Sudoku is a grid of eighty-one squares, some of them already holding a digit, and one rule about how the rest are filled. There is no arithmetic in it — the digits could as well be nine colours — and no luck: a well-made puzzle has exactly one answer, and you can reach it from the given squares by reasoning alone.
The rule
The grid is nine rows by nine columns, divided into nine boxes of three by three (the heavier lines). Fill every empty square with a digit from 1 to 9 so that every row, every column and every box contains each digit exactly once. That is the whole rule. The digits printed at the start — the givens, shown here in cream — can't be changed; the ones you write appear in gold.
Playing here
- Tap a square, then a number on the pad. Each key shows how many of that digit are still to place; a digit you've finished greys out. On a keyboard: 1–9, the arrow keys, Backspace to clear.
- Pencil switches the pad to small candidate marks — the digits a square might still be. All notes fills in every square's candidates at once, worked out from the digits on the board.
- With pencil marks set to Tidy (the default), writing a digit clears it from the marks of every square it rules out. Choose Leave them in settings if you'd rather do that yourself.
- The selected square's row, column and box are shaded, and every square holding the same digit lights up — the quickest way to see where a digit can't go.
- Undo steps back through everything, pencil marks included. Erase clears a square.
Mistakes
A digit that isn't the answer turns coral and counts as a mistake. On the Daily there's no mistake limit and no counter — a wrong digit still shows in coral, and costs you time and (quietly) the Spotless badge — while free play can stop at three, or just keep count. A digit that clashes with another in its row, column or box is tinted as well, so a slip shows up straight away.
The Daily
Every day brings three new puzzles — Easy, Medium and Hard — and they are the same three for everybody in the world. They change at midnight UTC.
Each one is against the clock: 10 minutes for the Easy, 20 for the Medium, 30 for the Hard. The countdown runs only while you're playing — open the menu or switch away and it stops, and the board is covered until you come back. Your progress and the time you've used are saved on your device as you go, so you can leave one half-done and pick it up later with exactly the time you had left. In the last minute the clock turns coral.
Solve it in time and your finish time goes on that Daily's leaderboard (when you're signed in). If the clock reaches zero first, time's up: that puzzle is a miss for the day — no leaderboard time, and your streak starts again tomorrow — and you can reveal the solution to see where it was going. Each level keeps its own streak, and solving any Daily keeps your daily streak going; the longest of those daily streaks has a leaderboard too. Free play has no clock to beat: it deals a fresh puzzle at the level you choose, as often as you like.
How the levels are graded
Before a puzzle is ever shown, two programs look at it. The first is a solver that proves it has exactly one solution. The second solves it the way a person does — writing candidates and applying named techniques, always the simplest one that works — and the hardest technique it needs sets the level. A puzzle that would need guessing is never dealt, at any level.
- Easy — singles only. (Daily clock: 10 minutes.)
- Medium — needs at least one locked candidate, pair or triple. (20 minutes.)
- Hard — needs at least one of the advanced patterns: an X-wing, swordfish, XY-wing, XYZ-wing or a quad. (30 minutes.)
The techniques
Naked single
A square where eight of the nine digits are already present in its row, column or box can only be the ninth. Pencil marks make these easy to spot: a square with one candidate.
Hidden single
A digit that has only one place it can go in a row, column or box goes there — even if that square has other candidates. Scanning one digit at a time across the grid finds most of these, and an Easy puzzle is nothing but singles from start to finish.
Locked candidates
If, inside one box, every place a digit could go lies on the same row, then that digit must be in that row within the box — so it can be crossed out of the rest of that row (pointing). The reverse works too: if in a row a digit can only go in squares inside one box, it can be crossed out of the rest of that box (claiming).
Pairs and triples
Two squares in a row that can only be 4 or 7 between them own the 4 and the 7: no other square in that row can be either (a naked pair). Turned around, if 4 and 7 can only go in the same two squares of a row, those squares can't be anything else (a hidden pair). The same reasoning works with three squares and three digits.
X-wing and swordfish
Suppose a digit can only go in two places in each of two rows, and those places are in the same two columns. Whichever way it falls, the digit takes both columns in those rows — so it can be removed from those two columns everywhere else. Three rows and three columns is a swordfish.
XY-wing
A square that can only be X or Y, seeing one square that can only be X or Z and another that can only be Y or Z: whatever the first turns out to be, one of the other two must be Z. So any square that sees both of those can't be Z.
Where it comes from
The puzzle was first printed in 1979 in Dell's puzzle magazines in the United States as Number Place, usually credited to Howard Garns. The Japanese publisher Nikoli took it up in the 1980s, gave it the name Sudoku and the convention of symmetrical clues, and in 2004 The Times in London began running it daily; within a couple of years it was in newspapers around the world.
Tips
Start with the busiest digit
Whichever digit is already placed most often has the fewest places left to go. Sweep it across the grid first.
Pencil in once the singles dry up
Marks pay for themselves in the middle of a puzzle, when the remaining squares are connected through each other. Use All notes to save the counting, then look for pairs.
Look along lines from inside a box
When a box has only two or three places left for a digit and they line up, that line is worth a look in the neighbouring boxes.
Let a mistake teach you something
A coral digit means a deduction went wrong somewhere. Undo back to it and look again at why you thought it was forced.
Good to know
- Puzzles are built on your device from a seed, so there's nothing to download and the Daily works offline once the page has loaded.
- Your games in progress, your settings and your streaks are kept on your device. Signing in adds the leaderboards and badges; it's never required.
- Every puzzle has one solution and can be solved without guessing. If you're stuck, there's a deduction waiting to be found.