The father of sudoku, Maki Kaji, took the inspiration for his company from an Irish horse, and no numbers game can ever compete with a day at the races, he tells David McNeill

Affable, chain-smoking, and slightly dishevelled in jeans and a sports-jacket, Maki Kaji is an unlikely corporate titan and happily admits he would rather be hanging around a racetrack betting on nags than plotting global domination. But for Japan's puzzle king and, as his business card proudly states, the father of sudoku, world domination is now very much on the agenda.

The maddening numbers game the 55-year-old college dropout unleashed on an unsuspecting planet now appears in more than 600 newspapers, thousands of websites and dozens of books in about 70 countries. Last year, 20 nations took part in the first sudoku world championship in Italy. In Britain, some fear its runaway popularity may even kill off the musty newspaper crossword.

Unsurprisingly then, most visitors to Nikoli, the Tokyo firm Kaji named after the Irish winner of the 1980 2,000 Guineas race at the Curragh, want to know one thing: what will he do for an encore? "I don't know," he says, smiling through an ever-present cloud of cigarette smoke. "We had no idea sudoku would be so successful. It depends on what our writers come up with."

We're sitting in what some have dubbed the puzzle palace, a narrow building in an unfashionable business district of Tokyo. Below us, in an atmosphere resembling a convention of chess players, a small earnest team edits and refines the 1,000 puzzles that flood into the company every month. Among the handful that will be added to the company's roster and road-tested in this puzzle-mad country could lurk the new sudoku.

It is from here that recent successes, including kakuro and slitherlink (see panel) - a local hit - first emerged. The creative engine room, however, is mostly elsewhere, in bedrooms, kitchens and commuter trains across Japan. Nikoli puzzle writers, who design 90 percent of the games and work for a flat fee, are drawn from a cross-section of ordinary Japanese life: teenagers, housewives, salary-men and pensioners. Two-thirds are high school and university students and the oldest is an 81-year-old retired teacher.

What they have in common, says Kaji, is inventiveness, a willingness to "serve" others, and time . . . lots of time. "Students like to sit around and dream up games," he says. Some, he explains, develop a couple of hit puzzles then don suits and ties, and disappear forever into company life. "They sometimes send us an apology before they begin working."

Kaji says he feels their pain. In the early 1970s his life appeared similarly mapped out when he began studying literature at Keio University, one of Japan's most prestigious private colleges and then a passport to corporate success. But he found it "boring" and began gambling and playing tennis. After he quit in his first year, he tried being a waiter, a roadie and a construction worker before setting up a small publishing business.

The one consistent thread in his life has been his love of gambling and chance. But the winning formula for a head-scratching classic remains a mystery to him, even after a quarter of a century pondering its alchemy. "We have no idea what makes something popular, so we try them out on the readers," he says in the spartan president's office, where virtually the only colour comes from portraits of racehorses on seat cushions. "About once every five years, one suddenly takes off. It's as big a surprise to us as anybody else."

He is also no wiser about why Japan is such a good incubator of puzzles, though he does have theories. "The Japanese like to improve and study and challenge themselves in their free time. In other parts of the world I've seen people just chill out and do nothing."

A love of number games has a long history here, unlike crosswords, which struggle to accommodate the complex written language. As for why sudoku was first embraced by the UK, he says its size and compactness helped: "Britain picks up on new trends quickly, like Japan." Kaji famously saw sudoku's ancestor, number place, in a US magazine in 1984, rearranged the numbers and grids, and released it in Japan. Over a decade later, retired Hong Kong court judge Wayne Gould picked it up on a trip to Tokyo, tinkered with it on his computer and sent it off to a UK newspaper.

Today, the popularity of the nine-by-nine grid has mushroomed across an ever-expanding range of formats, including computer games and internet downloads. Sudoku has firmly embedded itself in mainstream culture, joining a proud gallery of older brainteasers, such as the crossword, jigsaw puzzle and the Rubik's cube.

The man who launched it, however, has seen very little of the loot it has generated worldwide. Like Daisuke Inoue, the amateur inventor who put together the first karaoke machine, Kaji did not patent his discovery. And, like Inoue, he seems unfazed. "More than the money, it is gratifying to see the explosive worldwide growth of our puzzles. That makes me very happy."

The absence of copyright helped the game sweep unhindered across the world, allowing him to ride along in its jet-stream and sell Nikoli puzzle books, calendars and other merchandise. But Nikoli still has annual turnover of just $4 million (€2.95 million) and employs 22 people, six more than before the sudoku behemoth slipped its leash in 2005.

The company has never used a distributor or advertised in its 27-year history, and still relies heavily on its quarterly publication and books to spread the word. The puzzle operation is, in Kaji's words, still stubbornly analogue. "We make up the puzzles by hand, not on computers, because then the character and individuality of the writer are allowed to come out."

His team's priority when creating or accessing a game, he explains, is simply will it be interesting and fun? "We're not trying to make something educational. It is better to think of what we do as entertainment." The aim, he says, is to make the mind go blank; to change the mood of an average exhausted commuter riding home from a day's grind at the office.

"We started as amateurs so we're always thinking about the average person. We make the entry point for each game relatively easy but the exit point difficult, so that ordinary people can join in. Look at sudoku: anybody from five to 90 can play it." He recently told the Japan Times that his favourite puzzles make him laugh: "Ones with humour and pathos, ones you get angry with . . . that make you throw up your hand and cry, 'I can't do this'."

THE HUGE SUCCESS OF sudoku has inevitably made him a wanted man. On his dozen regular annual trips to Europe and America he is now harangued by publishers demanding a lucrative follow-up. Kaji does little to dampen the fervour, regularly telling interviewers that there are plenty more potential hits among the 300-or-so games on the company roster, most unknown outside Japan.

A couple of times a year a bigger company calls with an offer to take him over or turn Nikoli into the McDonald's or Toyota of puzzles. So far, he says he has had little difficulty turning them down. "I want to keep the company small and compact, like a submarine with a small family of employees who are close. We like to keep things free and easy-going." He says he has little interest in getting any bigger. "I like the idea of a specialist home-made cake-shop that runs out at 3pm; then we all just go home."

Oddly, Nikoli and its founder are better known in America and Europe than in the country that gave them to the world, but he says that will change as the internet helps spread the company's fame. "Our name is now linked to sudoku so a lot of people here are wondering, what's next?" He says he plans "sons of sudoku and kakuro and harder, more specialist games for puzzle-lovers". He is also negotiating the foreign launch of already road-tested puzzles including slitherlink.

The launch of a new game is inevitably followed by a tsunami of foreign-language e-mails, which crash the company's webpage. Two years ago, he says, the company rarely checked e-mails until they found thousands of new messages, following the UK launch of sudoku. "We had no idea what had happened," he says, admitting that they couldn't read most of them.

Otherwise, though, life is unchanged, except he no longer has to go out and beg people to buy his puzzles. "I always found it stressful having to bow to people, so lately life has been more comfortable. Now that I'm on a more equal footing I can finally relax and enjoy meeting people."

The late-life fame has had at least one drawback, however: it has robbed Kaji of his precious racetrack time. He says he started betting on horses when he was young and has been to most of the world's major racetracks. When he can, he still goes at the weekends. "It's a mental break from everyday life with my family and work. It makes me excited. There's the whole history of the track and the horses. As soon I set foot on a racetrack I lose all sense of time and money."

He describes watching the finish of a race as like trying to solve a puzzle; "the excitement of not knowing how it is going to end up is similar. But I control myself, only betting about 10,000 yen [ €62] a day. It is an exercise in self-control."

In 1986, he wanted to find out the fate of the Irish-born horse, Nikoli, that inspired his little company and eventually found him in Uruguay. "He was retired and taking it easy after a lifetime of entertaining people. I thought that was cool."