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 and no guessing required: a properly made puzzle has exactly one solution, and that solution can be reached by deduction alone.

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 and naked pairs. These are elimination techniques: they do not place a digit, they rule one out somewhere else, which then unlocks a single. 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.

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.

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.