INTRODUCTION TO MATCHING PUZZLES
In general
The best known kind of matching puzzles is made of 9 square cards with a part of a picture along each side of each card.
 For example this "Crazy Witch" puzzle: matching 2 cards, one with the 'head' and one with the corresponding 'tail' of a witch, is easy enough. But matching all 9 cards at the same time and matching each 'head' with a corresponding 'tail' is not really trivial.
This "Crazy Witch" is a typical example of the most popular type of matching puzzles: 9 cards, 'heads and tails', with 4 different pictures (in this case 4 different colors). Apart from the shown solution, the puzzle has another solution which you may want to find yourself. 
History
Nothing about any type of matching puzzles was ever found, until suddenly in the 1890s the first one (as known today) suddenly appeared out of the blue in the toy shops. This earliest known heads and tails puzzle was copyrighted 1897 in the USA by Parker Brothers as the "Chicken Coop" puzzle and it had exactly the same structure as the before mentioned Crazy With puzzle. In this case, the heads and tails were represented by high and low numbers (or as numbers of chicken) and correct matching meant numbers adding up everywhere to 10 (or 10 chicken in each coop). 


Variations of that puzzle were issued early 1900s in France, Europe as "Le Berger Malin" (the smart shepard) and "Le Fermier Avisé" (the cautious farmer), both shown in Slocum and Botermans, "The Book of Ingenious and Diabolical Puzzles". The first one showed sheep instead of chicken, the other one did it with chicken. 
Soon enough, especially in the period between the two World Wars, these (and many other) puzzles became a craze. Colorful and inexpensive to make, commercially available at game and toy stores and very widely used by advertisers as premium gifts, for example for cars, Soaps, banks, etc.. There were even several puzzle solving contests, back in the 1920s.
A broad variety was covered in Percy Alexander MacMahon's "New Mathematical Pastimes" in 1923, further popularized by Martin Gardner in his columns in Scientific American and later in his books.
Variations

A totally different type is the "Endless Chain" puzzle, describe 1893 by Professor Hoffmann in his famous book "Puzzles Old and New". Eighteen rectangular pieces of various sizes assemble into a square and at all edges, chain parts must match and eventually form an endless chain. Definitely not an easy puzzle to solve! Most likely, a physical version of this puzzle already existed in those days, which would then be the first matching puzzle ever.


The second puzzle describe by Hoffmann is "The Royal Aquarium Thirteen Puzzle". Nine squares each with four numbers, radiating from the center. Half of the numbers are printed in red, the other half in blue. Aim of the puzzle is to arrange the cards in a square, the red numbers forming vertical lines and the blue numbers horizontal lines, so that the three numbers in each line, whether horizontal or vertical, add up to 13. Clearly the matching of the cards is not governed by the numbers on adjacent edges but by groups of three numbers on the three cards in the same row or column.


Apart from the by far most common 'nine square cards' version, numerous variations saw the light: triangular cards, rectangles, hexagons, octagons and even circles. The number of cards varies from 4 to a staggering 100 and the number of different colors is not always 4 as with the Witches and much more difficult variations were issued with card printed on both sides.

Cardboard or even thick paper is not the only material used. Not uncommon are versions in wood, like this 'Puzzling Zoo' from 1999, but other materials like metal or ceramic gave some puzzles a more 'serious' appeal.

Other kinds of variation from the most popular 'heads and tails' are puzzles where two identical pictures must match; puzzles where pictures are not at the sides, but at the corners of the squares, again either to complement each other, or to match with identical ones. And of course the first version mentioned above: the continuous path puzzle.
Patents
Actually, the story started slightly earlier than mentioned before. The oldest known proof of existence of a matching puzzle is in U.S. Patents 487,797 and 487,798. Both were applied for in 1890 and patented on December 13, 1892. The inventor was named Edwin L. Thurston from Cleveland, Ohio.
In his Patent, a whole series of matching puzzles was described:
a 16 square cards corner matching puzzle;
a 16 square cards edge matching puzzle;;
a 6 diamond shaped cards edge matching puzzle.
All explicitly stating that the cards have no fixed orientation and that any number of colors may be used.
The next (known) Patent in time is British, applied for in 1892, accepted 28th January 1893. Major Percy Alexander MacMahon and Major Julian R.J. Jocelyn of the Royal Army specify a game with triangular cards divided into three triangular portions by lines drawn from the center of the card to the angular points. However, their text nowhere use the word 'puzzle': they only describe various
games that can be played by using these triangular pieces. Nevertheless, in all the games described, the cards really must match. So, in this MacMahonJocelyn patent, we are very close to the fundamentals of an edge matching puzzle, though apparently not yet recognized as such by these authors.
MacMahon later widened his horizon the his already mentioned book "New Mathematical Pastimes" from 1923.
Were these patents the first signs of matching puzzles? Or were these inventors triggered by already existing puzzles of a similar kind? We do not know and perhaps never will, unless such a puzzle, clearly dated before 1980, is found in an old attic or anywhere else.
Corner matching

U.S. Patent No. 1,006,878 by A.K. Rankin was filed February 3, 1911. This is the first example of a nine square cards corner dismatching puzzle with nonrotating cards. Also, it is the first puzzle of this kind of which commercially produced versions survive: this same puzzle was produced in many versions, like for "Grandpa's Wonder Soap" using 4 different color in quarter circles at the corners. At least twelve different versions were produced, differing in the distribution of these four colors among the corners of the nine cards. 
More recent variations

Heads and Tails puzzles based on nine triangular cards are relatively new. The first known specimen dates from 1983, named "The Magic Triangle", produced by Friedrich W. Heye Verlag in Germany. The unusual shape of the pieces, in this case also combined with head and tail parts that are not obvious different, make this a pretty difficult puzzle. 
In 1994, the Damert Company from California, USA introduced a series of puzzles: Instead of separate pictures along all card edges, larger pictures were used that extend over two edges of the same card. Well over 100 different puzzles in this "Scrambled Squares" series were issued, some of them, including this example, pretty confusing due to the relatively large size of the depicted objects. 


From Japan, there is a small family of 3D puzzles, based on the dodecahedron, with magnetic pentagonal cards to be placed at the faces of this solid. This example too is a 'heads and tails' type of puzzle

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© Jacques Haubrich, Eindhoven, April 2020
