Alex's Adventures in Numberland - Alex Bellos [94]
The Sudokus published in newspapers usually include around 25 given numbers. To date, no one has found a Sudoku that has a unique solution with fewer givens than 17. In fact, 17-clue Sudokus inspire something of a combinatorics cult. Gordon Royle, of the University of Western Australia, maintains a database of 17-clue Sudokus, and receives three or four new ones every day from puzzle-makers around the world. So far, he has collected almost 50,000. But even though he is the world’s expert on 17-clue puzzles, he says he doesn’t know how close he is to finding the total number of possible puzzles. ‘A while ago I would have said that we were close to the end, but then an anonymous contributor sent in nearly 5000 new ones,’ he said. ‘We never really worked out how 8220;anon17” could do it, but it clearly involved a clever algorithm.’
In Royle’s opinion, no one has found a 16-clue Sudoku because, as he said, ‘Either we are not clever enough or our computers are not powerful enough.’ Most likely, anon17 didn’t reveal his method because he was using someone else’s very large computer when he wasn’t supposed to. Answering combinatorics problems often relies on giving the hard work of number-crunching over to a computer. ‘The total possible space of 16-clue possible puzzles is far too vast for us to explore more than a tiny proportion of it without some new theoretical ideas,’ Royle claimed. But he has a gut feeling that no 16-clue Sudokus will ever be found, adding: ‘We have so many 17-clue puzzles now it would really be a bit strange if there was a 16-clue puzzle that we had not stumbled across.’
Maki Kaji’s business card has the words Godfather of Sudoku. Wayne Gould describes himself as the Stepfather of Sudoku. I finally met up with Gould over coffee in a West London deli. He was wearing a New Zealand rugby top and had a typically antipodean, easygoing manner. Gould has a gap between his front teeth, which together with his thick glasses, short silvery hair and youthful enthusiasm reminded me of a young university lecturer rather than a former judge. Sudoku has transformed Gould’s life. He has been busier in retirement than he ever was before. He supplies puzzles for free to more than 700 newspapers in 81 countries, earning money from selling his program and books, which he says gives him only about 2 percent of the global Sudoku market. Still, Sudoku has earned him a seven-figure fortune. And he is a celebrity. When I asked him how his wife felt about his unexpected fame, he paused. ‘We separated last year,’ he stuttered. ‘After 32 years of marriage. Maybe it was having all that money. Maybe it gave her a freedom she never knew she had.’ Through the silence the message I heard was a heartbreaking one: he might have launched a global craze, but the adventure had come at too high a personal cost.
I’ve always thought that one reason for Sudoku’s success is its exotic name, which resonates with the romance of superior Oriental wisdom, despite the fact that the American Howard Garns came up with the idea in Indiana. In fact, there is a tradition of puzzles coming from the East. The very first international puzzle craze dates from the early nineteenth century, when European and American sailors returning from China brought home sets of geometrical shapes, typically made of wood or ivory, that had seven pieces – two large triangles, two small triangles, a medium-sized triangle, a rhomboid and a square. Put together, the pieces made up a larger square. Accompanying the sets were booklets with dozens of outlines of geometrical shapes, human figures and other objects. The aim of the puzzle was to