The history of Sudoku

Latin squares: the idea underneath

A Latin square is a grid in which every symbol appears exactly once in each row and once in each column. The Swiss mathematician Leonhard Euler studied them at length around 1780 and gave them their name, because he filled his grids with Latin letters. One of his questions, about arranging 36 officers of six ranks and six regiments in a square, stayed open until 1900, when Gaston Tarry showed it could not be done.

Every finished Sudoku is a Latin square with one more condition: the nine boxes must each hold all nine digits too. That extra rule is what makes it a puzzle you can solve from a handful of clues. Euler was studying the mathematics of these grids and never set them as puzzles, so he is an ancestor of Sudoku and not its inventor.

Number puzzles in French newspapers

In the 1890s, Paris newspapers printed number puzzles on nine-by-nine grids that look strikingly familiar. Le Siècle ran one in 1892 that was partly filled in and divided into three-by-three squares, although it was a magic square, built on sums, and used numbers larger than nine.

In 1895 the paper La France came closer. Its puzzle used only the digits 1 to 9, once in each row and each column. The boxes weren’t marked or mentioned, but the published solution had every digit once in each of them. Puzzles of this kind appeared in French papers for some years and then faded from view around the First World War.

Nothing links these puzzles to the modern one. They show that the idea was close at hand, and that it was invented again later by someone who had probably never seen them.

Howard Garns and Number Place, 1979

The modern puzzle first appeared in May 1979 in Dell Pencil Puzzles and Word Games, an American magazine, under the name Number Place. It had the nine-by-nine grid, the nine boxes and the rule we still use: each digit once in every row, column and box.

Dell printed it without a byline. The puzzle is credited to Howard Garns, a retired architect from Indiana, largely through the work of the puzzle editor Will Shortz, who noticed that Garns’s name appeared in the list of contributors in the issues that carried Number Place and was missing from the ones that didn’t.

Garns died in 1989. Number Place was a regular feature in Dell’s magazines by then, but he didn’t live to see what it became.

Nikoli gives it a name

In 1984 the Japanese puzzle publisher Nikoli began printing the puzzle in its magazine. Maki Kaji, the company’s president, gave it a long title, Sūji wa dokushin ni kagiru, which means roughly “the digits must be single”. It was soon shortened to Sudoku: sū for number, doku for single.

Nikoli also changed how the puzzles felt. Its grids were composed by hand, and from 1986 the company kept the givens to 32 or fewer and arranged them in a symmetrical pattern. The result was a puzzle with a clear path through it, and it became one of the most popular in Japan.

Other Japanese publishers generally kept the older name, so in Japan the puzzle is still widely known as Number Place, or Nanpure for short. Kaji, who spent decades promoting Sudoku around the world, died in 2021.

Wayne Gould and The Times, 2004

In 1997 Wayne Gould, a retired Hong Kong judge from New Zealand, came across a book of Sudoku in a Tokyo bookshop. He spent the next six years writing a computer program that could produce puzzles quickly and grade their difficulty.

Gould offered the puzzles to newspapers. A small New Hampshire paper, the Conway Daily Sun, began running them in the autumn of 2004, and The Times of London printed its first Sudoku on November 12, 2004. A newspaper could now publish a fresh puzzle every day without a team of setters, and readers needed no vocabulary or general knowledge to solve it.