The Surprising History of Sudoku, From Latin Squares to Tokyo

Sudoku looks ancient. The grid, the elegance, the air of timeless puzzle-craft: it feels like something monks should have passed down for centuries. The truth is much stranger and much more recent. The puzzle as we know it is barely fifty years old. It was invented in Indiana, retitled in Tokyo, popularised in a small Japanese magazine, and detonated into a global craze by a retired New Zealand judge with a laptop and a newspaper deal. Almost every step of that journey was accidental.

The mathematical idea behind sudoku is much older. To explain how we got here, we have to start with Leonhard Euler.

1782: Euler and the Latin square

In 1782, the Swiss mathematician Leonhard Euler studied a puzzle he called the “Thirty-Six Officers Problem.” The question: can you arrange thirty-six officers, of six ranks from six regiments, in a 6×6 square such that each rank and regiment appears exactly once in each row and column? Euler conjectured no, and a 1959 computer search proved him right for that specific size.

Along the way, Euler formalised the notion of the Latin square: an n×n grid filled with n different symbols such that each symbol appears exactly once in each row and column. (He used Latin letters, hence the name; the 37 officers problem used two Latin squares overlaid, a Graeco-Latin square.) The Latin square is the pure mathematical ancestor of sudoku. Take a 9×9 Latin square, add the constraint that each 3×3 sub-grid must also contain all nine symbols, and you have a solved sudoku.

Euler never proposed the box constraint, though he’d have liked it. The additional structure makes the puzzle just constrained enough to admit unique solutions, while remaining rich enough to support meaningful logic.

1892: The proto-sudoku in Le Siècle

In late 19th century France, several Paris newspapers ran a regular feature called carré magique diabolique, the “diabolical magic square.” In 1892, the newspaper Le Siècle published a 9×9 puzzle that bears a striking resemblance to modern sudoku: rows, columns, and broken sub-diagonals all required to contain unique digits. The puzzle was a number variant of the magic square tradition, and used arithmetic in ways modern sudoku does not.

The newspaper La France ran similar puzzles at the same time, sometimes including a 3×3 sub-grid constraint. But these French puzzles never coalesced into a recognisable genre. World War I ended the run, and the format was forgotten for the better part of a century.

1979: Howard Garns invents Number Place

The first true sudoku puzzle, with the same rules, the same structure, and the same look, was published in May 1979 by Howard Garns, a 74-year-old retired architect from Indianapolis. It appeared in Dell Pencil Puzzles & Word Games magazine under the title “Number Place.”

Garns’ design was already in its final form: a 9×9 grid divided into nine 3×3 boxes, with the rule that every row, column, and box must contain the digits 1 through 9 exactly once. The clue placements he chose for that first puzzle wouldn’t look out of place in a modern app. He had simply invented the puzzle, all at once, and Dell ran it as one of many rotating features.

The puzzle was popular enough to recur, but Number Place was never a hit on the scale Garns might have hoped for. Dell didn’t market it heavily; Garns himself didn’t patent the format or seek attribution. He died in 1989, before sudoku became globally famous, and was never publicly credited as the inventor in his lifetime. Modern puzzle historians have since recovered his role; the credit is now standard.

1984: Nikoli, Maki Kaji, and a name change

In April 1984, the Japanese puzzle publisher Nikoli ran Number Place in their flagship magazine Monthly Nikolist. The president of Nikoli, the late Maki Kaji, had spotted the format in an American magazine and brought it to Japan. He gave it a Japanese name: Suuji wa dokushin ni kagiru, roughly, “the digits must be single” or “the digits are limited to one occurrence.” The phrase was quickly shortened to sudoku (数独, “single number”).

Two of Kaji’s editorial decisions defined sudoku as a format and probably saved it from obscurity. The first: Nikoli insisted that puzzle clue placements be symmetric, specifically, rotationally symmetric around the centre. This is purely aesthetic, and it’s why a hand-designed sudoku looks more elegant than a randomly-generated one. The second: Nikoli capped the number of givens. Originally Number Place puzzles in Dell had as many givens as the editor felt like. Nikoli set a cap of roughly thirty. The result was puzzles that looked tighter, emptier, and harder, trading brute clue-count for elegant logic.

Kaji also made a decision he later described as one of the few regrets of his career: he didn’t trademark the name “sudoku” outside Japan. Inside Japan, Nikoli holds the trademark. Outside, the word entered the public domain. He called this his “biggest financial mistake.” It is also the reason sudoku is universally known by its Japanese name rather than its English one.

1997: Wayne Gould, the New Zealand judge

On a holiday to Tokyo in 1997, a retired Hong Kong court judge named Wayne Gould walked into a bookshop and picked up a Nikoli puzzle book. He didn’t speak much Japanese, but the puzzles needed no translation. Hooked, Gould spent the next six years building a computer program to generate sudoku puzzles automatically, calibrate their difficulty, and lay them out for print.

In 2004, Gould walked into The Times of London with a floppy disk and a pitch: he’d give the newspaper sudoku puzzles for free if they would credit his website, sudoku.com, in the byline. The Times’ editor agreed. Sudoku ran in the paper for the first time on 12 November 2004.

It is rare in modern publishing for a single editorial decision to ignite a global craze. This was one of those rare cases. Within weeks, The Daily Mail launched a competing sudoku feature. The Guardian, the Telegraph, the Independent followed. By the spring of 2005, The New York Post ran sudoku in the United States. Bookshops emptied of sudoku titles and reprinted them. Cabinet ministers were photographed solving puzzles. The word “sudoku” appeared in the Oxford English Dictionary. A puzzle dormant for two decades suddenly defined a year.

2006: Television, world championships, and the peak

The first World Sudoku Championship took place in March 2006 in Lucca, Italy, organised by the World Puzzle Federation. Jana Tylová, an accountant from the Czech Republic, won. The tournament has run annually since, with winners almost always coming from countries with strong national puzzle scenes: Czech Republic, Japan, the United States, and Hungary.

Sky One ran a televised sudoku show in the UK in 2005. A live-action sudoku contest was painted onto the side of a hill in Hertfordshire. Sudoku books outsold cookbooks for a year. A researcher at the University of Sheffield published a paper demonstrating that solving a 9×9 sudoku is, in the general case, NP-complete. The puzzle was cited in serious newspapers as a public-health intervention against cognitive decline (the evidence for which we cover in a separate article).

At the same time, the format started branching. Killer sudoku appeared in The Times in 2005. Samurai sudoku, with its five overlapping 9×9 grids, spread internationally from a Japanese variant tradition; we have a full guide in Samurai Sudoku. By the early 2010s, hundreds of named variants had been published.

The mathematics, briefly

The number of valid completed 9×9 sudoku grids was first calculated in 2005 by Bertram Felgenhauer and Frazer Jarvis: precisely 6,670,903,752,021,072,936,960. Accounting for symmetries (rotations, reflections, and digit relabellings), the number of essentially different completed sudoku grids is 5,472,730,538. These are large numbers, but comfortably finite: a modern computer can enumerate all unique grids in days.

The minimum number of givens for a uniquely-solvable sudoku was an open question for years. In 2012, three researchers at University College Dublin (Gary McGuire, Bastian Tugemann, and Gilles Civario) published a computer-assisted proof that the minimum is 17. Below 17 givens, every starting position has multiple valid completions. The proof took roughly seven million CPU-hours.

Maki Kaji and the legacy

Maki Kaji, the man who named sudoku, died in August 2021. By the time of his death, sudoku appeared daily in over six hundred newspapers worldwide, in dozens of dedicated apps, and as a feature in nearly every word-and-puzzle compilation sold in airport bookshops. Kaji’s personal motto for puzzles was that they should be the kind of thing solvers could explain in a sentence and enjoy for years. Sudoku, despite all its variants and depth, still passes that test.

The strange shape of sudoku’s history (American invention, Japanese branding, British launch, global craze) turns out to be exactly the right shape. Sudoku is a puzzle of constraints. Its history is too: the right format meeting the right editor meeting the right newspaper at the right cultural moment. Howard Garns is buried in Indianapolis. Maki Kaji is gone. Wayne Gould is in his eighties and still designs puzzles. The grid persists.

Where the puzzle is now

Sudoku is no longer a craze; it’s a permanent fixture, like the crossword. The newspaper page where it lives may not survive another generation, but the puzzle has migrated cleanly to apps and web players. Modern sudoku apps (including ours) generate puzzles algorithmically and verify them with logical solvers, so difficulty calibration is precise in a way Nikoli’s human editors never quite achieved, though Nikoli still publishes hand-designed puzzles for the connoisseurs, and the difference is real.

If you want to follow the thread forward, our guide to sudoku techniques covers the modern logical methods that solvers around the world use, and our guide to samurai sudoku covers the most popular variant of the post-2004 era.