How to play Sudoku
Sudoku has one rule, and everything else follows from it.
Every row, every column and every three-by-three box must contain each digit from 1 to 9 exactly once.
That is the whole game. Some digits are printed at the start; the rest you work out. You never need arithmetic and you never need to guess — the digits are just nine symbols, and the puzzle would work identically with nine colours.
Despite the Japanese name, the puzzle is largely American: Howard Garns, a retired architect from Indiana, published it as Number Place in 1979. A Japanese magazine picked it up in 1984 and gave it the name it travelled the world under.
How to play it here
Tap a cell, then tap a number. Tap the cell again to deselect it.
Notes switches to pencil marks — small candidate digits that live in a cell alongside each other. Turning a cell’s real answer in replaces its marks. This is how most people hold “it is a 4 or a 7 here” in their head while working somewhere else on the grid.
You can also use the keyboard: arrow keys to move, 1–9 to write, N for notes,
Backspace to erase, Z to undo.
Clashing digits are marked in red. That is a rule being broken by digits already on the grid, not a verdict — the board never says which of the two clashing cells is the wrong one, and a grid with no clashes at all can still be wrong. Nothing marks a cell as incorrect, and nothing shades the digits that would fit. Working that out is the puzzle.
Why these puzzles can always be reasoned out
Most Sudoku sites label puzzles easy to evil and leave it there. The hard ones frequently cannot be finished by reasoning at all: past a certain point the only way forward is to pick a cell, guess, and see whether the grid collapses twenty moves later.
For a daily, that is fatal. Guessing turns a leaderboard into a lottery, and a player who guessed right is not better than one who guessed wrong.
So these puzzles are not merely generated and checked for having an answer. Each one is generated by removing digits only as long as what remains can still be solved by deduction — by the three techniques below and nothing else. A puzzle is only dealt if a solver using those techniques alone can finish it from the clues given.
Two things follow:
- Exactly one answer exists. Every digit the checking solver placed was forced, so there was never a choice to make. No second solution can exist.
- You never have to guess. There is always a next digit that can be proved from what is already on the grid. If you are stuck, there is something to be seen.
The three techniques, which are all you need
A naked single. A cell where eight of the nine digits already appear somewhere in its row, column or box. Only one digit is left, so that is the answer. This is the technique everyone finds by themselves.
A hidden single. Turn it around and look at a unit rather than a cell. Take a row and a digit — say 4. If every empty cell in that row except one is blocked from being a 4, then that cell is the 4, even if it could hold other digits too. Beginners miss these constantly; they are the bulk of a medium puzzle.
Locked candidates. If the only places a 7 could go in one box all sit in the same row, then the 7 in that box is somewhere along that row — so it cannot be anywhere else in that row, outside the box. This one eliminates rather than places, and it usually opens up a single somewhere else.
A few pointers
- Scan by digit, not by cell. Pick a number and hunt for where it must go across the whole grid. It is far faster than staring at one empty cell and asking what fits.
- Start where the grid is crowded. The box, row or column with the most clues has the fewest possibilities left and gives up its answers first.
- Use pencil marks sparingly at first. Filling every candidate into every cell takes ten minutes and often is not needed. Try scanning first, and mark up only the region you are stuck in.
- When you write a digit, look at its neighbours immediately. A newly placed digit is what makes a hidden single appear elsewhere, and the moment it lands is when it is easiest to spot.
- If you are stuck, change the question. Move from “what goes in this cell” to “where does this digit go in this box”. Nearly every stall is one of those two views being tried and the other not.