Sudoku

Sudoku is a placement puzzle on a 9×9 grid divided into nine 3×3 boxes. Some cells arrive already filled — the givens, or clues. Your job is to fill the rest so that every row, every column and every 3×3 box contains each of the digits 1 to 9 exactly once. There is no arithmetic involved. A properly made puzzle has exactly one solution, and on Easy, Medium and Hard here it can be reached by deduction alone, with the techniques each level is named for. An Expert puzzle is only guaranteed a single solution: it may need a guess, or a technique beyond the ones this tool rates by.

Every puzzle here is generated in your browser the moment you ask for one, and it is checked for a unique solution before you ever see it. Nothing is downloaded from a server, nothing about your game is uploaded, and the whole tool keeps working with the network switched off.

How the difficulty levels are decided

Most Sudoku apps rate difficulty by counting the givens, which is a surprisingly poor measure. The classic 30-clue board that opens the Wikipedia article on Sudoku has fewer givens than the average Medium puzzle here (about 31), yet it can be finished without ever doing anything more clever than "this cell has only one digit left". Clue count tells you how much writing you will do, not how hard you will have to think.

So the levels are defined by the solving techniques a person actually needs. Each generated puzzle is handed to a solver that knows only human techniques, and its level is the cheapest set of techniques that finishes it:

• Easy — naked singles only. Somewhere on the board there is always a cell with just one digit left that fits. Find it, write it, repeat. Easy puzzles average about 42 givens.
• Medium — adds hidden singles. Sometimes a cell has several candidates but a digit has only one place left to go in its row, column or box. Spotting those is the main skill Medium teaches.
• Hard — adds locked candidates, naked and hidden pairs, and naked triples. These are elimination techniques: they do not place a digit, they rule one out somewhere else, which then unlocks a single. A hidden pair is two digits that can only go in the same two cells of a row, column or box, so nothing else can go there; a naked triple is three cells that between them can only hold three digits, so those digits leave the rest of the unit. Hard puzzles average about 27 givens.
• Expert — anything goes. Expert puzzles still have exactly one solution, but that solution may be out of reach of the four techniques above, so finishing one can take a chain of inference or a trial line. They average about 25 givens.

Because the constraint is the technique and not the clue count, the clue count varies. A Hard puzzle is dug deeper only until it genuinely needs a Hard technique, which is why the levels overlap in size while staying separated in difficulty.

Every board shows the rating it actually achieved, under the clock. For a generated puzzle that is almost always the level you picked; the rating is what the solver measured, so if the two ever disagree, the rating is the one to believe.

Entering a puzzle from a newspaper or book

Enter a puzzle turns the board into a blank grid for someone else's puzzle. Type the givens in row by row: each digit moves on to the next cell, and a dot or a 0 skips an empty one. Or paste the puzzle as text. The usual 81-character line works, with . or 0 for each empty cell, and so does a grid laid out over nine lines with |, - and + rules between the boxes, since spaces and grid lines are ignored.

Before the puzzle is dealt, it is checked the same way a generated one is. Two givens sharing a row, column or box are named. A puzzle with no solution, or with more than one, is refused with the reason. A mistyped given is the usual cause of the first, and a missing one of the second. A puzzle that passes is rated by the same solver as the generated ones and saved as you play, so you can come back to it later. The check runs in your browser, in a background thread, so a sparse board takes a moment to check rather than freezing the page.

Pencil marks, undo and the daily puzzle

Pencil marks are the small candidate digits you jot into a cell before you are sure. Turn on Notes and the number pad writes marks instead of answers; Shift plus a digit does the same without switching modes. Fill notes pencils in every cell's candidates at once, which turns the board into the working view that elimination techniques need. Marks maintain themselves: placing a digit removes it from the pencil marks of all 20 cells that share its row, column or box.

Undo steps back through your moves one at a time, and it understands that one move can touch many cells — undoing a placement restores the pencil marks that placement swept away. Conflict highlighting turns a digit red as soon as it repeats in its row, column or box, so a slip is visible immediately rather than fifteen moves later. It flags rule violations, not wrong answers: a digit can be perfectly legal where you put it and still not belong there.

Check is for wrong answers. The first press says how many digits differ from the solution, and the second marks them on the board. Hint gives away as little as you ask for. The first press names the technique that finds the next digit, the second highlights the cells it looks at, and the third spells out the deduction and marks the cell it fills. When the next digit takes an elimination first, such as a naked pair, the hint walks through each step up to the placement. Hints reason from the digits on the board, not from your pencil marks, and refuse to reason from a board with a wrong digit on it, because every deduction after a wrong digit is wrong too. Cells are named by row and column: R3C5 is row 3, column 5.

Daily mode builds the puzzle from today's date, so everyone who plays the daily Easy puzzle on the same day gets the same board — no account, no server, just the date used as the seed. Each difficulty has its own daily puzzle, and the date rolls over at your local midnight.

Where to start on a board

Scan for the digit that already appears most often. If seven of the nine 5s are placed, the remaining two are heavily constrained and often fall out immediately. Then work box by box rather than cell by cell: a box with only two empty cells is asking a much narrower question than the grid as a whole. When scanning stops producing answers, that is the moment to fill in pencil marks — the techniques that get you unstuck all operate on candidates rather than on placed digits.