Hey everyone! Can you play Sudoku? Do you like this game? It is certainly not a game for everyone as it requires a lot of concentration and patience. But what exactly is Sudoku?
Sudoku is a logic-based, combinatorial number-placement puzzle. In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid (also called “boxes”, “blocks”, or “regions”) contain all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.
French newspapers featured variations of the Sudoku puzzles in the 19th century, and the puzzle has appeared since 1979 in puzzle books under the name Number Place. However, the modern Sudoku only began to gain widespread popularity in 1986 when it was published by the Japanese puzzle company Nikoli under the name Sudoku, meaning “single number”. It first appeared in a U.S. newspaper, and then The Times, in 2004, thanks to the efforts of Wayne Gould, who devised a computer program to rapidly-produce unique puzzles.
Number puzzles appeared in newspapers in the late 19th century, when French puzzle setters began experimenting with removing numbers from magic squares. Le Siècle, a Paris daily, published a partially completed 9×9 magic square with 3×3 subsquares on November 19, 1892. It was not a Sudoku because it contained double-digit numbers and required arithmetic rather than logic to solve, but it shared key characteristics: each row, column, and subsquare added up to the same number.
On July 6, 1895, Le Siècle’s rival, La France, refined the puzzle so that it was almost a modern Sudoku and named it carré magique diabolique (‘diabolical magic square’). It simplified the 9×9 magic square puzzle so that each row, column, and broken diagonals contained only the numbers 1–9, but did not mark the subsquares. Although they were unmarked, each 3×3 subsquare did indeed comprise the numbers 1–9, and the additional constraint on the broken diagonals led to only one solution.
These weekly puzzles were a feature of French newspapers such as L’Écho de Paris for about a decade but disappeared about the time of World War I.
The modern Sudoku was most likely designed anonymously by Howard Garns, a 74-year-old retired architect and freelance puzzle constructor from Connersville, Indiana, and first published in 1979 by Dell Magazines as Number Place (the earliest known example of modern Sudoku). Garns’s name was always present on the list of contributors in issues of Dell Pencil Puzzles and Word Games that included Number Place and was always absent from issues that did not. He died in 1989 before getting a chance to see his creation as a worldwide phenomenon. Whether or not Garns was familiar with any of the French newspapers listed above is unclear.
The puzzle was introduced in Japan by Maki Kaji, president of the Nikoli puzzle company, in the paper Monthly Nikolist in April 1984 as Sūji wa dokushin ni kagiru (数字は独身に限る), which can be translated as “the digits must be single”, or as “the digits are limited to one occurrence” (In Japanese, dokushin means an “unmarried person”). The name was later abbreviated to Sudoku (数独), taking only the first kanji of compound words to form a shorter version. “Sudoku” is a registered trademark in Japan and the puzzle is generally referred to as Number Place (ナンバープレース, Nanbāpurēsu) or, more informally, a shortening of the two words, Num(ber) Pla(ce) (ナンプレ, Nanpure). In 1986, Nikoli introduced two innovations: the number of givens was restricted to no more than 32, and puzzles became “symmetrical” (meaning the givens were distributed in rotationally symmetric cells). It is now published in mainstream Japanese periodicals, such as the Asahi Shimbun.
Cognitive scientist Jeremy Grabbe found that Sudoku involved an area of cognition called working memory. A subsequent experiment by Grabbe showed that routine Sudoku playing could improve working memory in older people.
Although the 9 × 9 grid with 3 × 3 regions is by far the most common, many other variations exist. Sample puzzles can be 4 × 4 grids with 2 × 2 regions; 5 × 5 grids with pentomino regions have been published under the name Logi-5; the World Puzzle Championship has featured a 6 × 6 grid with 2 × 3 regions and a 7 × 7 grid with six heptomino regions and a disjoint region. Larger grids are also possible, or different irregular shapes (under various names such as Suguru, Tectonic, Jigsaw Sudoku, etc.). The Times offers a 12 × 12-grid “Dodeka Sudoku” with 12 regions of 4 × 3 squares. Dell Magazines regularly publishes 16 × 16 “Number Place Challenger” puzzles (using the numbers 1–16 or the letters A-P). Nikoli offers 25 × 25 “Sudoku the Giant” behemoths. A 100 × 100-grid puzzle dubbed Sudoku-zilla was published in 2010.
Under the name “Mini Sudoku”, a 6×6 variant with 3×2 regions appears in the American newspaper USA Today and elsewhere. The object is the same as that of standard Sudoku, but the puzzle only uses the numbers 1 through 6. A similar form, for younger solvers of puzzles, called “The Junior Sudoku”, has appeared in some newspapers, such as some editions of The Daily Mail.
Another common variant is to add limits on the placement of numbers beyond the usual row, column, and box requirements. Often, the limit takes the form of an extra “dimension”; the most common is to require the numbers in the main diagonals of the grid to also be unique. The aforementioned “Number Place Challenger” puzzles are all of this variant, as are the Sudoku X puzzles in The Daily Mail, which use 6×6 grids.
Alphabetical variations have emerged, sometimes called Wordoku; no functional difference exists in the puzzle unless the letters spell something. Some variants, such as in the TV Guide, include a word reading along a main diagonal, row, or column once solved; determining the word in advance can be viewed as a solving aid. A Wordoku might contain words other than the main word.
“Quadratum latinum” is a Sudoku variation with Roman numerals (I, II, III, IV, …, IX) proposed by Hebdomada aenigmatum, a monthly magazine of Latin puzzles and crosswords. Like the Wordoku, it presents no functional difference from a normal Sudoku but adds the visual difficulty of using Roman numerals.
Hyper Sudoku or Windoku uses the classic 9×9 grid with 3×3 regions but defines four additional interior 3×3 regions in which the numbers 1–9 must appear exactly once. It was invented by Peter Ritmeester and first published by him in Dutch Newspaper NRC Handelsblad in October 2005, and since April 2007 daily in The International New York Times (International Herald Tribune). The first time it was called Hyper Sudoku was in Will Shortz’s Favorite Sudoku Variations (February 2006). It is also known as Windoku because with the grid’s four interior regions shaded, it resembles a window with glazing bars.
In Twin Sudoku two regular grids share a 3×3 box. This is one of many possible types of overlapping grids. The rules for each individual grid are the same as in normal Sudoku, but the digits in the overlapping section are shared by each half. In some compositions neither individual grid can be solved alone – the complete solution is only possible after each individual grid has at least been partially solved.
The Killer Sudoku variant combines elements of Sudoku and Kakuro.
Puzzles constructed from more than two grids are also common. Five 9×9 grids that overlap at the corner regions in the shape of a quincunx is known in Japan as Gattai 5 (five merged) Sudoku. In The Times, The Age, and The Sydney Morning Herald, this form of puzzle is known as Samurai Sudoku. The Baltimore Sun and the Toronto Star publish a puzzle of this variant (titled High Five) in their Sunday edition. Often, no givens are placed in the overlapping regions. Sequential grids, as opposed to overlapping, are also published, with values in specific locations in grids needing to be transferred to others.
A tabletop version of Sudoku can be played with a standard 81-card Set deck. A three-dimensional Sudoku puzzle was published in The Daily Telegraph in May 2005. The Times also publishes a three-dimensional version under the name Tredoku. Also, a Sudoku version of the Rubik’s Cube is named Sudoku Cube.
Many other variants have been developed. Some are different shapes in the arrangement of overlapping 9×9 grids, such as butterfly, windmill, or flower. Others vary the logic for solving the grid. One of these is “Greater Than Sudoku”. In this, a 3×3 grid of the Sudoku is given with 12 symbols of Greater Than (>) or Less Than (<) on the common line of the two adjacent numbers. Another variant on the logic of the solution is “Clueless Sudoku”, in which nine 9×9 Sudoku grids are each placed in a 3×3 array. The center cell in each 3×3 grid of all nine puzzles is left blank and forms a tenth Sudoku puzzle without any cell completed; hence, “clueless”. A new variant mixes Sudoku with the sliding tile puzzle in Sudoku Slide Extreme. In this variant, all of the positions are filled in. Tiles are moved to the proper position to solve the puzzle. This variant contains power-ups and a campaign mode. Examples and other variants can be found in the Glossary of Sudoku.
Dear readers!
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