Sudoku
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A new puzzle every time, with two promises the generator checks before it hands one over: it has exactly one answer, and it can be finished by reasoning, without ever guessing. Both are things free sudoku commonly gets wrong, and both are the difference between a puzzle and a maze. The level is worked out by actually solving the puzzle and seeing which techniques it needs, so easy, medium and hard each mean one thing rather than counting how many squares are blank.
Pick a square and type a number. Arrow keys move, N switches to pencil marks.
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Click a square and type 1 to 9, or use the buttons. Arrow keys move around, Backspace clears, N switches between writing an answer and pencilling a note. Check says how many of your entries disagree with the answer, and never which ones. Best times are kept on this machine only.
It is not a Japanese puzzle, and the name is the only Japanese part
The grid people play today first appeared in 1979, in Dell Pencil Puzzles & Word Games in the United States, under the name Number Place. It is credited to Howard Garns, a retired architect from Indiana, whose name appears in the contributor lists of the issues carrying it and nowhere in the puzzle's own history: he died in 1989, before it became famous anywhere.
It travelled to Japan, where the publisher Nikoli printed it in 1984 under the name suuji wa dokushin ni kagiru, roughly "the digits must be single", which was shortened to sudoku. Nikoli also added the two conventions that make a puzzle look like a puzzle rather than a grid with holes in it: the clues are placed symmetrically, and they are set by hand.
It came back the long way. Wayne Gould, a retired judge from New Zealand who had come across it in Japan, spent years writing a program to generate the puzzles, and persuaded The Times in London to print one in November 2004. Within months it was in newspapers everywhere. The puzzle was twenty five years old and almost nobody outside Japan had heard of it.
The deeper ancestor is the Latin square, a grid where every symbol appears once in each row and column, studied by Leonhard Euler in the eighteenth century. Sudoku is a Latin square with one extra rule, the box, and that one extra rule is what turns a piece of combinatorics into something worth doing on a train.
What makes one puzzle harder than another
Not the number of blanks, which is the thing most generators count and the thing that correlates worst with difficulty. A puzzle with 24 clues can be easier than one with 30. What decides it is which techniques you have to reach for, and the ones below are the whole ladder this page uses.
| Technique | What you are looking at | Level |
|---|---|---|
| Naked single | A square where eight of the nine digits already appear in its row, its column or its box, so only one is left. The move everyone finds without being taught. | Easy |
| Hidden single | A digit that can only go in one square of a row, column or box, even though that square still has several candidates of its own. Harder to see, because you are looking at the digit rather than at the square. | Medium |
| Locked candidate | Every place a digit could go inside a box happens to sit in one row. That digit is therefore somewhere in that row inside the box, so it can be struck off the rest of the row. It places nothing by itself; it removes possibilities, and a single falls out later. | Hard |
| Naked pair | Two squares in a unit that between them have only two candidates. Those two digits belong to those two squares, whichever way round, so nothing else in the unit can take either. | Hard |
A puzzle is labelled by the hardest of these it forces you to use, worked out by solving it. That is why the levels here mean the same thing every time, and why there is no expert: puzzles that genuinely require a naked pair are rare enough that promising one and delivering it half the time would be worse than not offering it.
Frequently asked questions
Is anything sent to a server?
No, and there is no server to send it to. The site’s security policy sets connect-src ‘none’, so the browser blocks network requests from these pages. The puzzle is generated in this tab and your best times are kept in this browser on this machine.
How do you know each puzzle has only one answer?
Because it is counted. Every time a clue is taken out, the grid is handed to a solver that counts solutions and stops at two; the clue only stays out when the count is still exactly one. A puzzle with several answers is not a sudoku: you reason your way to a wall, guess, finish, and are told you are wrong. It is the commonest fault in generated puzzles and it is invisible until it ruins a game.
What does no guessing needed actually mean?
That the puzzle can be finished using named techniques a person can apply: a square with only one candidate left, a number that fits in only one square of a row, column or box, and two candidate-elimination rules called locked candidates and naked pairs. The generator solves each puzzle that way before shipping it, and throws away any it cannot finish. Somewhere to guess is not difficulty, it is a broken puzzle.
Why are there only three levels?
Because a fourth was built, measured, and thrown away. It was defined as needing a naked pair, and puzzles that genuinely need one are rare: it landed five times in ten and took up to two and a half seconds to find, against a tenth of a second for hard. Half the time a player asking for expert would have waited, then got a medium puzzle wearing an expert badge. Three levels that always mean what they say are worth more than a fourth that is a coin toss.
How is the level decided?
By solving the puzzle and recording the hardest technique it needed. Easy means singles alone finish it. Medium means it also needs a number that fits in only one square of a unit. Hard means neither of those is enough. That is a definition rather than an adjective, and the tests check it. Counting blank squares, which is what most generators do, barely correlates with difficulty at all: a puzzle with 24 clues can be easier than one with 30.
Sometimes it says the puzzle is easier than what I asked for.
A hard request lands about nineteen times in twenty. On the twentieth, no arrangement of that particular solution grid needed a hard technique, and rather than hand you a medium puzzle with a hard label on it, the page tells you what it actually is. The label always describes the puzzle in front of you.
What does Check tell me?
How many of the numbers you have entered disagree with the answer, and not which ones. Enough to know you have gone wrong somewhere, not enough to do the finding for you. Squares that clash with each other are always highlighted anyway, because that is something you could see for yourself.
Can I play with a keyboard only?
Yes. Arrow keys move around the grid, 1 to 9 fill a square, Backspace clears it and N switches to pencil marks. Every square announces its row, its column and what is on it. The number keys are read by their position on the keyboard, so a Thai layout, where the top row types ๅ ภ ถ ุ ึ, works exactly the same.