How sudoku got from a New York magazine to the whole world
Sudoku did not start in Japan. The puzzle was first published in 1979 in an American puzzle magazine, Dell Pencil Puzzles and Word Games, under the name Number Place. It was given its Japanese name a few years later in Tokyo, and it only became a worldwide habit after a British newspaper started printing it in 2004.
The rules have stayed the same the whole way. Fill a nine by nine grid so that every row, every column and every three by three box contains the digits 1 to 9 exactly once.
Number Place in New York
The puzzles in Dell’s magazine carried no byline, and for years nobody outside the company knew who had made them. The setter was later identified as Howard Garns, a retired architect from Indiana, who is now generally credited as the inventor.
The underlying idea was older. A grid where each symbol appears once in every row and column is called a Latin square, and mathematicians had studied them since the eighteenth century. What Garns added was the third constraint, the boxes, and the format of a partly filled grid with a single correct completion. That extra rule is what turns a mathematical object into a puzzle you can solve with a pencil, because each empty square is now limited by three groups at once.
A name from Tokyo
In 1984 the Japanese puzzle publisher Nikoli came across Number Place and began printing it. Nikoli gave it a long name that translates roughly as “the digits must be single”, which was soon cut down to Sudoku, meaning “single digit”.
Nikoli also shaped how good sudoku puzzles are made. Its setters composed puzzles by hand and treated the grid as something to be designed, with the given digits usually placed in a symmetrical pattern. A well-made puzzle has exactly one solution and can be solved by reasoning alone, without guessing. Those two standards are still what separates a good sudoku from a bad one.
The newspaper that made it famous
Wayne Gould, a New Zealander who had worked as a judge in Hong Kong, found a book of the puzzles in a Tokyo bookshop in 1997. Gould then spent several years writing a computer program that could generate sudoku puzzles at different levels of difficulty.
The Times in London started printing Gould’s puzzles in November 2004. Other British papers followed within weeks, and by 2005 sudoku was in newspapers across the world and filled whole shelves of puzzle books. It crossed back to the United States, where it had started, now carrying its Japanese name.
Part of the appeal was that it needed no language at all. A crossword has to be written for one language and one culture, but a sudoku grid works the same way for anybody who can tell nine symbols apart. The digits are not even used as numbers. No arithmetic is involved, and the puzzle would work just as well with nine letters or nine colours.
What mathematicians found
The craze drew mathematicians in, and they answered some natural questions. In 2005 Bertram Felgenhauer and Frazer Jarvis counted the number of completed sudoku grids: 6,670,903,752,021,072,936,960. There is no danger of running out.
A harder question was how few given digits a puzzle can have and still have only one solution. Puzzles with 17 clues had been known for years, but nobody had found one with 16 or proved it impossible. In 2012 Gary McGuire, Bastian Tugemann and Gilles Civario settled it with an exhaustive computer search: no 16-clue sudoku has a unique solution, so 17 is the minimum.
The number of clues says little about difficulty, though. A puzzle with few clues can be easy if each step is obvious, and one with many can be hard if it needs a long chain of reasoning to make progress. Difficulty comes from the techniques a solver needs, which is why newspaper grades such as easy and fiendish are decided by the setter rather than by counting digits.
