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Sudoku
Puzzle · Classics · plays in your browser, no download
Nine rows, nine columns, nine boxes, and every digit once in each. No arithmetic: despite being made of numbers, sudoku is a pure logic puzzle, and the digits could just as well be nine colours or nine animals.
Where it comes from
The mathematics is eighteenth-century. Leonhard Euler studied Latin squares: grids in which each symbol appears exactly once in each row and column. French newspapers in the 1890s printed number grids that come close, but they were arithmetic puzzles — you added things up — which is a different kind of problem.
The puzzle we actually play was invented in 1979 by Howard Garns, a retired architect from Indiana, and published by Dell Magazines as Number Place. His addition to Euler was the one that matters: the nine three-by-three boxes. Dell did not print constructors’ names, so for years nobody knew who he was; he was identified later only because the puzzles appeared in exactly the issues his name appeared in. Garns died in 1989, before any of what followed.
What followed started in Japan. In April 1984 the publisher Nikoli ran it in Monthly Nikolist under the name sūji wa dokushin ni kagiru — roughly, the digits must be single — soon shortened to sudoku. Nikoli also added the two rules that make a puzzle feel hand-made rather than generated: a cap on how many digits are given at the start, and rotational symmetry in the pattern of those givens.
Then one tourist. In 1997 Wayne Gould, a retired judge from Hong Kong, found a book of them in a Tokyo bookshop. He spent about six years writing a program that could generate puzzles with a single solution, took it to The Times in London, and the paper started printing them in November 2004. Within a year sudoku was in newspapers on every continent. Garns had been dead for fifteen years.
How to solve one
The only rule is that each digit appears once in every row, once in every column and once in every box. Everything below follows from it.
| Single candidate | A cell where eight of the nine digits are already ruled out by its row, column and box. The ninth goes in. |
|---|---|
| Single position | A digit that has only one place left to go in a given row, column or box — even though that cell has several candidates of its own. |
| Pointing pair | If a digit within one box can only sit in cells that share a line, it can be struck off the rest of that line. |
| Naked pair | Two cells in a unit holding the same two candidates and nothing else. Those two digits belong to them, and come out of every other cell in the unit. |
A properly built puzzle has exactly one solution and can be reached by reasoning alone. If you find yourself guessing, you have either missed something or you are working on a badly made grid.
Our version
Grids of nine and of sixteen, in five levels from easy to diabolical, and no limit on how many you play. The sixteen-by-sixteen uses the digits together with the letters A to G, and it is a genuinely different experience: the same logic, but the units are too big to scan at a glance, so you have to be systematic instead of quick.
Three things that help
Work the digit, not the cell. Pick a number and walk all nine boxes asking where it can go. It is much faster than staring at one empty square.
Pencil in only when you are stuck. Filling every candidate into every cell at the start turns a clean grid into noise.
Never guess. A guess that is wrong does not announce itself for another twenty moves, and then the grid is ruined and you cannot tell where it went wrong.