MECHANICAL PUZZLES
by Jerry Slocum
excerpted from his book, “Puzzles Old & New”
[Photos by Bruce Whitehill; games from the BGH collection]
Jerry Slocum, recipient of the AGPC 2006 Loyd Award for exceptional work in the promotion of mechanical puzzles
A mechanical puzzle is a self-contained object, composed of one or more parts, which involves a problem for one person to solve by manipulation using logic, reasoning, insight, luck, and/or dexterity. The puzzles range from ancient tangrams, two-dimensional assembly puzzles, to modern-day sophisticated and complex three-dimensional interlocking solid puzzles, from simple wire puzzles which were so popular around the turn of the century, to beautiful and intriguing Chinese ring puzzles, from secret boxes with hidden openings to sequential movement puzzles, as well as nineteenth-century secret puzzle pitchers, puzzles in which images appear to vanish without a trace, and objects which seem to be completely impossible to construct.
PUT-TOGETHER PUZZLES
The oldest and largest class of mechanical puzzles consists of those puzzles that are solved by assembly or by fitting pieces together. The most popular member of this class is the jigsaw puzzle. Dissected puzzles of a completely different type were popular much earlier in Greece, and they appeared in the mid-18th century in Japan, and at the turn of the 19th century in China. The earliest known example is the Loculus of Archimedes, or the Stomachion (‘the problem that drives one mad’!). This appeared in the 3rd century B.C. and was a 14-piece dissection of a square. The Tangram, another 7-piece puzzle, became popular in China about 1800, and by 1820 it had spread to Europe and the United States. It has remained popular to this day.
Towards the end of the last century, the German firm Richter began producing dissection puzzles using manufactured small bricks or stones. These were known as the Anchor Stone Puzzles and were very popular during World War I, when they were used by soldiers in the trenches. Other interesting dissection puzzles are those obtained by cutting up crosses or letters. The best known is probably the ‘T’ puzzle. Another class of puzzles is that of Magic Squares, arrays of numbers where the sum of the numbers in each row, column and diagonal is the same.
T-Puzzle, Wocester Salt
The first checkerboard puzzle seems to have originated in 1880, when a certain Henry Luers obtained a U.S. patent for a ‘Sectional Checkerboard’, consisting of fifteen differently shaped pieces of complete squares of a checkerboard. Luers claimed that his puzzle offered ‘much amusement and employment of time to those who have no better use for it’.
Tangrams are dissection puzzles – plane or solid figures cut into various pieces. They are among the oldest and most popular forms of recreational mathematics. There are only seven pieces, called tans, and they are of the simplest possible shapes – two large, a medium-sized and two small triangles, a square and a rhombus (lozenge).
Tangram, Diset, Intl., Spain; Chinese characters
Yet these seven simple pieces can be assembled in an extraordinary variety of ways. By using artistic skill and geometrical ingenuity an almost infinite number of human and animal figures can be formed from the tans. The puzzle certainly originated in China; its earliest known reference is a woodcut from 1780 by Utamaro. The ‘Chinese Puzzle Game’ swept through Europe and America at the beginning of the 19th century and its popularity continues to this day. Although there is little factual evidence of the origin of the Tangram, there is a rich and detailed body of legend, largely due to the efforts of Sam Loyd, the great American puzzle expert, who devised a bogus history of the Tangram.
Instant Insanity was designed about 30 years ago by a California computer programmer who designed a puzzle consisting of four plastic cubes, each face of each cube having one of four colors.
Instant Insanity, ca. 1975, Siam Sanuk, Thailand; wood blocks with colored pips
The problem is simply to arrange the cubes in a straight row so that all four colors appear on each of the row’s four sides. The puzzle has, in fact, been around in many forms for over 90 years.
The original version was designed and patented in Detroit in 1900. The puzzle consisted of four cube blocks decorated with one of the four suits of cards.
The Soma cube was devised in 1936 by the Danish poet and puzzle inventor Piet Hein. It must be one of the few puzzles in the history of puzzledom to have inspired its own newsletter! The seven Soma pieces represent all the ways in which three or four cubes can be arranged other than in straight lines; in elegance and versatility it is the 3-dimensional equivalent of the Tangram. The name ‘Soma’ is derived from the drug in Aldous Huxley’s Brave New World, a drug which transported its user into a dreamlike trance.
Soma, Gem Color Co., Patterson, NJ; invented by Piet Hein; double set.jpg
TAKE-APART PUZZLES
The ‘Golden Age’ of secret opening puzzles was the period from 1879 to 1895. Famous stores such as Marshall Field of Chicago and Peck and Snyder of New York sold a variety of very clever secret opening puzzles. These were beautifully made of polished boxwood, ebony, brass or nickel plated steel. Some of these puzzles were used to carry matches, rings, snuff and even drugs such as cocaine, but the object of most of them was to amuse and puzzle. Often the puzzle was to remove an object such as a marble or a ring from a barrel, a tower or a cannon. More complex are the Japanese puzzle boxes which have been exported to the West since before 1920. These require several sliding panels to be moved in a specific order before the box can be opened.
Takitapart
The Takitapart puzzle is a wooden puzzle patented in the United States. It consists of four square blocks, two interlocking bars and four pins or dowels. The object is to take the puzzle apart. You get a penny back when you do.
Japan has exported secret opening boxes to the West since before 1920. One or more sliding parts in one end are moved, allowing the end to be moved slightly. This partially unlocks a side panel, which allows other pieces to be moved. These, in turn, partially unlock the top or bottom. This method is continued, moving around the box, until the top panel can slide, opening the box.
INTERLOCKING SOLID PUZZLES
At some time or other most of us have been baffled by one of those puzzles made of pieces so cleverly interlocked that they seem almost impossible to separate. There is usually a single piece, called the key, which must be removed first in order to disassemble the puzzle. In many such puzzles the pieces must be replaced in a certain sequence and the key is always inserted last to lock the other pieces in place. Puzzles of this type used to be known as ‘Chinese’ puzzles, but nowadays they are commonly known as burr puzzles, presumably because of their resemblance to a seed burr. During the 19th century, the 6-piece burr evolved into solid, interlocking puzzles such as cubes, balls and barrels. Puzzles of this type were mainly produced in Germany, but by the late 1930’s the market had been largely captured by Japanese manufacturers. They designed many new interlocking puzzles in the form of animals, vehicles, and weapons. The ancient Japanese skills and techniques of joining wood without nails to make buildings and other wooden structures were applied to making interlocking puzzles.
Most of us have probably owned a keychain puzzle at some time or another during our lives. They are quite like interlocking wooden puzzles, the most important difference being that they are made of plastic. Keychain puzzles seem to have originated in 1939. During that year the World Fair was held in New York. Irving Steinhardt patented a small plastic puzzle which represented the 200-ft. ball-like structure, called a Perisphere, with the Trylon, a 700 ft. high obelisk, sticking out of it. The piece representing the Trylon was soon replaced by a keychain and the puzzle became quite popular. By the mid-1950’s dozens of different keychain puzzles were on the market and sold in drug stores and dime stores everywhere.
DISENTANGLEMENT PUZZLES
Disentanglement puzzles deal with the problem of freeing (or attaching) a part of the puzzle, usually a ring or a handle. They are made of various materials such as cast iron and sheet metal, wire, and string. The Bent Nails Puzzle may be the most popular, or most common, disentanglement puzzle; it still is played. As long ago as the first half of the 17th century, a bent nails puzzle existed. The Chinese Rings Puzzle is by far the oldest puzzle we know that’s usually made of wire. These puzzles often consist of beautiful figures or shapes. According to legend, the puzzle was invented in the second century by a famous Chinese hero. It became popular in China around 800 years ago, and was viewed as a kind of wisdom game, conducive to the training of intelligence.
SEQUENTIAL MOVEMENT PUZZLES
Sequential movement puzzles require a series of steps or moves, following a set of rules, to reach a predetermined goal. Puzzles in this category include solitaire puzzles, sliding block puzzles, counter puzzles (hop-over), rotating cube puzzles, and maze and route puzzles.
A sliding block puzzle has been defined as a group of pieces of any shape(s) enclosed within a confined area, in which the purpose is to rearrange the pieces either into a certain order or to get a particular piece to a specified position. This is accomplished by sliding the pieces or ‘blocks’, usually one at a time, into areas not occupied by other pieces. The lifting of pieces is never allowed, nor must they hop or jump over other pieces. Finally, rotation of individual pieces is only allowed if specifically stated. Some puzzles contain obstacles or immovable barriers. Others introduce restrictions: for example, pieces may have to follow specific routes or there may be a requirement that certain pieces do not touch certain other pieces. Sometimes a piece may not be allowed to move at all. A great many puzzles have no set start position. It is usually required only to muddle up the pieces to ‘set’ the puzzle. Most of these, when solved, form some kind of picture or design. Using rectangular pieces among square ones was an idea which originated around 1909. These puzzles are usually much more difficult than puzzles consisting only of square pieces.
The earliest sliding block puzzle known is the Puzzle of Fifteen, which consisted of 15 square blocks in a 4 x 4 square box and included a piece numbered 16 to allow the 4 x 4 magic square to be made. The fifteen Puzzle has been one of the most successful of all puzzles. In 1957, the American Larry Nichols thought of a way to improve and extend the concept of the Fifteen Puzzle in a 3-dimensional (cube) puzzle. The Hungarian Erno Rubik, independently of Nickols, reinvented the Cube puzzle in 1974. Rubik’s patent included a very clever mechanism to hold together the pieces of a 3 x 3 x 3 cube.
Peg solitaire is shown in an engraving dated 1697. The Puzzle Peg was first produced in the early 20’s by the Lubbers & Bell Mfg. company of Iowa. It was sold together with a booklet with problems submitted by the avid puzzlers of so long ago.
DEXTERITY PUZZLES
Dexterity puzzles have been popular for centuries in many different cultures and civilizations. Although they are often called games, they are puzzles since they are solved by only one person. Manual dexterity puzzles include Throw and Catch, Mazes with Balls, Glass Topped Rolling Ball Puzzles and many more. Long ago, dexterity puzzles may have been used to teach eye-hand coordination and other hunting skills to children.
The Cup-and-Ball is thought of as a traditional folk toy of Mexico, but its original home probably lies in the East. In the United States, in 1889, Charles Crandall started producing a rolling ball puzzle called Pigs in Clover. This dexterity puzzle took the country and the world by storm almost instantly.
FOLDING PUZZLES
“The easiest way to refold a road map is differently,” according to Jones’ Rules of the Road. The folds are confined to the creases, and the final result must be a packet with any rectangle on top and the others under it. The object of a folding puzzle is to achieve a specified goal by folding. The Hitler Folding Puzzle had an illustration of four pigs with the instruction “to find a fifth one, fold as indicated.” When the puzzle was folded correctly, Hitler’s face appeared. The Palace Puzzle was produced as a souvenir of the Royal Wedding in 1981 of Lady Diana Spencer and His Royal Highness, the Prince of Wales. The problem is to fold the puzzle to correctly make the Royal couple.
PUZZLE VESSELS, VANISH PUZZLES, AND IMPOSSIBLE OBJECT PUZZLES
Other types of puzzles include puzzle vessels, that involve drinking or pouring a liquid, or filling a vessel, without spilling; vanish puzzles, puzzles which when turned or moved cause an image to change or vanish; and impossible object puzzles, the puzzle element being to discover how the object was made (such as an arrow through a bottle, or a a bottle with an object inside that is larger than the opening of the bottle).
For more information contact Jerry Slocum at: JSlocum@Earthlink.net.
SAM LOYD’S AMUSEMENT
by Jerry Slocum
No one seems to know when the first sliding block puzzle was invented or made. In the 1870’s, America’s greatest puzzle expert, Sam Loyd, “drove the entire world crazy” (as he himself put it) with his newly invented 14-15 puzzle. He offered a $1000 reward to anyone who found the solution and his puzzle created a world-wide interest not seen again until the Rubik’s Cube craze. But no solution to the puzzle existed. It was impossible. When Loyd applied for a patent he was asked if the positions of the 14 and 15 could be changed. He replied that it was mathematically impossible. The Commissioner retorted, “Then you can’t have a patent. If the thing won’t work, how can you file a working model of it?”
CUTTING THE GORDIAN KNOT
by Jerry Slocum
The most famous disentanglement puzzle is probably the Gordian Knot, which is named after Gordius, a simple farmer, who by his extreme cleverness became King of Phrygia. It is told that when he assumed power he tied his former implements in such a peculiar way that the knots could not be unfastened. The oracles proclaimed that whoever could untie them would become emperor. Alexander the Great, or so the story tells, made many ineffectual attempts to untie some of the knots, but finally became so enraged at this lack of success that he drew his sword and cut the cord–hence the expression: “I have cut the Gordian knot!’”
INTRODUCTION TO MECHANICAL PUZZLES
by Martin Gardner
“Mechanical puzzle” is the term most widely used today for a puzzle made of solid pieces that must be manipulated by one’s hands to obtain a solution. The degree of difficulty in solving a mechanical puzzle varies enormously. The two twisted nails, for example, can be solved by some children in a matter of minutes. Other puzzles such as Rubik’s Cube may take an intelligent adult days or months to solve. Before the craze faded, dozens of paperbacks were written about the cube. In the 18th century, the popularity of peg solitaire produced a similar flurry of books around the world.
Many mechanical puzzles require a vast amount of patience and a careful exploration of all possible manipulations. Some may require a computer program. A few years ago, a Japanese company brought out the Panex Puzzle. It is a fiendish elaboration of the ancient Tower of Hanoi, and it is so difficult that the smallest number of moves needed to solve it remains unknown. In a broad sense, every mechanical puzzles has certain mathematical elements. It is true that many delightful mechanical puzzles seem non-mathematical because they are solved by only an ‘aha!’ insight that is unrelated to mathematics. Yet even such insights, mysterious though they may be to a psychologist, are part of the kind of heuristic reasoning that is used by mathematicians when they discover an elegant proof of a theorem, or by scientists when a flash of insight leads to a fruitful theory.
–taken from the introduction to the book “Puzzles Old & New,” by Jerry Slocum and Jack Botermans.
BOOKS ON MECHANICAL PUZZLES
Slocum, Jerry, and Botermans, Jack. Puzzles Old and New. Seattle, WA: University of Washington Press, 1986. Excellent book on mechanical, dexterity, and paper puzzles, including those made by the Embossing Co., McLoughlin Bros., Parker Bros., Pressman, Selchow & Righter and other game companies; 160 pages of historical data, color photos, puzzle plans, bibliography.
—. New Book of Puzzles. W.H. Freeman, 1992. 101 classic & modern puzzles to make & solve.
—. The Book of Ingenious and Diabolical Puzzles. New York, NY: Times Books/Random House, 1994. Guide to antique and modern puzzles with color photos includes 600 antique & new puzzles on 160 pages, with history & photos.
—. Optical Illusions and Other Puzzles. Books UK, Ltd., 1995. Optical illusions, hidden figures & other puzzles.
Slocum, Jerry. The Puzzle Arcade. Palo Alto, CA: Klutz Publ., 1996. Mechanical, word and logic puzzles for all the family from 7 to 100 years. – Spiral bound with puzzles in pouches; includes hints and solutions.
—. Swipe This Pencil. Klutz Press, 2003.
—. The Tangram Book. Sterling, 2003.
—. The 15 Puzzle Book. Beverly Hills, CA: Slocum Puzzle Foundation, 2006.
—. The Tao of Tangram. New York: Sterling, 2007.
—. Tangram Master. New York: Sterling, 2008.
—. The Famous 15 Puzzle. New York: Metro Books, 2009.
—. The Cube: The Ultimate Guide to the World’s Bestselling Puzzle – Secrets, Stories, Solutions. New York: Black Dog & Leventhal, 2009.
For more information contact Jerry Slocum at: JSlocum@Earthlink.net.
