Sudoku · Complete guide
Sudoku: how to play, where it came from, and how to solve anything
One rule stated three ways, no arithmetic, and no guessing ever required. Invented in 1979 by an American architect nobody credited.
Sudoku has one rule, stated three ways: every row, every column and every 3×3 box must contain the digits 1 to 9 exactly once. No arithmetic is involved — the digits are nine distinct symbols and could just as well be colours.
Everything else people write about Sudoku is technique rather than rules. Each square belongs to three units and "sees" twenty others, and every deduction in the puzzle follows from that. Scanning for a digit that can only go in one place, finding a square with only one candidate left, spotting a pair of squares that share the same two candidates — those three moves solve most puzzles up to hard.
A properly made puzzle has exactly one solution and never requires guessing. If you find yourself picking one of two options to see what happens, either there is a deduction you have missed or the puzzle is broken.
The history is unusual too. Sudoku has a real inventor — Howard Garns, a retired Indianapolis architect, whose puzzle Dell Magazines published in 1979 as Number Place — who was never credited and died before the game bore his name. It was renamed in Japan, and made a worldwide craze in 2004 by a retired judge with a puzzle-generating program.
How to play
One rule stated three ways, the twenty squares each cell can see, how to use pencil marks without confusing yourself, and what actually makes one puzzle harder than another.
Where it comes from
Invented by an uncredited American architect in 1979, named in Japan in 1984, and turned into a worldwide craze in 2004 by a retired judge with a puzzle-generating program.
- Sudoku is a Latin square with one extra constraint — the 3×3 box.
- It was invented by Howard Garns and published as Number Place by Dell Magazines in 1979.
- Nikoli published it in Japan in 1984 as sūdoku and added the symmetry and clue-count conventions.
- Wayne Gould placed it in The Times in November 2004, starting a global craze.
How to win
Cross-hatching and singles for beginners, pairs, pointing pairs and box-line reduction for medium puzzles, and X-Wing, XY-Wing, colouring and uniqueness for the hardest grids.
- Work in order: hidden singles, naked singles, pairs and pointing pairs, then the named patterns.
- Cross-hatching — scanning one digit across all nine boxes — is the highest-yield technique.
- Naked and hidden pairs remove candidates; pointing pairs and box-line reduction do most of the work on medium puzzles.
- X-Wing, Swordfish and XY-Wing are the standard advanced patterns, and all are chains in disguise.
Common questions
Do you need maths for Sudoku?
No. The digits are just nine distinct symbols; replacing them with letters or colours would make no difference. Sudoku is pure logic.
Is guessing ever necessary?
Not in a well-made puzzle. Every square can be deduced, although the hardest grids need long chains of reasoning that feel close to trial and error.
What is the minimum number of clues?
Seventeen. A 2012 exhaustive computer search proved no 16-clue puzzle has a unique solution.
What is the best way to start?
Cross-hatching: take one digit at a time and scan all nine boxes for a square where it must go. It finds more entries per minute than any other technique.
When should I use pencil marks?
Only when scanning stops producing entries — and then mark every candidate in every empty square. Partial marks cause more errors than none at all.
Guides
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