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A BRIEF HISTORY OF CHECKERBOARD PUZZLES

A "checkerboard" in the U.S.A. is exactly the same as a "chessboard" or "draughtboard" in most other countries: a square board with 8 rows each of 8 squares, alternatingly coloured dark and light. Such a board is often used to play chess, though it has several other purposes. Such a checkerboard can be turned into a checkerboard puzzle by cutting it (along the lines) into any number of pieces. Here is an example:

Obviously, cutting a board into either 2 or 64 pieces is not a very smart way to produce an interesting puzzle. In practice, the not-too-easy checkerboard puzzles are made from 10-15 pieces. Less than 10 usually makes the puzzle quite easy; more than 15 results first in extremely difficult puzzles, but from 25 pieces or more, the difficulty rapidly vanishes and only very easy puzzles are obtained.

The oldest known checkerboard puzzle is "The Sectional Checkerboard Puzzle" which dates with certainty from the early 1880's. It was patentend by Henry Luers in 1880. Another puzzle, made by D. Ballard, claims to be patented May 20, 1873, but unfortunately, the patent that might prove this claim has not been found.

These puzzles, especially when made from printed cardboard, are usually inexpensive and many of them were used as promotional gifts. With waves in time, they were more or less popular in certain eras. In fact, despite their popularity, is was only 1978 when Dale Overy (England) publishes his "PUZZLE WORLD" issue no 4, describing the pieces of 12 different "Chess Board Dissection Puzzles". At the end, he asked the readers if anyone knows of any other standard 8 x 8 draughtsboard puzzle. Four years later, in 1982, he published "An Introduction To Checkerboard Puzzles" in which 37 different checkerboard puzzles were described. The next year, 1983, Jerry Slocum published his first "Compendium Of Checkerboard Puzzles". It described 61 different puzzles of 33 different designs, and it showed not only the pieces, but also at least one solution and a picture of the puzzle wherever possible.

In 1993, a second edition of this compendium was published, this time with the help of a computer for much of the pre-press work and also for completely solving all the puzzles. This edition included 162 puzzles of 91 different designs. At the time, the authors believed that although not all, at least most of the checkerboard puzzles ever produced were described in that edition. How wrong they were! Avid collectors kept sending information on newly discovered old puzzles and also of newly designed puzzles, forcing the same authors in 1997 to publish a third edition that included 76 puzzles of 217 different designs.

Finally, 2005 brought the last publication, which included full information on 681 different puzzles or publications of 356 different designs, too much to fit into one even very thick compendium. So the puzzle designs were put into chronological order and the data split into two more or less equal parts. It turned out that the first part would comprise more or less the first 100 years of these puzzles, and the second part would comprise the most recent (at the time) 20 years.

Once ready, this double volume finally described over 440 puzzle, patents, publications and variations of over 190 different designs. Since then, only very few puzzles have been brought to my attention or have been commercially introduced. The last known new checkerboard puzzles saw daylight in 2013 when Cheatwell Games from England issued 4 new and interesting puzzles. But The Great Wonder Puzzle referred to in this 1896 advertisement in Munsey's Magazine remains, unfortunately, still undiscovered, and it seems unlikely that this would be the only old puzzle that has not been seen so far by any collector.

Nevertheless, occasionally an old and so far unknown checkerboard puzzle pops up. In June 2015, a puzzle collector found and reported a puzzle named "Teddy and his Bear" which dates from 1907, and in July 2015 I received a second report about a puzzle named CHEQUIT, which could be dated around 1935, then issued in England to raise funds, one version for churches and schools in Bedfordshire & Hertfordshire, the other to raise funds for St. James' Church in Middlesbrough. And these are just very recent discoveries...

Popularity of checkerboard puzzles came only slowly over the years, but in the 1920s and especially in the 1930s, many new puzzle designs came to light and checkerboard puzzles were apparently very popular. This popularity faded only slowly until the end of the 1950s. A kind of revival came in the 1980s, when the home computer enabled increasing numbers of people to make new designs according to predetermined rules.


FAQ

1. Are all checkerboard puzzles 8x8 puzzles?
A: Since a regular chessboard is an 8x8 board, the obvious answer is yes. However, there are other similar puzzles with different dimensions, both smaller and larger than 8x8. Unfortunately, these are inappropriate for a game of chess.

2. Are they all cut into pieces along the lines?
A: No. A few of these puzzles were cut otherwise, most (if not all) using diagonal cuts. Apparently, some puzzle producers do not really understand the principles of a dissected chessboard.

3. Is there fun in solving a checkerboard puzzle?
A: That's a funny question! My answer is No. There is absolutely no fun in solving a checkerboard puzzle. The shapes of the pieces give no clue at all to the solution. It is nothing else than a lot of trial and error. And when I say "a lot" I do mean "a lot". The only fun perhaps may be when you are absolutely convinced that a certain piece can go nowhere else but in a corner or at least at an edge, when later it turns out that the piece does goes somewhere inside. Yeah: that's fun!

4. Are all checkerboard puzzles made of cardboard?
A: not all, 'only' about 70% of them. 20% is made from plastic and other materials are: metal, acrylic, magnetic rubber, ceramics, cloth, since a few years also 3D printed plastic, and finally, very recent in 2019: origami paper.


All pieces made from uncut squares or rectangles

5. What size have these puzzles?
A: The average size of the unit squares is 17.9 mm or 0.7 inch and 80% of these puzzles has a size ranging from 10 mm to 1 inch. The smallest known puzzle is made from matchsticks with heads of 1.5 mm and the largest one was designed to be used as a coffee table and this one has 4.5 inch until squares, so the entire table measures around 90 x 90 cm.

6. Are there other shapes than squares?
A: Yes. For example: Hexagons, based on triangular units instead of squares do exist.

7. Are there other variations?
A: Yes. There are a few folding puzzles which, when folded correctly, show a nice 8x8 checkerboard or even a hexagonal board. Also, there is at least one such puzzle where the individual pieces are made of transparent plastic with a few black squares printed onto them. Stacking these pieces the right way results in an 8x8 checkerboard. And of course, there are puzzles with pieces that look like checkerboard puzzle pieces, in which the aim of the puzzle is to form a cross or other non-square shapes.

5. Can a checkerboard be used for any other purposes?
Apart from playing chess: play checkers. And the famous eight queens problem requires a checkerboard and so do several other games that require a subset of the full set of 32 checkers discs on a checkerboard. And not to forget: all kinds of variations as shown in this original picture by Sam Loyd.

7. Do you know any interesting stories about checkerboard puzzles?
A: Well, eh, yes. Back in 1935 and 1937, there were International Congresses of Recreational Mathematics. In those days, checkerboard puzzles were very popular, including among mathematicians. For one particular puzzle, a group of these mathematicians already had found 4963 different solutions for that particular puzzle. Using statistics and some well thought experiments, they calculated the total number of solutions. The result was that there should be between 4631 and 5361 different solutions with 1-10^-9 certainty. Many years later, in the early days of the home-computer era, it was found that the same puzzle had (and still has) 6013 solutions. The report may be interesting food for statistics students and professors, especially to find how they could be so sure about their incorrect results and also for finding the false assumption(s) made in those days.


References:

Luers, Henri, U.S. Patent No. 231,963, 7 September 1880 (Sectional Checkerboard Puzzle)

Overy, Dale, Puzzle World, Dale Overy, Stafford Staffs, England, 1978.

Overy, Dale, Introduction to Checkerboard Puzzles, Dale Overy, The Martlets, Shropshire, England, 1982

Huber-Stockar, Emil, Comptes-Rendus du Premier Congrès International de Récréation Mathématique, Bruxelles 1935, (p. 93-94)

Huber-Stockar, Emil, Comptes-Rendus du Deuxième Congrès International de Récrétion Mathématique, Paris 1937, (p. 64-98)

Huber-Stockar, Emil, L'Echiquier du Diable, SPHINX, Revue Mensuelle des Questions Récréaives, Bruxelles, 1938, (p. 36-41)

Slocum, Jerry, Compendium of Checkerboard Puzzles, Beverly Hills, 1983

Slocum, Jerry & Jacques Haubrich, Compendium of Checkerboard Puzzles 2nd edition, 1993

Haubrich, Jacques, A Century of Checkerboard Puzzles, 2005

Haubrich, Jacques, Additional Checkerboard Puzzle Designs, 2005


© Jacques Haubrich, Eindhoven, May 2015