LAST WEEKEND, somewhere along the Northern Line, the girlfriend and I had a rather savage disagreement about the number 4. She thought it should go on the top line; I on the one below. There was a brief, bloody skirmish over the pencil.

We were playing Su Doku, the new puzzle game that begins in T2 on Monday. It’s a bit like a crossword, without words. It’s almost impossible to stop doing once you’ve started, but it does not necessarily lend itself to co-operation. Take it from me.

“Addictive is not a word that I would use,” says Wayne Gould, 59, the brains behind Su Doku. “To me, a puzzle is something you keep at, and it’s hard, and you get that wonderful sensation like . . . no, I’d better not say that. A great sense of release, shall we say.” Understood, Wayne. Say no more.

Until recently, puzzles were just a hobby for this rather diminutive New Zealander. Professionally, he was a High Court judge in Hong Kong. “I was due to retire when Hong Kong was handed back to China,” he tells me. “I had some unused leave that I was going to lose if I didn’t take it, so I took myself off to Tokyo for a week. I was just mooching in the Ginza, and I saw the cover of a book of puzzles, face up. The instructions were all in Japanese, but I’ve always been extremely keen on this kind of thing, so I gave it a shot.”

Many people are. For most of us, a puzzle might be a thing to fiddle with now and again on the back of a newspaper, but for some, puzzling is a passion. The World Puzzle Championships have been held since 1992, in a different country every year. Last year it was in the Netherlands, and this year in Croatia.

“Not very many women enter,” admits Peter Ritmeester, a Dutchman who is the general secretary of the World Puzzle Federation. “Maybe seven out of 100 people who enter are women. I think there are many women who do puzzles, but they are not competitive in the same way as men.”

Gould himself has never entered. “I fear that might be a little too serious for me,” he says. “At university I think I did more puzzles than I have done since in my entire life. I have this theory that people never enjoy puzzles quite as much as when they shouldn’t be doing them. It’s like the round of golf you sneak in on a Thursday afternoon. It’s much more enjoyable than the one at the weekend.”

A few weeks after his trip to Japan, Gould spent a month in Rome with his wife, Gaye, an academic. “I had time to spare,” he says, “so I got this book out. I did think, straight away, that this should be more popular outside Japan.”

After creating a few puzzles from scratch, Gould had a little think, and then spent the next six years devising a computer program to do it for him. As you do.

“I had to type 25,000 individual puzzles into my program to make sure that it could solve all of them,” he says, and still seems a little awe-struck at his own efforts. “It’s been a completely new departure for me. You don’t normally think of judges as being particularly computer-savvy, do you?”

The actual origins of Su Doku are unclear. The 18th-century Swiss mathematician Leonhard Euler developed something very similar, which he called Latin Squares. These are similar to Su Doku puzzles but are based upon a much simpler concept and, as a result (in that crazy puzzle way), much harder to do. Put simply, Latin Squares requires every digit from 1 to 9 to be arranged horizontally and vertically in a grid. Su Doku does the same, but also groups digits in boxes. And please, don’t worry if this doesn’t make much sense to you at this point. Give it time. It will.

Japan’s main publisher of Su Doku puzzles first spotted them in puzzle books in the US, under the title “Number Place” (literally translated, su means number and doku, place). Being largely pictorial, the Japanese alphabet doesn’t lend itself very easily to crosswords. The Japanese now do Su Doku puzzles instead, in their thousands.

The language-neutral nature of Su Doku has led to its appearance, several times, in the World Puzzle Championships. “People of all nationalities compete,” says Ritmeester. “We need to be sure that our puzzles don’t give anyone from a particular language or culture any advantage.” When puzzles do need to use actual words, the puzzle-makers will often pick words in languages that no competitor is likely to speak, such as Swahili.