The History of Sudoku — Born in America, Named in Japan
The history of Sudoku is not one country’s invention story but a relay across three stages. The rules were completed in the United States in 1979 under the name “Number Place”; the name and the puzzle-making culture flourished in Japan in the 1980s; and the decisive push into a global craze came from a British newspaper in 2004. Each of three names gets called the inventor at one point or another—the lines “Maki Kaji invented it,” “Wayne Gould made it,” and “Euler was the original” each circulate widely. The contributions the records credit to the three men, though, sit at different stages. Separating their roles brings each contribution into sharper focus.
1979, United States — The rules take hold
The direct starting point of modern Sudoku is the American magazine Dell Pencil Puzzles & Word Games, in May 1979. It appeared in issue 16 under the name “Number Place.” Early puzzles included an extra device—placing separately given numbers into circled cells—but the core rule that each row, column, and 3×3 box must contain 1 through 9 exactly once was already complete, and that extra device later disappeared (Ed Pegg Jr.’s survey).
The person credited as its creator is Howard S. Garns (1905–1989), a retired architect from Indianapolis. He was 74 when the first puzzle ran. Here a precise point is worth making: the original pages carried no author’s name. The basis for regarding Garns as the creator is a pattern that Will Shortz, the New York Times puzzle editor, found by combing through back issues of Dell. Garns appeared on the contributor list in the issues that carried Number Place, and his name was absent from the issues that did not. So the phrasing this circumstantial evidence supports is “Garns is widely credited as its creator.” In that it reconstructs a blank’s answer from surrounding clues, the very way the creator was identified resembles Sudoku itself (Crown Hill Heritage Foundation biography).
Garns died in 1989. He never saw the puzzle he made blanket the globe fifteen years later.
1984–1988, Japan — A name and a culture attach
The puzzle was brought to Japan by the puzzle company Nikoli. Nikoli does not claim to have invented it. On the contrary, its official history states that the company discovered Number Place in the American magazine and introduced it to Japanese readers in 1984 (Nikoli’s official history). The person who led this was Nikoli’s founder, Maki Kaji.
The origin of the name also breaks into two stages, more than the compressed version usually told. According to the Japan Sudoku Association’s records, in April 1984 Kaji ran a puzzle of his own in Monthly Nikolist under the long title “数字は独身に限る” (“the digits must be single”) (Japan Sudoku Association history). It is a pun: within the same row, column, or box, no digit may be paired with a copy of itself. The abbreviated form used today, 数独 (Sudoku), took firm hold when Nikoli’s book edition appeared in 1988. It is a compound of the first characters of 数 (number) and 独 (single). So the naming happened across two moments rather than one. The common summary that “the name Sudoku was coined in Japan in 1984” points to the earlier of them: the long-titled introduction in 1984, and the settling of today’s abbreviation 数独 in 1988 (Kaji’s recollection in Japan Policy Forum).
Nikoli’s larger legacy is an editorial culture. From 1986, Nikoli made symmetric placement of the clue numbers a principle of its puzzle-making. Symmetry is not a mathematical rule required to force a unique solution. But it makes a puzzle look like a visual work, and it let a handmade puzzle carry its setter’s personality. The participatory culture in which readers submitted their own puzzles and refined one another’s also grew from here. It is thanks to this tradition that, in the 2005 British newspaper rivalry, The Guardian later made a point of difference out of using Nikoli’s handmade puzzles instead of computer-generated ones.
A paradox around the name is also worth noting. Nikoli is said to have secured the 数独 trademark in Japan while not registering it broadly abroad. As a result, inside Japan other publishers avoid the trademark by using the English-style name “ナンプレ” (nanpure, short for Number Place), while in the English-speaking world the Japanese-style name “Sudoku” serves as the genre’s name. The English name stayed in Japan, and the Japanese name became the global word in English. Kaji recalled that not monopolizing the trademark abroad hurt revenue but helped the puzzle spread.
1997–2005 — Wayne Gould and globalization
The person who ended the roughly twenty years in which Sudoku remained nearly unknown outside Japan is Wayne Gould, a New Zealander who served as a judge in Hong Kong. By his own account, he came across a Sudoku book in a Tokyo bookstore in 1997. He could not read Japanese, but he says he understood the rules from the grid alone. This independence from language later became a key condition for globalization (The Independent, “The rise and rise of Sudoku”).
What Gould did was less the invention of a puzzle than the invention of a supply chain. Over about six years he built a computer program that generated new puzzles and graded their difficulty. It could produce far more puzzles than a person making them by hand, and newspapers could now be supplied a steady stream of puzzles at different difficulty levels every day.
Gould’s first newspaper puzzle ran in September 2004 in The Conway Daily Sun, a local paper in New Hampshire, United States. The popular turning point, though, was London. Gould went to The Times newsroom carrying a mock-up page he had assembled himself with a Sudoku in place. The features editor Mike Harvey at first tried to send him away, but by his recollection, on seeing the finished page mock-up he decided to adopt it in about two minutes (The Guardian, 2005). The Times ran its first puzzle on 12 November 2004, spelled “Su Doku.”
What followed was fast. By May 2005, national British papers—The Telegraph, The Independent, The Guardian, the Daily Mail, The Sun—were running Sudoku as if in competition. The Sun promoted it with its own name as “Sun doku,” and the first print run of a dedicated magazine was on the order of 100,000 copies. According to the TIME 100 profile written by Will Shortz in 2006, Gould’s puzzles ran in more than 400 newspapers worldwide and related books sold more than four million copies (TIME 100 — Wayne Gould).
So the 2005 boom was not merely “a good puzzle being discovered naturally.” It was a media event where Japan’s handmade-puzzle culture, computer generation technology, competition among newspapers for readers, and free-distribution marketing all met in one place. On top of that layered the conditions that it needs no translation because it is numbers, that its rules take a few lines to explain, that printing it takes just one grid, and that a new puzzle can be issued every day.
Sudoku by the numbers
Sudoku has also been good material for mathematicians. All three numbers below are values that were computed or proven.
6,670,903,752,021,072,936,960 — the total number of completed 9×9 grids that satisfy the rules, about 6.67×10²¹. Bertram Felgenhauer and Frazer Jarvis computed it in 2005, and Ed Russell checked it with a separate program (the Felgenhauer–Jarvis calculation page). Note that this is not “the number of puzzles you can make” but the number of valid completed solution grids. Even from a single completed grid, many puzzles arise depending on which cells you leave as clues, and a great many of them do not have a unique solution.
5,472,730,538 — the number of “essentially different” grids, counting as one all those that become identical under rotation and reflection, relabeling of the digits, and rule-preserving row and column swaps: about 5.47 billion. Russell and Jarvis computed it (Russell–Jarvis, Mathematics of Sudoku II). The earlier 6.67×10²¹ and this 5.47 billion are not the same thing counted differently; they are answers to different questions in the first place.
17 — the minimum number of clues needed for a puzzle to guarantee a unique solution. Puzzles with 17 clues and a unique solution had long been known, but whether one with 16 could ever exist stayed open for years. In 2012 a team of Gary McGuire, Bastian Tugemann, and Gilles Civario proved that it cannot (the University College Dublin announcement). They did not blindly try every way of choosing 16 of the 81 cells. They found sets of cells that could switch to a different completion (an “unavoidable set”) and searched efficiently by considering only candidates that touch all of those sets. It took about a year and seven million CPU hours on equipment at the Irish Centre for High-End Computing (ICHEC). The result was released in 2012 and the peer-reviewed publication in the journal Experimental Mathematics came in 2014, so “proven in 2012” and “paper published in 2014” do not contradict each other (arXiv:1201.0749).
One thing is worth stating candidly. This is not a pencil-and-paper proof but one that leans on a vast computer search, so in principle the possibility remains that the search code had an error. The reason the result is nonetheless accepted lies not in the authority of the journal but in its structure: it is a claim that would collapse the instant even a single 16-clue puzzle with a unique solution were found, yet no counterexample has appeared since its release, and across the tens of thousands of 17-clue puzzles collected beforehand, a 16-clue one never turned up.
The range this number 17 covers is worth noting too. 17 refers to “the fewest clues for which a puzzle with a unique solution can exist.” At the level of individual puzzles, a 17-clue arrangement need not have a unique solution, and the tie between clue count and felt difficulty is loose—the difficulty a person feels is known to depend more on the reasoning techniques a solution requires than on the number of clues.
Championships, Euler, and two anecdotes
The first international competition was the inaugural World Sudoku Championship, held in Lucca, Italy, in March 2006. Eighty-five contestants from 22 countries took part, and the winner was Jana Tylová, a 31-year-old accountant from the Czech Republic. At the ceremony, Wayne Gould handed over the winner’s trophy (Guinness World Records). It means the hobby became an international discipline about sixteen months after the newspaper craze began.
When people discuss Sudoku, the Latin squares of the 18th-century mathematician Leonhard Euler are often mentioned as an ancestor. The two clearly resemble each other in that no symbol appears twice in a given row or column. But a Latin square has no condition that each 3×3 block must contain 1 through 9. So, put as a relationship, a completed Sudoku grid is described as a special Latin square with the 3×3-block constraint added. The origin statement “Euler invented Sudoku” and the relational statement of being “a structural relative” are claims on different levels.
Finally, one anecdote showing how much Sudoku can grip people. According to Australian news reports, in 2008 a drug trial in Sydney was aborted. After more than 100 witnesses had testified over about three months, it emerged that several jurors had been solving Sudoku instead of listening to the testimony. They appeared to be taking diligent notes, but what was written in their notebooks was numbers, not the trial record, so the reports say (ABC News Australia).