Sudoku: the rules and the solving techniques

Fill each empty cell with a digit from 1 to 9, never repeating a digit in a row, a column or a 3 × 3 box. The digits given at the start stay put. Begin with a digit you see often and look for a box where it has only one place left.

First place everything scanning gives you, then write the candidates and look for locked candidates and naked pairs. On our 300 Hard grids, those two techniques were always enough, and at least half the time the grader got stuck only once. After each one, go back to scanning before anything else.

Scan again from the start, digit by digit, because a hidden single may have slipped past you. Then check your notes, remove what is no longer possible and look for candidates lined up in a box or two cells with the same two candidates. Avoid betting: the error only shows at the end.

Yes, a properly built sudoku always yields to logic, although some published puzzles demand techniques well beyond the usual ones. On Neurostim, the game's grader solves each grid with its allowed techniques before keeping it, so there is always a deduction available and you never have to guess.

No, classic sudoku only checks rows, columns and 3 × 3 boxes, so a digit can repeat along a diagonal. Some variants add diagonals with no duplicates, but Neurostim's grids do not use them, and a repeat on a diagonal is never flagged as an error by the game.

A proper sudoku has exactly one solution; a puzzle with two is considered badly built, and it forces a guess. Neurostim's generator counts the solutions each time it removes a clue and only keeps the removal if a single solution remains, so every grid you see has just one answer.

Not originally: the modern form appeared in the United States in 1979 as Number Place. Japan gave it its name, short for Sūji wa dokushin ni kagiru, roughly "the digit is limited to one", where sū means digit and doku means single. Nikoli claims the trademark in Japan.

Howard Garns, a retired American architect, most likely designed the modern form, published by Dell in 1979 as Number Place. Maki Kaji of Japan then named and spread it, and Wayne Gould, a retired judge from Hong Kong, brought it to the rest of the world from 2004. French newspapers printed ancestors of it in the 1890s.

No, sudoku uses no arithmetic: you never add, multiply or compare the size of the digits, and nine letters or symbols would give the same puzzle. It is a logic puzzle that rests on one constraint. For a similar grid where arithmetic really matters, try calcudoku, which adds an operation to each cage of cells.

Nothing proves it for certain. According to the University of Exeter press release carried by ScienceDaily, more than 19,000 adults aged 50 and over reported how often they play: the more often they do crosswords or sudoku, the better they score on tests of attention, reasoning and memory. The study's lead says this does not show that puzzles necessarily reduce the risk of dementia. A University of Illinois press release sums up a 2016 review of brain-training programmes: people mostly improve at the task they practise, and it is premature to conclude there are wider benefits. We only read these two summaries, not the papers.

There are about 6.67 × 10²¹ finished grids, of which 5,472,730,538 are truly different once symmetries are removed. A puzzle needs at least 17 clues to have a single solution, as an exhaustive computer search released in 2012 found no valid 16-clue puzzle. Neurostim's Hard grids go down to 21 in our measurements.

The reference time we found is 54.44 seconds on a 9 × 9 grid, by Wang Shiyao at the 2018 World Championship in Prague, according to Xinhua and Radio Prague, checked in November 2026. Guinness World Records gives an older time, 1 min 23.93 s on a "very easy" grid, which does not compare directly with that one.