Sudoku

How to play

Fill the nine by nine grid so every row, every column and every three by three box contains the digits one to nine exactly once. Tap a cell, then tap a number to place it. Turn on Notes to pencil in candidates for a cell instead of committing to an answer. Every puzzle here is generated fresh and has exactly one solution, so you never need to guess. Four difficulties change how many digits you start with and how much chained reasoning the puzzle demands.

Tips

• Hunt for cells with only one candidate left before anything else. Easy grids fall entirely to this.
• Work the boxes that are already crowded. The more digits present, the fewer places the rest can go.
• Scan a single digit across the whole grid. Asking where all the sevens go beats staring at one cell.
• Use notes on hard puzzles. A pair of cells in a box holding the same two candidates locks both digits out of the rest of that box.
• Never guess. If nothing is forced, you have missed something, and a hint costs less than an unwinding grid.

Where Sudoku came from

The puzzle most people call Sudoku was published in the United States in 1979 under the name Number Place, designed by a retired architect named Howard Garns. It reached Japan in 1984, where the publisher Nikoli gave it the name it has now, a contraction of a phrase meaning the digits must be single. It was a Japanese puzzle for two decades before a New Zealander named Wayne Gould wrote a generator, persuaded The Times of London to print one in 2004, and set off the global craze.

The puzzles here are generated on the spot. The game fills a valid grid, then removes clues one at a time, keeping each removal only if the puzzle still has exactly one solution. That check is what lets the page promise you never have to guess, and it is also why a harder difficulty may leave slightly more clues than you asked for: some removals are simply not allowed.

Clue count alone is a poor measure of difficulty: before this was fixed, most 26-clue deals could be finished with nothing but singles. So Hard and Expert are now dealt again until naked and hidden singles run out with the grid still unfinished, at least 8 cells short on Hard and at least 20 on Expert. Past that point you need something from further down the list, a naked pair or a pointing pair at the least, which is the whole reason to pick those levels.

Techniques, from easy to hard

• Naked single: a cell with only one candidate left. Easy puzzles fall entirely to this.
• Hidden single: a digit that can only go in one cell of a row, column or box, even if that cell has other candidates. Scanning one digit across the whole grid finds these.
• Naked pair: two cells in a unit holding the same two candidates. Those digits are locked out of the rest of the unit.
• Pointing pair: when a digit's only candidates in a box sit in one row, that digit is eliminated from the rest of the row outside the box.
• Notes are not cheating. Pencil marks are how every serious solver works; the skill is in what you do with them.

Common questions

Is every puzzle guaranteed to have one solution?

Yes. Clues are removed only while the solution stays unique, so a puzzle with two answers can never be dealt.

Do I ever have to guess?

No. Uniqueness means every cell can be reached by reasoning. If nothing seems forced, a hint costs less than an unwinding grid.

Why does Expert sometimes have more clues than I expect?

Because a removal that would create a second solution is refused. Difficulty targets a clue count but never at the expense of uniqueness.