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Although Su Doku has its roots outside Japan, it is no surprise that it is here that people such as Nishio have taken the idea to new levels of devotion. Lodged deep in the heart of Japanese culture is the spirit of monozukuri — a concept that translates roughly as “craftsmanship” but implies an obsessive attention to detail. Nishio and his cohorts are in a special class that arises from this concept — of so-called “puzzle-otaku”, or “Su Doku-nerds”.

Nishio spends most of his time in his puzzle studio in Higashimurayama, churning out about 15 puzzles a day. At the moment, he is particularly hard-worked because of a dramatic social phenomenon on the Japanese horizon. “From next year, all the baby boomers born after the Second World War are going to retire at 65, and they are all going to start doing Su Doku to fill their time. The puzzle community and I have to be ready.”

When he does venture outdoors there are certain things he always takes with him. One is a battered, yellowing copy of a 20-year-old American crossword magazine which published the first Su Doku puzzle that Nishio saw. It was included in the magazine as a curio, and never took off in the US. Nishio not only enjoyed the puzzle — as the pencil markings surrounding the grid attest — but gave up his job writing standard logic puzzles to take the Su Doku idea forward.

The other thing that he always carries is a small pad of empty Su Doku grids, “always ready for the next great idea”, he says, taking the pad out and jotting down a secret “work in progress” Su Doku that seems to involve a lot of arrows. “Train, café, bar — you never know when genius will strike.”

Nishio’s mastery of Su Doku has put him at the centre of a huge network of former pupils in Japan and other puzzle masters from around the world. They come to him for advice, for unsweetened criticism of their new offerings, and to seek judgment on the great Su Doku debates of the day.

When one of his apprentices, for example, came up with a new theory that allows certain squares to be filled in earlier than regular logic would allow, the debate raged for months. Eventually, Nishio was won over by the argument, and an explanation of Hamada’s Logic now has pride of place in the front pages of Nishio’s puzzle books.

“Hamada’s Logic makes things fun,” says Nishio. “It gives you the chance to try out some truly mind-bending puzzles that involve a dozen leaps of logic just to fill in a single number.” The master also once engaged in a lengthy debate with Wayne Gould, the compiler behind the Times Su Doku puzzles. Gould complained about a particular Su Doku puzzle of Nishio’s devising, arguing that it required a leap of more than just logic to complete. Nishio argued fiercely against this sacrilege, eventually persuading Gould that it was a puzzle with which Mr Spock would have been perfectly satisfied.

The greatest lesson that Nishio has tried to instill in the members of his stable is that the ideal Su Doku puzzle — of any genre — should involve the solver in a single path of logic. It is perfecting this, he says, that makes it immediately obvious to him which are mediocre Su Doku and which are great.

“I spend every moment thinking about new puzzles and how to make the existing puzzles more interesting. To write a simple puzzle (by his definition, the sort that appears in The Times) takes me around 15 minutes. But a more complicated one will take me as much as two hours.

“The time is spent ensuring that there is a unique solution that can be navigated only by logic.”

As Britain prepares to take on the new challenge of next-generation Su Doku, Japan’s puzzle master offers a simple word of warning: “Do not get too addicted. We can make these puzzles so difficult that it would take a champion six hours to complete one.”