Sudoku

Sudoku is a placement puzzle with one rule. Fill the grid so that every row, every column and every one of the nine 3×3 boxes holds each digit from 1 to 9 exactly once. The digits are only symbols — you could play it with nine colours or nine letters — so there is no arithmetic in it at all. What there is, is logic: every square you fill has to be the only thing that can go there.

That is the promise behind every grid on this page. Each puzzle has exactly one solution, checked by a solver before you ever see it, and none of them asks you to guess. If you are stuck, there is a deduction you have not found yet — never a coin toss you have to take.

Where it comes from

The modern puzzle first appeared in 1979, in Dell Magazines in the United States, under the name Number Place; its constructor is generally credited as Howard Garns, a retired architect. It travelled to Japan, where the publisher Nikoli gave it the name it carries now — a shortening of a phrase meaning "the digits must remain single" — and set the conventions most puzzles still follow, including clues laid out with rotational symmetry. It reached the rest of the world in 2004, when The Times in London began printing it daily, and within a year it was in newspapers everywhere.

The Daily

Every day there are three new puzzles here — an Easy, a Medium and a Hard — and they are the same three for everybody in the world. The day turns over at midnight UTC. Each is a race against the clock: ten minutes for the Easy, twenty for the Medium, thirty for the Hard, counting down while you play and stopping whenever you step away (the board is covered while it's paused). Solve it before it runs out and your time goes on the leaderboard; if the clock reaches zero, that puzzle is a miss for the day — no leaderboard time, and your streak starts again tomorrow — and you can reveal the answer. There's no mistake limit or counter on the Daily — a wrong digit still shows in coral, but the clock is the only stakes. Each level keeps its own streak, and solving any of them keeps your daily streak going — the longest one has its own leaderboard if you are signed in. Free play has no clock at all: it deals a fresh puzzle at the level you choose, as many times as you like.

How the levels are graded

Difficulty here is not a count of clues. Each puzzle is solved by a program that works the way a person does — with candidates and named techniques, cheapest first — and the hardest technique the puzzle needs is its level.

• Easy falls to singles alone: a square with one possible digit, or a digit with one possible square in a row, column or box.
• Medium needs at least one step of the next kind: a digit locked into one line of a box, or a pair or triple of squares that share their candidates.
• Hard needs one of the classic advanced patterns — an X-wing, a swordfish, an XY-wing — somewhere in the solve.

A few habits that help

• Scan before you write. Pick a digit and look across the whole grid for where it must go. Most of an easy puzzle is just that, digit by digit.
• Use pencil marks for the middle game. Once the obvious squares are gone, writing the candidates in shows you the pairs and lines that are invisible otherwise. The All notes button fills every square's candidates in one go; with marks set to Tidy, placing a digit clears it from the squares it rules out.
• Look for pairs. Two squares in a row that can only be the same two digits own those digits; nothing else in that row can be them.
• Take a mistake as information. A digit in coral is not the answer. On the Daily it costs you only time (and, quietly, the Spotless badge); free play can stop you at three, or just keep count.
• Watch the clock, not the mistakes. On the Daily the countdown turns coral in its last minute. If you're stuck with time running low, a pass of pencil marks is often quicker than staring.

The rules in full, the techniques with pictures, and the history at more length are in the Sudoku guide.