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COMPUTING SCIENCE

Unwed Numbers

The mathematics of Sudoku, a puzzle that boasts "No math required!"

Brian Hayes

A Puzzling Provenance

The name "Sudoku" is Japanese, but the game itself is almost surely an American invention. The earliest known examples were published in 1979 in Dell Pencil Puzzles & Word Games, where they were given the title Number Place. The constructor of the puzzles is not identified in the magazine, but Will Shortz, the puzzles editor of The New York Times, thinks he has identified the author through a process of logical deduction reminiscent of what it takes to solve a Sudoku. Shortz examined the list of contributors in several Dell magazines; he found a single name that was always present if an issue included a Number Place puzzle, and never present otherwise. The putative inventor identified in this way was Howard Garns, an architect from Indianapolis who died in 1989. Mark Lagasse, senior executive editor of Dell Puzzle Magazines, concurs with Shortz's conclusion, although he says Dell has no records attesting to Garns's authorship, and none of the editors now on the staff were there in 1979.

The later history is easier to trace. Dell continued publishing the puzzles, and in 1984 the Japanese firm Nikoli began including puzzles of the same design in one of its magazines. (Puzzle publishers, it seems, are adept at the sincerest form of flattery.) Nikoli named the puzzle "suji wa dokushin ni kagiru," which I am told means "the numbers must be single"—single in the sense of unmarried. The name was soon shortened to Sudoku, which is usually translated as "single numbers." Nikoli secured a trademark on this term in Japan, and so later Japanese practitioners of sincere flattery have had to adopt other names. Ed Pegg, writing in the Mathematical Association of America's MAA Online, points out an ironic consequence: Many Japanese know the puzzle by its English name Number Place, whereas the English-speaking world prefers the Japanese term Sudoku.

The next stage in the puzzle's east-to-west circumnavigation was a brief detour to the south. Wayne Gould, a New Zealander who was a judge in Hong Kong before the British lease expired in 1997, discovered Sudoku on a trip to Japan and wrote a computer program to generate the puzzles. Eventually he persuaded The Times of London to print them; the first appeared in November 2004. The subsequent fad in the U.K. was swift and intense. Other newspapers joined in, with The Daily Telegraph running the puzzle on its front page. There was boasting about who had the most and the best Sudoku, and bickering over the supposed virtues of handmade versus computer-generated puzzles. In July 2005 a Sudoku tournament was televised in Britain; the event was promoted by carving a 275-foot grid into a grassy hillside near Bristol. (It soon emerged that this "world's largest Sudoku" was defective.)

Sudoku came back to the U.S. in the spring of 2005. Here too the puzzle has become a popular pastime, although perhaps not quite the all-consuming obsession it was in the U.K. I don't believe anyone will notice a dip in the U.S. gross domestic product as a result of this mass distraction. On the other hand, I must report that my own motive for writing on the subject is partly to justify the appalling number of hours I have squandered solving Sudoku.




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