A puzzle is a problem having one or more specific objectives, contrived for the principal purpose of exercising one's ingenuity and/or patience. This definition, whilst separating the recreational aspects of puzzles from the undesirable features of problems, in no way explains why humans find them so necessary or enjoyable. A random survey will usually show that nearly everyone has recently played with a jigsaw, a crossword, or a mechanical puzzle and that they have answered a riddle or composed a pun. One might have anticipated that, with lives full of worries about the unavoidable problems of survival, mankind would studiously avoid volunteering to solve any unnecessary puzzles. The reality is different. Puzzles are found in every culture from their early myths and religions through to their airport shops and internet websites. It seems that evolution has identified the didactic value of puzzles and now they are a part of what makes us a successful species.
In the past when most people could not read, pub signs and coats of arms often incorporated visual puns. In much early art there is imagery that appears puzzling to us today only because we have forgotten either the meaning of the symbols or the function of the object depicted. Many word puzzles were produced combining the visual and riddling context into anagrams and acrostics. There is a book (
Anagrammata regia) published in 1626 which contains anagrams, chronograms (where the capitalized letters are added together to produce the date of publication), and a triple acrostic. Rebuses, in which pictures replace some or all of the words, were very popular in the 18th century; some are more puzzling today than when they were produced — from looking at a tiny picture, would you recognize a porter's knot? The porter's knot could be used to represent 'not'. Some were very silly: a 'snake' might be used to represent 'Hiss' or 'His' as in 'His Royal Highness'.
Riddles, like crossword clues and rebus picture puzzles, usually rely on special, often culturally exclusive, knowledge whereas mechanical puzzles transcend cultural and language barriers. A mechanical puzzle is a physical object that incorporates the definition given at the beginning of this article. The mechanical puzzle contains all that is required for its solution within itself.
Legend tells that Gordius, a minor king in Anatolia
c.300 bc, had tied his ox cart to the temple gate with an intricate knot. As it was prophesied that whoever untied the Gordian Knot would rule all Asia, it may be considered as early example of both a topological puzzle and a puzzle competition. Alexander the Great arrived and promptly cut the knot. This has been held up as an example of lateral thinking, of decisiveness, and of tackling problems in novel ways; however, what succeeding generations have generally failed to notice is that this was cheating and, just as validly, it may be reasoned that this is why Alexander never did rule the whole of Asia.
Archimedes is reputed to have played with a dissected square puzzle; did this perhaps start with the accidental breaking of a tile? If you drop a china plate, have you just invented an assembly puzzle? Tangle a ball of wool — is it a topological puzzle? Even these accidental problems can become puzzles if approached in a recreational way.
'Cup and ball' is one of the earliest dexterity puzzles and together with its variants, where you have to try and stab a stick through bone rings, has probably been popular since neolithic times, to develop stabbing skills.
Two thousand years ago, Hero of Alexandria wrote in his work about pneumatics of various 'trick' vessels, among others for pouring wine and water from the same jug, and for producing 'magic' fountains. The Exeter Museum in England has a magnificent puzzle jug made
c.1300 in France. This is a true puzzle jug with the challenge of drinking from the jug without spilling any liquid through the many holes below the rim.
Before the existence of local banks, one concealed one's valuables in secret compartments, which were the precursors of puzzle boxes. Before the technical sophistication of the 1800s, many locks relied on puzzling mechanisms in addition to, or instead of, a key. The so-called 'Chinese rings puzzle' was used in many parts of the world as a lock (Fig. 1), and, though it was probably more of a delayer than a real deterrent to a thief, it certainly qualifies as an early tanglement puzzle. The mathematician Cardan wrote about it in 1550.
A six-piece burr puzzle is illustrated in Sebastien Leclerc's engraving of
The Academy of Science and Arts in 1698. However objects manufactured solely as puzzles did not really manifest themselves until the start of the Industrial Revolution and the advent of a relatively wealthy middle class and a wider number of people seeking and able to afford an education for their children. Initially puzzles were produced as paper or wood versions of problems that were appearing in books of recreational mathematics and 'natural philosophy', as Science was called. The jigsaw was initially invented to teach geography, but history, religion, and other subjects soon followed and finally they were developed for purely recreational purposes.
Around 1810 tangrams (a puzzle in which seven geometric pieces are used to create many pictures) and other ivory puzzles began to arrive in Europe and the USA from China. However there is no evidence, other than hearsay, that any puzzles, other than the tangram, were made in China for the Chinese prior to this date. Of the ivory puzzles that came from China apart from the tangram, most had been documented as existing in Europe beforehand and so it is not unreasonable that they were originally made exclusively to the order of Westerners for the export trade. The most significant feature of these puzzles is that, apart from jigsaws, they were the only puzzles that most people ever saw; thus 'Chinese puzzle' became the generic term for any mechanical puzzle other than jigsaws or dissected maps. To Europeans the Chinese were an enigmatic race full of mystery and secrets and so it would be natural, albeit maybe incorrectly, to credit them with the invention of such devious objects.
As industrial society developed, both leisure time and the number of puzzles being manufactured increased. William Jones's
Catalogue of Optical, Mathematical, and Philosophical Instruments (1788) lists only a few puzzles among his scientific apparatus. In the 1840s a Mr Crambrook was producing a catalogue with over 100 puzzles and holding what is believed to be the first ever puzzle exhibition. In 1893 Hoffmann published his
Puzzles Old and New listing several hundred puzzles in then current production, but even he was only scratching the surface of what had become available.
Puzzle crazes probably started with a tangram craze in the 1820s, followed by the 'fifteen-puzzle' craze in the 1870s. There was a well-known puzzle of arranging the numbers 1 to 16 on a four by four grid so that each line adds up to 34. Sam Loyd removed the number 16 and arranged the remaining numbers in order apart from the numbers 14 and 15. He then offered the huge prize of $1,000 to anyone who could put the puzzle in order by only sliding the pieces. Today it does not take us long to understand that a solution only exists for half the possible starting arrangements of the fifteen blocks, and that an arrangement with only 14 and 15 in the wrong order is one with no solution. However at that time most people could not comprehend why, having randomly put the pieces in the tray, sometimes they could find the solution and sometimes not. This lack of comprehension led to a craze, which spread from the USA to Europe. Loyd never actually claimed to have invented the fifteens puzzle, but he certainly started a craze the like of which was not seen again until the Rubik's cube of the 1980s which generated similar hysteria, with possibly up to 160 million being sold worldwide. It raises the interesting thought that perhaps in 2100 people will look at the cube and wonder why in the 1980s we found it so difficult to solve.
Before the computer and communications revolution the same puzzle ideas were reinvented again and again. Today there are more different types of puzzle than ever before. The exchange of ideas and information on the internet is reducing the duplication of effort and enabling the creation of ever more baffling puzzles. There is now a continuous and entertaining struggle between metagrobologists (people who are puzzled or puzzling): some use computers to solve puzzles, some use computers to make puzzles more difficult, and some search for puzzles that cannot be solved on a computer at all. Craftsmen who could never have made a living by making such exclusive items twenty years ago can now find customers for highly complex puzzles anywhere in the world. Thus the latest technology is enabling a revival of traditional crafts applied to new ideas. Computers are also enabling the modelling of puzzles in virtual reality that cannot exist in our physical three-dimensional world; for example, assembly puzzles where pieces are composed of cubes joined by their corners, and mazes in non-Euclidian space where taking three right turns on a square grid does not bring you back to your starting point.
When playing with a puzzle we are having too much fun to notice that we are exercising our brains. Puzzles play tricks with the way we think and teach us to think in new ways.
Fig. 1. Ivory cup and ball, Chinese rings, tangram, and six-piece burr.
(Published 2004)— James Dalgety
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