Puzzle

A puzzle is a game, problem, or toy that challenges a person's ingenuity or knowledge. To solve one, the solver typically assembles or disassembles pieces in a logical manner to reach the correct answer. Puzzles come in various types, such as crosswords, word searches, number puzzles, relational puzzles, and logic puzzles. The formal study of puzzles is known as enigmatology.

Puzzles are often made for entertainment, but they can also stem from serious math or logic issues, where solving them might contribute meaningfully to mathematical research.

The word "puzzle" first appeared as a verb in the 16th century, with its earliest recorded use around 1595 in a travel narrative. It later became a noun, first meaning a state of confusion, then a perplexing problem. The first clear use as a toy that tests skill comes from Sir Walter Scott's 1814 novel *Waverley*, referring to a "reel in a bottle." The verb's origin is unknown, though guesses include an Old English word for "pick out" or a derivation of "pose."

Puzzles can be grouped into many categories. Lateral thinking puzzles, also called situation puzzles, rely on creative reasoning. Mathematical puzzles include the missing square puzzle and impossible ones like the Seven Bridges of Königsberg. Sangaku are Japanese temple tablets with geometry puzzles. Chess problems, such as the knight's tour, use chess pieces on a board. Mechanical or dexterity puzzles, like the Rubik's Cube and Soma cube, are popular toys. Other types include combination puzzles (Peg solitaire), construction puzzles (stick puzzles), disentanglement puzzles, folding puzzles, jigsaw puzzles (including 3D variants like Puzz 3D), lock puzzles, puzzle boxes for hiding items, sliding puzzles (like the 15 Puzzle and Sokoban), and tiling puzzles (like Tangram). Metapuzzles combine elements from other puzzles. Paper-and-pencil puzzles include connect the dots and nonograms, plus logic puzzles from Nikoli such as Sudoku, Slitherlink, and Kakuro. Spot the difference, mazes, and word puzzles (anagrams, ciphers, crosswords, Hangman, word searches) also fall under this umbrella. Tabletop and digital word puzzles include Bananagrams, Boggle, Scrabble, and Words with Friends. Puzzle video games cover tile-matching games, puzzle-platformers, adventure games, hidden object games, and Minesweeper.

Solving puzzles often requires recognizing patterns and following a specific order. People with strong inductive reasoning may solve some puzzles more easily, while those with good deduction skills might handle inquiry-based puzzles better. Deductive reasoning improves with practice. Mathematical puzzles frequently use BODMAS (Bracket, Of, Division, Multiplication, Addition, Subtraction) or PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to set the order of operations. Some puzzles use a top-to-bottom convention to avoid ambiguity.

Puzzle makers create puzzles. A puzzler or puzzlist is someone who composes or solves them. Notable creators include Ernő Rubik, Sam Loyd, Henry Dudeney, Boris Kordemsky, Will Shortz, Oskar van Deventer, Lloyd King, Martin Gardner, and Raymond Smullyan.

The nine linked-rings puzzle, which requires math to solve, was invented in China during the Warring States period (475-221 BCE). Jigsaw puzzles were invented around 1760 by John Spilsbury, who mounted a map on wood and cut around each country for geography teaching. This teaching aid remained the primary use of jigsaw puzzles until about 1820. The largest puzzle (40,320 pieces) is made by Ravensburger; the smallest, the size of a sand grain, was created at LaserZentrum Hannover. The earliest documented puzzles were riddles, including the riddle of the Sphinx from Greek mythology, with many more produced in the Middle Ages. By the early 20th century, magazines and newspapers boosted readership with puzzle contests, starting with crosswords and later sudoku.