Puzzle.

« Visual puzzles involve searching a picture to find hidden or disguised figures or answering a question about some part of a visual illusion.

For instance, the popular 19th- century prints of American lithographic company Currier & Ives featured hidden people, animals, and other objects.

A 16th-century painting from Bukhara, Uzbekistan,of a camel includes hidden figures of 17 people, 10 rabbits, a monkey, and a dragon (Metropolitan Museum of Art, New York City). B Mathematical Puzzles and Logic Puzzles While most fields of mathematics have created puzzles for both academic study and recreational use, recreational puzzles have also led to important developments inmathematics.

The fields of topology and graph theory have their origins in the analysis of a popular puzzle by Swiss mathematician Leonhard Euler.

The puzzle is to finda path over the seven bridges of Königsberg, Germany, without traveling over the same bridge twice.

Similar to mathematical puzzles are logic puzzles —puzzles that require deductive reasoning with little or no numerical calculation. B1 Mathematical Puzzles Some of the first number puzzles were included in an important ancient Egyptian mathematical document composed about 1650 BC and known as the Rhind Papyrus. Magic squares , another early form of number puzzle, originated in China before the end of the 1st century.

A magic square puzzle forms a square array of numbers so that the rows, columns, and major diagonals all have equal sums. In 1924 Henry Dudeney published a popular number puzzle of the type known as a cryptarithm, in which letters are replaced with numbers.

Dudeney's puzzle reads: SEND + MORE = MONEY.

Cryptarithms are solved by deducing numerical values from the mathematical relationships indicated by the letter arrangements.

The onlysolution to Dudeney's problem: 9567 + 1085 = 10,652. Geometric puzzles were studied by Greek mathematician Archimedes in the 3rd century BC, although it is not known whether he also designed the puzzles.

The Loculus of Archimedes is a dissection puzzle in which a square is cut into 14 pieces that are to be reassembled (a type of put-together puzzle ) to form silhouettes of people, animals, or objects.

In 1902 Dudeney published another type of geometric puzzle: Cut an equilateral (equal-sided) triangle into four pieces that can be reassembled intoa square. Logic puzzles and paradoxes were part of the study of logic in the 4th century BC by Greek philosophers, including Aristotle.

Zeno of Elea wrote famous paradoxes that attempted to prove that apparently obvious sensory experiences, such as the perception of motion, are in fact impossible.

In the 19th century Lewis Carroll popularizedseveral logic puzzles in storybooks such as A Tangled Tale (1880). One of the first computer puzzles originated in the mid-1970s as the computer program Adventure, an interactive series of written puzzles created by American computer programmers Willie Crowther and Don Woods and distributed on the computer network ARPANET, the predecessor to today's Internet.

The program's successled to a computer series titled Zork, a text-only story with puzzles that sold more than 1 million copies ( see Electronic Games: Computer Games ). C Physical and Mechanical Puzzles C1 Labyrinths and Mazes Labyrinths and mazes in life-size structures provide collective amusement in Japan and many other parts of the world.

More common are books of mazes designed to be solved by drawing a line from a starting point to an ending point without crossing various obstacles.

Also popular are hand-held dexterity mazes, in whichobjects—usually small balls—are manipulated in a small maze structure. C2 Mechanical Puzzles Put-together puzzles begin with several components that require a unique method of assembly or combination.

An early example is the Loculus of Archimedes, also called Stomachion. In jigsaw puzzles, flat interlocking cut-out pieces form a picture or figure when properly assembled.

These puzzles were invented by British mapmaker John Spilsbury about 1760 as an educational toy.

In the Chinese Tangram, prevalent since about 1800, seven regular geometric pieces cut from a single square are used to form hundreds of silhouettes of people, animals, and objects. Take-apart puzzles are mechanical puzzles that require opening a device, finding a secret compartment, or disassembling an object.

As early as the 17th century, trick- locks or puzzle-locks incorporated hidden keyholes to thwart thieves.

In the late 19th century, Native American women used decorated puzzle purses with a hiddencompartment to protect their money and gambling dice. The challenge of interlocking puzzles is found both in taking them apart and in putting them back together.

Beginning about 1800, popular puzzle shapes such as wooden-cross puzzles and burr puzzles (originally named for their resemblance to seed burrs) were sold by the German toy company Bestelmeier.

Since 1970,hundreds of interlocking puzzle designs in the shape of polyhedrons, three-dimensional geometrical objects, have appeared on the market. Disentanglement puzzles require the removal of trapped parts from loops or other assemblies.

Some of the earliest disentanglement puzzles, made of string, were described in Italian mathematician Jerome Cardan's publication De Rerum Varietate (1557).

A difficult mother-of-pearl string puzzle known as Solomon's Seal was owned by 18th-century American patriot John Hancock. Sequential-movement puzzles involve the maneuvering of puzzle parts, and they usually require a large number of steps, executed according to prescribed rules, to reach a goal.

This diverse class includes puzzles such as peg solitaire, described by German mathematician G.

W.

Leibniz about 1600; Chinese rings, described byCardan in 1550; sliding-piece puzzles such as the one known as the 14/15 Puzzle in the 1880s; and the Rubik's Cube of the early 1980s.

In peg solitaire, a player triesto remove all but one of the pegs by jumping one peg over another and removing the jumped peg.

The Chinese Rings puzzle consists of a series of linked rings (usuallyfive to ten) encircling a hairpin-shaped double-bar.

The object of the puzzle is to free all the rings from the double-bar.

The 14/15 Puzzle is made up of 15 consecutivelynumbered sliding blocks, all placed in a square tray large enough to hold 16 blocks.

After the pieces are scrambled, the solver tries to reorder them.

The Rubik's Cube isa three-dimensional extension of the same puzzle.

Initially each of the six sides of a Rubik's Cube is a different solid color.

The colors of the cube faces can be scrambledby twisting various sections of the cube around any of its three axes.

The challenge is to restore a scrambled cube to its original configuration. Another type of sequential-movement puzzle is the river-crossing puzzle, first described by Alcuin in one of his 9th-century texts.

The puzzle presents a farmer who has to transport a goat, a wolf, and some cabbages across a river in a boat that will only hold the farmer and one of the cargo items.

In this scenario, the cabbages will beeaten by the goat, and the goat will be eaten by the wolf, if left together unattended.

Solutions to river-crossing puzzles usually involve multiple trips with certain itemsbrought back and forth between the riverbanks. Dexterity puzzles are mechanical puzzles that depend—or seem to depend—upon hand-eye coordination, though logical techniques are often required to solve them.. »