "Place the cubes in a straight line so that all four long sides add up to the magic number... one hunder and eighty!" There are six cubes, and the following 12 symbols appear: inner bullseye (50 pts), triple 2 (6 pts), double 3 (6 pts), triple 4 (12 pts), double 6 (12 pts), 9, double 9 (18 pts), triple 9 (27 pts), 12, double 17 (34 pts), 18, triple 20 (60 pts). 
The Pig Puzzle
The Pig Puzzle Images & Editions 
Poker Puzzle
Poker Puzzle 1987 Wellingtons "Place the dice in a line so that one of each design appears on each of the four long sides  the order and directions of the designs are not important." There are 5 cubes. The designs are: 10, Jack, Queen, King, Ace. 
Rugby
Rugby  1995 Images & Editions  Dr. Kenneth Miller Two puzzles based on the two versions of Rugby  for the Rugby League fan, place the cubes in a straight line so that each long side shows exactly 13 pieces of muddy lace. For the Rugby Union fan, place the cubes in a straight line so that each long side shows exactly 15 pieces of muddy lace. I don't have this. 

Seams Impossible
Seams Impossible  1986 Wellingtons I don't have this. "Place the cubes in a square so that wherever two cubes join (top, bottom, and sides) complete legs are formed." 
Snookered
Snookered  Wellingtons "Place the cubes together in two rows of four, to make a snooker "table." Then rearrange them to show three sets of snooker balls: one on the top, one on the bottom, and one on the four sides of the "table." A set of snooker balls comprises: 15 reds and one each of white, black, pink, blue, brown, green, and yellow." 
Snookered Again
Snookered Again  Wellingtons "Arrange the cubes in a block (two rows of three) so that one, and only one, of each of the eight colours shows on the top, sides, and base of the block." 
Soccer
Soccer  "You may need extra time!" Appears in a box and a blister package. Images & Editions 1996  designed by Dr. Kenneth Miller Thanks to Rob Hegge for photos. 
Soccer
Soccer Puzzle  "Make it your Goal"  Wellingtons 1987 
Spellbound
Spellbound 
Spellbound (alt.)
Spellbound  alternative version  Onsworld Ltd. 1980 
Suit Yourself
Suit Yourself 1990 Wellingtons "Place all six cubes together in a block of two rows of three to show (on top, bottom, and sides) a full pack of 52 cards with no duplicates." 
Tantalizer
Crossword I don't have this. This and the other Tantalizer puzzles seem to be more dexterity than Insanitytype. 
Tantalizer
Frustration I don't have this. (Photo from Slocum collection.) 
Tantalizer
Jet Set I don't have this. (Photo from Slocum collection.) 

Top Dart
Top Dart 
Total Distraction
Total Distraction 1988 Wellingtons "Put the cubes together to form one large cube with all rows, columns, and diagonals having the same total: 99." 
Walk Up
Walk Up 1980 Onsworld Ltd. "Place the four cubes on top of each other in a column. Arrange cubes so that ladybird (sic) tracks reach from top to bottom on all four sides. Ladybirds need not point all the same way." Devised by Stephen Leslie. 
Watch It
Watch It  1998 Images & Editions I don't have this. 
World Puzzle
World Puzzle  Wellingtons I don't have this. 
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Various pamphlets or sheets accompanying the different puzzles mention other puzzles in the lineup. Several mention 5 puzzles but list 6; one describes Mindbenders as "a fiendish series of six diabolical puzzles" but then lists eight. I have found ten altogether.
The most frequently mentioned, most dating from 1969, are:

Less often mentioned, dating from 1970 and 1971, are:



The Perfect Square 1969 #505 Assemble a square using 12 pieces  like colors must not touch. 
The Tricky Triangle 1969 #505 Using 10 barbellshaped pieces composed of two linked circles each, and one single circle, build an edge6 equilateral triangle (of 21 circles) such that "no two circles of the same color are in the same line of the triangle." Each circle is 1 of 6 colors. The Tricky Triangle puzzle by Waddingtons is a 2dimensional analogue of Oops Again. 
The Perfect Circle 1969 #505 Assemble a circle from 16 pieces in 4 basic shapes and 3 different colors, such that likecolored pieces don't touch. 

The Wobbly Web Copyright 1969 No. 505 Create a rectangle from the 15 square tiles such that web strands join (edgematching). JH Vol.2 p210 
The Perplexing Pyramid 14 square tiles each of which has a colored circle in each corner. Create a "pyramid" of cards  a 3x3 base, then a 2x2 layer, then one card on top  layers must align over spots, and spot colors must match vertically. 
The Reluctant Rectangle 1970 #345 Form a rectangle from the 12 3x2 Lshaped pieces such that no two pieces of the same color touch in any way. There are 3 pieces each of four colors. All the pieces are "normallyhanded" L's except for two of one color are reversed. 

Little Circles 1970 #346 Pack 18 pieces formed from circles into the box. (The instructions are printed on the box, and there is no mention of a colordismatching constraint.) No Pamphlet. 
Coloured Square 1971 #340E Form a square from 12 Lshaped colored tiles such that like colors don't touch. 
Rectangle Tangle 1971 #340F Form a rectangle with a bicolor perimeter from the 10 tricolor and 2 bicolor LTrominoes. 

Beat the Elf  by House of Games Corp. Ltd. Don Mills, Ontario 1970 Build a 3x3x3 cube with the 13 blocks so that no face shows three squares in a row of either color, horizontally, vertically, or diagonally. There are 11 1x1x2 blocks of 1 light and 1 dark. There is one 1x1x2 block of two darks. There is one 1x1x3 block of two lights (adjacent) and 1 dark. 
Kolor Kraze  by House of Games Corp. Ltd. Don Mills, Ontario 1970 Discussed in Slocum and Botermans' Puzzles Old and New on page 43. The Kolor Kraze puzzle consists of 12 dicubes and a tricube, each made of differently colored cubes. There are 3 each of 9 different colors. As in the Gram's Cube, the goal is to create a 3x3x3 cube from the pieces, such that each of the 9 colors appears only once in each of the six faces of the cube. Sivy Fahri wrote an article about the Kolor Kraze and the Nine Color Puzzle called "Nonahuebes" he developed based on it. A PDF of Fahri's article is available at the Gathering 4 Gardner Wiki. 
Cube Fusion Alright, it's a game not a puzzle, but I remembered these pieces from my childhood and now I know what they belonged to! 
Gram's Cube was made by Gram Toys of Birkerod, Denmark. The puzzle consists of 27 Legolike cubies that mate sidetoside as well as upanddown. There are 3 cubies each of nine different colors. The objective is to construct a 3x3x3 cube such that each side shows all 9 colors. At first I thought a trick was necessary, but I found a solution using all 27 cubies. I picked this up in a trade with Norman Sandfield, at the January 2005 New York Puzzle Party. 
Level Q, by Eng's IQ Co. Ltd. 1987 Hong Kong. I purchased this quite some time ago. Level Q consists of a hexagonal board and twelve barbell shaped pieces. There are three challenges  first, build seven stacks of six disks each. Next, again build seven stacks of equal height, but such that one bar lies on each side of the hexagon and on each of the six spokes. Finally, satisfy the constraints already mentioned, and also ensure that each stack contains only one of each color disk. 

The Trapagon and Magzphere Six pieces interlock  arrange them so that there are five different colors on each "face." 
The object of Oops Again is to build a pyramid with the 2sphere pieces so that no two spheres of the same color touch at all. The Golf Smarts Pyramid (a gift from Brett) is similar. 

Spot Cube  Hikimi Designed by Ichiro Sengoku, this puzzle was entered in the 2004 IPP Design Competition. I bought it at Torito.

Vier Farben Block  Logika Build a cube with the 12 ushaped pieces such that like colored pieces do not touch. Each piece is one of four colors. 

Instant Indecision marked "Patent Pending"  the Green Gate Co. Sherman Oaks CA, 1972 Four cubic frames and a stepped pedestal. Each cubic frame contains twelve bars, 3 each of four overall different colors, arranged in various patterns. The four cubes are of graduated sizes and nest on the pedestal. The objective is to arrange the cubes in nested form on the pedestal so that each of the twelve sets of four aligned bars, one from each cube, contains one of each of the four colors. My version has a nice keylike tab that locks into the pedestal and holds the cubes in place for storage/transport. 
Cube Edu  eLogIQ Build a 2x2x2 cube and match colors on all faces. 

Octamania Arrange the 8 cubes into a 2x2x2 cube such that each face shows four copies of a digit. 
The vintage 8 Blocks to Madness puzzle  invented by Eric Cross of Ireland, and issued by Austin Enterprises of Ohio. Create a 2x2x2 cube having a single color on each side. Then create a 2x2x2 with each of four colors on every side. 

The Maze Cube  stack the four bricks together to make a 2x2x2 having four colors on each face. 
Poker Cubes I don't have any documentation with this puzzle, so I don't know the provenance or goal. However, I suspect the goal is to create a 2x2x2 having one of each of the four suit symbols on every side, while also ensuring each 2x2 face is a single color with each face a different color. 

The Ten Spot Domino Puzzle Issued by Valentine & Sons, Ltd. Westfield Works Dundee The instructions inside the box top read, "Valentine's Series of Popular Puzzles The New 10 Spot Domino Puzzle Instructions  Arrange the four pieces so that they form a solid square block, every side of which shows 10 spots. Solution sent on receipt of 1d. stamp."
Discussed by Slocum & Botermans in their 1994 book The Book of Ingenious & Diabolical Puzzles,
on page 34. The layout of the pieces and one solution are provided on page 143.

I finally found a Cover Up  issued by Ideal in 1982, it originally appeared as
Hepta in 1974 and was designed by the famous Alex Randolph.
See the
entry for Hepta at Boardgamegeek.
I had wanted to try this puzzle since reading about it at
Celia Seide's website.
Celia also pointed out
Spielarchiv.de which has a reference to a version called Magic 7 under Spiele>nach Autoren>R>Randolph,Alex > Magic 7.
There are seven plastic 1x3 straight pieces and seven angle pieces. The plastic 7x7 board is colored using 7 colors each of which appears 7 times. For each of the 7 colors, use all the pieces to cover all the spots not of the target color. It's pretty large  I put a quarter coin on the cover.


Cubic Mania Puzzle Blocks was issued by Dale Seymour Publications. It comprises eight cubes, each colored with four colors. Each cube uses each color at least once. Using the chart of cube graphs I developed, the included cubes can be mapped to the tan set { 24 x 3, 27, 34, 42, 43 x 2 }. There are several challenges, including building a 2x2x2 where every side shows all four colors, and another where every side is a solid color. 
Brain Wave Arrange the bicolored pieces in the slots so that no color is repeated along any line of the triangle on both sides of the head. 

Lucky 13, Edition No. 7, by Fireside Games Inc. of Northbrook Illinois, 1973.
24 different puzzles  in each, arrange 13 pieces to
form a 7x7 square such that like colored pieces do not touch, even at the corners.
Any piece may be flipped.

If each of the n faces of a regular solid is colored with one of n colors, the number of different ways the solid can be colored with all n colors excluding rotations but including reflections is given by n!/(2*E) where E is the number of edges of the solid. For cubes with 6 faces and 12 edges, the number of possible colorings is 6!/(2*12) = 720/24 = 30. These 30 cubes form the set of MacMahon Colored Cubes.
You can choose any of the 30 cubes to use as a "prototype" and it will be possible to find eight other cubes in the set which can be used to build a 2x2x2 model of the prototype having the same arrangement of solid colors on the six external 2x2 faces as on the prototype's six faces, and also satisfying the additional constraint that internal touching faces are colored alike. MacMahon credited his friend Colonel Julian R. Jocelyn with the discovery that this can always be done regardless of which of the 30 cubes is chosen as the prototype.
For each prototype, there is only one set of eight cubes which will work, and there will always be two ways to build the prototype with these eight cubes. A procedure to transform one solution into the other was devised by L. Vosburgh Lyons and is shown in [2] on page 190. The eight cubes to be selected will not possess any of the same pairs of opposing face colors as the prototype. This means that 13 of the 29 cubes can be eliminated as candidates, leaving 16 from which to choose.
Lyons also discovered that after a 1st prototype is selected along with the eight cubes to model it, it is always possible to select another prototype from the remaining 21 cubes, and find another 8 cubes from the remaining 20 to model this 2nd prototype. The 2nd prototype must be a mirror image of the 1st, and the eight cubes to model it are the eight not chosen from the 16 eligible for the modeling of the 1st prototype [2].
MacMahon sold an eightcube puzzle patented in 1892 (UK 8275?) to the London company R. Journet, which marketed it as the Mayblox puzzle [4]. Its eight cubes are one of the sets which can model a prototype and meet the internal colormatching constraint. However, the Mayblox puzzle does not specify the configuration of the prototype  so it must be deduced, which makes the puzzle more difficult.
I made my own version of a Mayblox puzzle using LiveCube. I chose a prototype arrangement of six colors at random, then colored the 8 subcubes as required based on the solution instructions in [1]. I finally found a good use for the LiveCube face plates! Fortunately, they provide enough different colors with the addition of cyan and pink to their previously available black, red, yellow, green, and blue.
You are to build a 2x2x2 cube using 8 of the 9 included numbered dice, so that every face displays a unique number.
There have been several issues of sets of "pattern blocks" under various names.
Pattern Pending designed by Fred Horowitz and issued by Parker Brothers (General Mills) in 1971. A set of 12 black and white cubes. Fred had the basic idea for these in the 50's, and intended these to be more of an openended creative playset than a puzzle. 
KDron  Janusz Kapustra (I don't have this.) 
Trac 4 game issued in 1976 by Lakeside. Redandwhite blocks and cards specifying various patterns to construct. (Sadly, this got lost in the mail and I never received it.) 
Quiet Cubes (I don't have these.) Also designed by Fred Horowitz, a set of 18 cubes, issued in Holland. 
Rebus A set of nine patterned blocks, issued by the German company "Pussy." Create various silhouettes. 
Magritte Cube 
Tedco Mirage Numbers Up 
At Games People Play, I found a Magic Mirror puzzle from Schmidt Spiele. 
Escher Blocks from RecentToys, purchased from Bits & Pieces. 
Puzzling Reflections Ivan Moscovich 1990 Tarquin Publications 
The Mirror Puzzle Book Marion Walter Tarquin 1986 ISBN 0906212391 
You and Einstein Mirrorkal Invented by Ivan Moscovich Produced 2010 Recent Toys USA 
You and Mona Lisa Mirrorkal Invented by Ivan Moscovich Produced 2011 Recent Toys USA 
This is the "Fool's Spool" (made in Hong Kong). "Mix up the four wheels  rearrange them so that all lines total twelve!" One of my kids found the following solution in minutes: 5115, 1254, 5223, 4341, 2334, 3513, 4422, 3333. 
Here are more puzzles with a math theme. One is "DigiDisc"  arrange the discs so that all equations are true. The discs adhere via magnets and I also show this puzzle in the Magnetic category. Another, from Asia, is a similar stack of discs with the same goal, but it is not magnetic. Yet another is an elongated stack, nonmagnetic, called "Magic Numbers." 
Sudoku 3D Ball  22 Advance www.3djp.com There are 5 circular indents on each pentagonal face of the spherical dodecahedron, and 10 indents in a "ring" bordering each face. Each indent is a member of 2 "rings"  those around the two faces adjacent to the vertex where the indent is located. Some indents already contain a digit from 0 through 9. Fill in empty indents with digits from 0 through 9 such that every ring contains all 10 digits. (The sphere is not meant to be disassembled.) 



A Washington Monument "sums" puzzle, from Lambert Bright. Thanks! 
Kenken 4  in maple, from the kind folks Adele and Peter Plantec at Puzzle Me Please. Arrange 1x1x2 blocks in the frame to form a 4x4x4 cube such that a valid KenKen 4 appears on each face. The blocks only have figures on the outside. 
Kenken 6  in maple, from PuzzleMePlease.com Arrange 27 cubelets in the frame to form a 3x3x3 (6x6x6) cube such that a valid KenKen 6 appears on each face. The cubelets only have figures on the outside  the central cubelet has none. So, all figured faces will be used in the solution. 

The Enigma puzzle is a representative of this type, but with letters rather than numbers on the wheels. Form words. 
This is the Daily Mail Crossword Disc puzzle by Chad Valley. 
Daily Mirror Double Words 

There are several "Slivers" puzzles  this is the Anakin Skywalker version. 
Zen Blocks 
Cubits 

ThatAWay by Binary Arts. Introduced at IPP 20 by its creator Greg Dye. There are 10 cards/tiles each with two arrows in various orientations, and a booklet of problems and solutions. Play ThatAWay online. 
Flower Finder  William Waite Arrange the six pieces in the tray so that every flower has six petals. Also solve so that every flower has three petals. 
Rubik's Dice flop interior plates around until all pips show red. 

Binary Arts, now Thinkfun, has supplied many puzzles, including their various "something by something" puzzle/games: Brick by Brick, Square by Square, Block by Block, and Shape by Shape. 

Dice Stacker by Elverson Eight wooden dice, each with a unique arrangement of spots  form a cube having four of a kind (one through six) on each side. Also, form a cube such that diagonals on each side add to seven. 

Pakostar Purchased during IPP28 in Prague 

Ubongo Purchased in Berlin on the way to IPP28 in Prague. Really a game for 24 players, but can be played solitaire. Given a set of pieces and a deck of cards showing shapes made from those pieces, take a card and try to arrange the pieces to match the silhouette. 
IdenticaL episode II Concept by Tadao Kitazawa, 2008. Purchased from Torito. Four pieces, each of which has a pattern of light and dark squares on each side. Arrange the four pieces so that the light squares form a connected shape, and the dark squares form the same shape simultaneously. The pieces can be flipped. See analysis at Ishino's site. 

Hinomaru by Pavel Curtis Build the Japanese flag in the tray, using the 12 twosided domino pieces. 
Anansi's Maze by Pavel Curtis. Purchased at IPP 29 in SF. Also available via Pavel's website. A multistage challenge. 
The Blockword Crosspuzzle from "Products of the Behavioral Sciences" ca. 1970 

Gamesters of Triskelion, a multistage challenge by Pavel Curtis. 
Tiger and Panther  designed by Takahisa Nakanishi  IPP30 There are four Ttetromino and four Ppentomino pieces, each checkered. Pack them in the 6x6 tray to make stripes, and then to make a checkerboard. 
Figure Puzzle  designed by Hide Ue presented at IPP30 by Naoyuki Iwase (Osho) Seven pieces, colored light and dark variously on both sides. Arrange the pieces in the tray to form each digit 09 in turn. 

Tridio Twist! by FatBrain Toy Co. Three mutable pieces and 48 pattern challenges. Designed by Marijn van Herel and Eliane Scharten. 
Designer Colin James very kindly sent me a copy of his Qboid puzzle. It offers over 1000 challenges at four different levels. 12 cubes, with patterned faces. When properly arranged, the patterns form digits and letters. Entered in the 2009 IPP Design Competition. Thanks, Colin! 
Royal Flush Arrange the seven L trominoes and 2 dominoes in a 5x5 grid such that every row, column, and both main diagonals contain a Royal Flush (in spades). Thanks, Dave! 

Dewey's Dilemma From Dave Janelle at Creative CraftHouse. Arrange 12 consecutively numbered "books"  each being one of three heights, and by one of three authors  on the included "bookshelf" such that no adjacent books are the same height, or by the same author, or consecutively numbered. 
PrimEvil, designed and made by Louis Toorenburg, exchanged at IPP32 by Paul Dudding 
Liberty Cubes, designed and exchanged at IPP32 by Kate Jones, made by Kadon Enterprises Inc. 

Double D Insanity, designed, made, and exchanged at IPP32 by Louis Toorenburg 
The Bricklayer's Challenge, purchased at IPP32 from Pavel Curtis 
Nats Win!, designed in 1938, made by Creative Crafthouse, exchanged at IPP32 by Michael Tanoff 

Bendit  from
Smart Games.

JiGaZo  website  issued by Tenyo in Japan and Hasbro in the US. Designed by puzzlefriend and magician Mark Setteducati. Kind of a colorbynumber set. 300 pieces, in various shades of a color. Use supplied software to input an image and receive instructions on how best to arrange the pieces to produce the image. Similar to the art of Ken Knowlton. 
J Puzzle, designed and exchanged at IPP32 by Tsugumitsu Noji, made by ASUNARO Four pieces, three challenges: make a symmetric shape from 3 pieces; make four holes with an arrow pointing at each hole; make outlines of two pentominoes. 

Noah's Ark  designed by Raf Peeters, issued by Smart Games My daughter's favorite. Place the pairs of animal pieces in the ark, ensuring that the animals are upright and mates touch. Each challenge specifies the required position of one or more pieces. 

