Sudoku

Sudoku is a placement puzzle on a nine-by-nine grid divided into nine boxes. Fill every square so that each row, each column and each three-by-three box contains the digits one to nine exactly once.

There is no arithmetic involved and no guessing required. Every puzzle here is generated fresh and proven to have exactly one solution before you see it.

How to play

1. Tap a square, then tap a number — or move with the arrow keys and type.
2. Dark digits are the starting clues and cannot be changed. Blue digits are yours.
3. Selecting a square highlights its row, column and box, and any square holding the same digit.
4. Fill the grid correctly to finish. The timer runs from the moment the puzzle appears.

The two techniques that solve most grids

Scanning is the first one and it will carry you through easy and most medium grids. Choose a digit — say 7 — and look at every 7 already on the board. Each one eliminates its row, its column and its box. Often that leaves exactly one square in some box where a 7 can go.

Candidate counting takes over when scanning dries up. Pick a single row, column or box, and for each empty square work out which digits are still legal. If a digit is legal in only one square of that unit, it belongs there — even if that square has several candidates of its own. This is the step most players skip, and it is what separates people who stall on hard grids from people who finish them.

Why difficulty is about clues, not tricks

The four levels here differ in one thing: how many digits you start with. Easy grids give you 42 and almost solve themselves by scanning. Expert grids give you around 24, which means long stretches where no square is immediately determined and you have to count candidates to make progress.

None of the levels require guessing. If you are guessing on an expert grid, there is a deduction available that you have not found yet — which is, more or less, the entire appeal.

Tips

• Scan by digit, not by square. Pick a number, look at where it already appears, and cross out the rows, columns and boxes it rules out. Whole placements fall out of this in seconds.
• Look for boxes with only two or three empty squares before anything else. They are the cheapest source of certain placements and each one you fill makes the next scan easier.
• When scanning stops producing placements, switch to counting candidates in a single row or box. A digit that can only go in one place there is a placement even when nothing else looks obvious.
• Never place a digit you are not certain about. A single guess on a hard grid produces contradictions twenty moves later that are almost impossible to unwind.