Edge-Matching puzzles usually consist of a set of tiles whose edges have various distinct patterns, symbols, or colors. The objective is to arrange the tiles in a grid such that abutting edges "match" according to some rule.

Since the tiles can be printed on cardboard, these puzzles can be relatively inexpensive to produce, and in the past have served extensively as advertising promotions and giveaways. There are many modern edgematching puzzles - you may have heard of "Scramble Squares" for example.

Jacques Haubrich has 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 book "Puzzles Old and New" (1986 Plenary Publications), the first edge-matching 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 edge-matching 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.

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 discusses his Colored Cubes, first introduced in a lecture he gave in 1893.

In Hoffmann's 1893 Puzzles Old and New, the only edge-matching type puzzles mentioned are "The Royal Aquarium Thirteen Puzzle" (equivalent to the French Le Nombre Treize) #72 in chapter IV, and "The Endless Chain" (equivalent to the French La Chaine sans Fin) #18 in chapter III.

Some puzzles have tiled surfaces other than a plane - e.g. the platonic solids, or a cylinder.

Tile-laying puzzles (in German, "Legespiel") of both the edge-matching 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 Color-Matching Dissection of the Rhombic Enneacontahedron." Also see Peter Esser's page. And Toby Gottfried's site.

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. Presumably the difficulty of Eternity II is high enough to challenge current computational power, but I suspect it won't be long before a winner claims the prize.

• EM - Edge Matching
• HT - Heads/Tails - an elaboration of the edge-matching theme - instead of matching equals, one must match corresponding pairs.
• CP - Continuous Path (I have categorized these under Route Building)
• CM - Corner Matching
• CD - Corner Dismatching (e.g. Grandpa's Wonder Soap)
• JS - Jigsaw-type (each tile's edge has only one possible mate)
• HY - Hybrid

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.

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 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 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 quarter-circles on the corners of the tiles meet (either four or two), there are always different colors on each of the meeting quarter-circles. 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 half-circle. 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
The OXO Triangle puzzle. This was published in 1922 by the OXO Company for a contest. There are 25 equilateral-triangular cards/tiles, numbered 1 through 25. The tiles must be arranged into a side-5 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	The Nestle's puzzle, published around 1930-1940, was the first 7-tile hexagonal edgematching puzzle. This one is printed in Spanish. There have been many variants, including the modern "Drive Ya Nuts." JH Vol.1 p30 - 1 soln
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 (Casse-Tete) 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.	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
Tile-O-Rama Called the "Wonder Mosaic Puzzle" when it first appeared circa 1925, this was the first design with rectangular tiles. (I have a loose copy but it was also included in the F.A.O. Schwartz Deluxe Puzzle Chest No. 3006.) I also have the Mosaik and Tesa Mosaic Square puzzles discussed in Slocum and Botermans' "The Book of Ingenious & Diabolical Puzzles" on p.23. According to them, Edwin Thurston patented the first mosaic square puzzle in Dec. 1892.	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.

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.	Pel-Freeze JH Vol.1 p93 - two solns
A-Treat Mystery Puzzle - A-Treat Bottling Co. PA Two versions.	Jacques' Compendium, Volume 1, pp72-4, indicates that the following 9-square puzzles are isomorphic and have only one solution: Le Berger Malin Le Fermier Avise The Calumet Puzzle Pabst 33 to 1 cans Pabst 33 to 1 bottles The Vess Cola Mystery Puzzle (bottles) Vess Cola Mystery Puzzle (caps - violet,brown,green,red) Vess Mystery Puzzle (caps - violet,orange,blue,red) A-Treat Mystery Puzzle	Nestle Nine-Square
Lionstone Whisky, Kentucky 1973	Camel - an advertising promo from a cigarette manufacturer.	Dunlop Hexagons
Lyon's Tea	Match the Colors - Adams ca. 1953	Gemstone - Nordevco
To me, the edge-matching puzzle is exemplified by the more recent but none-the-less 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 well-known. 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.
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 Mah-Jong tiles.	Tri-Puzzle - Lagoon	Contack
Pressman's Think-Ominos	Bits and Pieces distributed a similar 2-d puzzle - match the color dots on the squares' edges	Melissa & Doug make a similar puzzle called the "Space Edge Matching" brain-teaser
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.	Block Shock
Ovals - Nob - O-Pico/Color Match Puzzland Hikimi JH Vol.1 p151 - 6 solns	Chelona Pocket Puzzle - Cats A nine-square 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
Butterflies Mini	Travel Triazzle	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.
Vintage Set of Four Colorful Circular Torture Puzzles by Shackman	The Ultimate Puzzle versions I (4x4) and II	Zoki
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).	One Tough Puzzle is a 3x3 heads/tails edge-matching 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 7-piece hexagonal heads/tails edge-matching puzzle. JH Vol.1 p35 - 1 soln
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	IZZI 2 - Binary Arts Color Matrix made by Binary Arts for The Museum Company is the same. JH Vol.2 p198
DaMert 3D Squares Cars	4D Metapuzzle	4D Metapuzzle No. 4
Instant Insanity - Hexagon Puzzles 1986 JH Vol.1 p151 - 2 solns	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.	A four-piece glass edge-matching puzzle made by Brett.
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.)
12 Triangles - Majak	Peek-a-Boo Snakes	Eye-Cue
Pin Pin Kan	The Great Canadian Puzzle	Double Half - Interkemia 1981
New Departure Puzzle - advertising New Departure coaster brakes for bicycles. An uncut card. Copyright 1953.	Celtic Knotwork	Lagoon Group Safari series - Tiger Puzzle
"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.	Level 4 - BrainArt	Infinity - BrainArt

Mental Blocks - Creative Playthings A 3-dimensional challenge - build a 2x2x2 cube with the pieces, such that the embedded colored rods match where the pieces touch.	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 2-sided pentagonal tiles. The tiles are numbered 1-5 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
This puzzle consists of six plastic pieces each with four color spots on the sides. It is marked "Copyright 1972 Gabriel Ind. Inc." I believe it is a version of Piet Hein's Triple Cross puzzle (that I do not own). I made an xyz-axes center piece from some pipe cleaners. At each intersection, ensure there are three different color spots.
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.
In Reiss' Flat Top, arrange the eight pegs in the four holes so that each stack ends up at 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. Really closer to Flat Top.
Tekozuru Z2 from Hikimi - purchased from Torito	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 mini-puzzle in itself - a 2-piece trick box.
Another oldie but goodie is On-the-level by Mag Nif. Fit 9 multi-level 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.	Binary Arts 4 Cubes - ensure patterns match where they adjoin.
Chain of Colors - Haubrich IPP26	Ey-Ko-Se 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 5-letter word on every pentagon.	Einstein Cube

The following is my graphical (or tabular) solution to the Drive Ya Nuts puzzle. I have not seen any solution technique like mine applied to this type of puzzle - even Jaap's page says one must try all combinations. My technique is a considerable savings and allows a solution - and negative results - to be derived easily by inspection - the hallmark of a graphical technique. I have worked this entirely "by hand."

Using this technique I can prove fairly easily that this puzzle has only one distinct solution.

• A) 1 6 5 4 3 2
• B) 1 4 3 6 5 2
• C) 1 6 4 2 5 3
• D) 1 6 2 4 5 3
• E) 1 6 5 3 2 4
• F) 1 4 6 2 3 5
• G) 1 2 3 4 5 6

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 re-arrange 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:

1. each row (i.e. nut) is used once and only once
2. each column (i.e. number on the central nut) is used once and only once
3. the last number of the triple in the selected cell in a given column matches the first number of the triple in the selected cell in the next column - i.e. the numbers on abutting sides match

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 sub-class 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.

Tantrix is a well-known modern route-building puzzle/game. [Jaap's Tantrix page.]	Rubik's Tangle set of #1 thru #4, and the 9 double-sided plastic tiles version The original sets have 25 one-sided cardboard tiles, and come in four versions distinguished by which particular tile is duplicated within the set. JH Vol.2 pp272-3
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	La Chaine Sans Fin JH Vol.2 p244
It's Knot Easy - Milton Bradley JH Vol.2 p240	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
Go-Getter 3 - DaMert		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 double-six in the top left corner. (There are six faces among four of the cubes showing a double-six.) 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 Jig-Saw Puzzle Fit the pieces into the tray and build a loop.

This category requires you to arrange the pieces to satisfy some rule or goal relating to a pattern on the pieces or 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 three-piece 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.	The Rabbit Silhouette or "Question du Lapin" - layer the cutouts to form a rabbit (play the rabbit silhouette on-line).
Arrange the 5 layers so the cumulative cutout area forms the shape of a pipe. You will then have "Not A Pipe" - "Ceci n'est pas une pipe" - as from Rene Magritte's "The Treason of Images." A miniature puzzle in a matchbox.	Demon Dino - William Waite
Mattel's Virtual Illusion puzzle contains a base and a series of transparencies each containing a portion of a three-dimensional image. You need to order the transparencies in the base so that the image appears correctly.	Dino Try - William Waite
Cliko by Foxmind Comes with a set of blocks and a booklet of problems. Arrange specific blocks to form different silhouettes.

Using just a set of matchsticks (or sticks without the matchheads), form a figure, then transform the figure into some other figure moving only a specific number of matchsticks.

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 on-line...

• zefrank's site
• puzzles.com
• Jim Loy's site
• iamawiz.com
• quizbox.com

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.

Toyo Glass issued a series of puzzles where you stack clear glass coasters with various patterns: Red All Through Animal Land Starry Skies
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 quarter-squares 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 3-piece burr appears. I bought it at Torito.
The Transposer series of puzzles has been created and developed by Albatross Games Ltd. of London, and distributed by the Toysmith Group. Available from In and Out Gifts. Each puzzle consists of a set of cards with various design fragments and cutouts. Stack the cards to achieve specific patterns, such as uniform color front and back, or unbroken paths of given colors from point to point. Transposer 6 Transposer Bonbons Transposer Genesis Transposer Kaboozle Transposer Tiffany Transposer Tower of London Transposer Struzzle
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.		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!
Four well done puzzle challenges from Smart Games.

The Brain Drain is a form of the Eight Queens puzzle (play the Eight Queens puzzle on-line) - arrange the four squares such that in the resulting 8x8 grid, no two holes appear in the same row, column, or diagonal. The tiles may be flipped over. I have had this puzzle for a long time and it remains one of my favorites despite its simplicity.

Slocum and Botermans state in their "Puzzles Old and New" on p.37, that the 8 Queens problem was first proposed by Max Bezzel in 1848, and the 12 possible solutions were first published by Franz Nauck in 1850. A proof that these are the only solutions was published in 1874 by J.W.L. Glaisher.

For another version using battleships, see U.S. Patent 1151615 - Reibstein 1915.

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.

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.

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."

According to the Wikipedia entry, a Latin Square is an NxN matrix filled with N different symbols such that no symbol appears more than once in any row or column. Sometimes the additional restriction of disallowing a repeated symbol along either main diagonal is also added. See Terry Ritter's page, Latin Squares: A Literature Survey for a nice collection of facts and terminology about Latin Squares. Also see a nice article by Elaine Young.

Leonard Euler (1707-1783) 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:

In 1992, in Discrete Mathematics, J. Shao and W. Wei published a formula for the number of Latin Squares of any order. (It is non-trivial to specify.)

The Safari Puzzle by the German company "Pussy" or "Pussycat." A 7x7 Latin Square puzzle presented as a sliding-piece 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 order-5 Latin Square.

A Graeco-Latin (or Greco-Latin) Square (also known as an Euler Square) is constructed by superimposing two Latin Squares having the same order but different sets of symbols (usually designated by using Latin letters for one of the squares' symbols and Greek letters for the other, hence the name Greco-Latin), such that each combination of symbols (one from each Latin square) occurs only once in the superposition. They are also known as mutually orthogonal Latin squares or MOLS. There are none of order N=2, but N=3,4, and 5 all exist. While searching for (and failing to find) a solution to the Thirty-six Officers Problem, Leonard Euler conjectured that solutions don't exist for any order N = 4i+2 (i.e. 2, 6, 10, 14, etc.). Euler demonstrated methods for constructing Graeco-Latin Squares when N is odd or a multiple of 4.

The Thirty-six 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.

It turns out that there are no Graeco-Latin 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 Greco-Latin 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 n-1, but some Latin Squares have no mutually orthogonal mates.

In Greco-Latin 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 Graeco-Latin 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 Graeco-Latin Square that meets all those conditions:

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 Graeco-Latin Square puzzle.

Four Square from the Embossing Company, Albany, NY Combines a Graeco-Latin 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 Graeco-Latin 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.

A Magic Square is to contain a sequence of numbers such that the numbers appearing in each row, column, and main diagonal add up to the same sum, known as the magic constant of the square. If all diagonals (main as well as partial) also sum to the magic constant, the square is a pandiagonal or panmagic square. If replacing each number by its square also results in a magic square, the square is bimagic. If the sequence of numbers used in a square of order n is from 1 to n², it's known as a normal magic square. Magic Squares exist for all orders except N=2. There is only one distinct Magic Square of order N=3. There are 880 of order 4, and over 275 million of order 5. Supposedly the order 3 magic square was invented in China between 650 and 400B.C. and known as Lo Shu.

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:

An order 4 Magic Square appears in Albrecht Durer's famous engraving called Melencolia I:

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 order-3 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 order-5 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 There is a single magic hexagon of side 3, with 19 cells. Its magic constant is 38. It was discovered in 1895 by William Radcliffe. In 1964 Charles Trigg published a proof that this is the only magic hexagon of any size (save the trivial single hexagon). Additional historical anecdotes about this puzzle are given in Slocum and Botermans 1994 The Book of Ingenious & Diabolical Puzzles on pages 26-27.

"Catch-21" by Gabriel (U.S. Patent 3833222 - Castanis 1974) and "Hi-Q 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 Hi-Q 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, Catch-21 is more logically straightforward. It includes a set of domino-like pieces.

     

Here is my solution "diary" for the 2nd side puzzle of Catch-21. 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:

• Jurgen Koller's page
• Domino Logic
• Frans Faase's page

One of the earliest mechanical puzzles I ever had was an Instant Insanity given to me by my mother. Instant Insanity was marketed by Parker Brothers and invented by Franz O. Armbruster, a California computer programmer. 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." The objective for all of them is to find a linear arrangement of the cubes such that all four long sides show each color only once.

"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.'"

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." They show the layout of each of the four cubes. Each block is a different color - orange, pink, green, and yellow. I am missing the fourth block from the top in the illustration in the book, which I believe is the yellow one.

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.	This is a vintage advertising premium called Symington's Puzzle. It contains four cardboard cubes, each with a different arrangement of four Symington's product advertisements on their faces: Soup, Custard Powder, Ideal Cream, and Gravy. It is shown in Slocum and Botermans' "Puzzles Old & New" on page 38.	Here is another vintage cube matching puzzle called The FourAce Puzzle. The four wooden cubes are decorated with various arrangements of the four playing card suite symbols: hearts, diamonds, clubs, and spades. The box says "Provisionally Protected" but does not identify the manufacturer or date of manufacture.
The Great Tantalizer	Tantalizer	RGee's version
Logi-Qubes	Those Blocks	Krazi Kubes
Taktikolor	Hlavolam Iribako	Tantalizing Ten - Shackman
Dorobo - Hanayama		Levenger Cubes
Daffy Dots - Reiss 1971	Crazy Cubes
"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.
Hungarian Tactics	The Buvos Golyok is a clever variant using balls enclosed in a tube.	Bognar Planets (Bolygok) - brown, white
This is Meffert's "Drives You Crazy." It includes six cubes instead of the usual four.	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. Celia Seide notes that in Germany these are known as "Trikki 4."	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 sub-graphs are needed, and they are not independent.
Crazy Blocks Color Puzzle Created for Jak Pak Inc. of Milwaukee Made in British Crown Colony of Hong Kong	six cubes
Coloured Cubes Peter Pan Series Regd.	Nice Cubes	Color Cubes
Twenty Teazer Arrange the cubes so that each side totals 20.	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 re-ordered.

This type of puzzle can be arranged vertically, too, as in the Steiffel Tower and Totemania

Wellingtons Ltd. and Onsworld Ltd. of Stamford UK offer several variants.

			Not shown: Snookered II Suit Yourself Nuts Are there others?

Ivars Peterson has a page devoted to graphical solution techniques pertaining to this type of puzzle. I used this technique to solve Nice Cubes. Here is my solution using this graphical technique:

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?

Here is a series of puzzles issued by House of Games Corporation Limited of Bramalea, Ontario, Canada. They're all made of sturdy cardboard. Some of them are shown elsewhere on this site.

Per the pamphlet that came with the Rectangle Tangle puzzle, John Waddington Ltd. of Castle Gate, Oulton, Leeds England also made these under license from House of Games.

Waddington was bought by Hasbro in 1994 for 50M pounds. Read an article about Hasbro's spree.

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:
• The Perfect Square (1969)
• The Tricky Triangle (1969)
• The Perfect Circle (1969)
• The Wobbly Web (1969)
• The Perplexing Pyramid (?)
• The Path (1969)

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

• The Reluctant Rectangle (1970)
• Little Circles (1970)
• The Coloured Square (1971)
• Rectangle Tangle (1971)

Also mentioned once is "The Coloured Pyramid" which I believe is the same as The Perplexing Pyramid.

The brochures also mention Beat the Elf, Kolor Kraze, and Cube Fusion.

The Path 1969 #505 Form a 3x4 rectangle using 12 colored square tiles which are each printed at from 1 to 3 of their corners with small circles. There are 4 tiles each of 3 different colors, blue, orange, and pink. All pink must be in the first row, all orange in the second, and all blue in the 3rd. One circle on a pink tile is marked START and must be in the upper left, and one circle on a blue tile is marked FINISH and must be in the lower right. Create a path of circles from START to FINISH such that circles are not adjacent unless they form a path connection.
The Perfect Square 1969 #505 Assemble a square using 12 pieces - like colors must not touch.	The Tricky Triangle 1969 #505 Using 10 barbell-shaped pieces composed of two linked circles each, and one single circle, build an edge-6 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 2-dimensional 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 like-colored 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 L-shaped 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 "normally-handed" 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 color-dismatching constraint.) No Pamphlet.	Coloured Square 1971 #340-E Form a square from 12 L-shaped colored tiles such that like colors don't touch.	Rectangle Tangle 1971 #340-F Form a rectangle with a bi-color perimeter from the 10 tri-color and 2 bi-color L-Trominoes.
	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!

Percy Alexander MacMahon was a mathematician who lived from 1854 to 1929. He is noted for, among other accomplishments, his results in the field of combinatorics. In 1915 and 1916 MacMahon produced a two-volume treatise on Combinatory Analysis which remains a respected work today. MacMahon also produced New Mathematical Pastimes, published in 1921. This work discusses his Colored Cubes, first introduced in a lecture he gave in 1893 [4].

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 eight-cube puzzle patented in 1892 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 color-matching 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 sub-cubes 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.

References:

1. Mathematical Recreations and Essays, by W.W. Rouse Ball, Macmillan 11th ed. 6th printing 1973, pp.112-113
2. Torsten Sillke provides a good bibliography which led me to other sources, including the Martin Gardner books I already have but hadn't realized contained pertinent information
3. New Mathematical Diversions from Scientific American, by Martin Gardner, 1966 Simon and Schuster, pp.184-195
4. Fractal Music, Hypercards, and More, by Martin Gardner, 1992 W.H. Freeman and Co., pp.88-99; discusses the Conway matrix
5. my section on Journet
6. Juergen Koeller's site
7. MacMahon bio

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 open-ended creative playset than a puzzle.	K-Dron - Janusz Kapustra Physlink has it. (I don't have this.)	Trac 4 game issued in 1976 by Lakeside. Red-and-white 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.

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 "Digi-Disc" - 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, non-magnetic, called "Magic Numbers."
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
Tedco Mirage Numbers Up	Zen Blocks	Cubits
That-A-Way 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 That-A-Way on-line.	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.
Dice Stacker	At Games People Play, I found a Magic Mirror puzzle from Schmidt Spiele.	There are several "Slivers" puzzles - this is the Anakin Skywalker version.
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.