How to Play Sudoku

Sudoku has one rule and a ladder of ideas for applying it. This page covers the rule, the tools on this site, and every technique our difficulty tiers are graded by, from scanning to forcing chains. Bookmark it; the play pages link back to individual sections when a puzzle calls for them.

The rules

The board is a 9x9 grid divided into nine 3x3 boxes. Some cells arrive filled; these givens never change. Here is a fresh puzzle exactly as it deals:

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You fill every empty cell so that each row, each column and each box contains the digits 1 through 9 exactly once. Solved, the same puzzle looks like this. The green digits are the ones a player supplied, and the shaded row, column and box each contain a full set of nine:

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No digit repeats in any of those three units, and that constraint is the entire game. Every puzzle on this site has exactly one solution, verified when it was generated, and none of them require guessing at any point.

Using this site

Tap a cell, then a digit on the pad, or type it. The pencil icon (or the N key) switches to note mode for small candidate marks. On desktop the arrow keys move around the board, 1 to 9 place digits, Shift with a digit toggles a note, Backspace erases, Ctrl+Z undoes and Ctrl+Y redoes. The four controls you will touch most sit in the action row above the number pad:

The hint button fills your selected cell with its correct digit. Auto notes pencils every legal candidate onto the board in one tap. The gear opens settings: three mistake-checking modes, input styles, highlighting, themes, sound, and switches for the timer and the mistake count, which both start hidden. Your game, notes and history autosave on every action, one saved game per difficulty.

Scanning

Pick a digit and sweep. Its placed copies block their rows and columns, and where those sweeps cross a box, few cells survive. When exactly one cell in a box survives, the digit goes there. Scanning is the fastest technique on the board and the one you will use most, at every difficulty. Full guide: scanning.

Naked singles

A cell whose peers (its row, column and box) already show eight different digits has one candidate left, so it takes the ninth. Crowded regions produce these constantly. Our easy puzzles are solvable entirely with scanning and singles. Full guide: naked singles.

Hidden singles

Sometimes a cell could hold several digits, yet one of those digits has nowhere else to go in the unit. That digit claims the cell regardless of the other candidates. Count homes for a digit inside a unit; a count of one is a placement, whatever else seemed possible. Full guide: hidden singles.

Locked candidates

When all of a digit’s possible cells within a box fall in one row or column, the digit is pinned to that line inside that box, so you can erase it from the line outside the box. The reverse holds too: a digit confined to one box within a row or column disappears from the rest of the box. This is the gateway technique of medium sudoku. Full guide: locked candidates.

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Naked pairs

Two cells in one unit holding exactly the same two candidates claim both digits between them. Every other cell in the unit drops those candidates. The same logic scales to naked triples: three cells drawing on the same three digits lock all three up. Full guide: naked pairs.

Hidden pairs

Two digits that fit in only the same two cells of a unit own those cells, and any other candidates penciled there can be erased. Hidden triples work the same way with three digits and three cells. Hidden sets hide behind clutter, which is why they mark the start of hard territory. Full guide: hidden pairs.

X-wing

One candidate, two rows, and in each row exactly two possible cells, sharing the same two columns. The four cells form a rectangle, the digit must take opposite corners, and both columns are spent: erase the candidate from those columns everywhere else. Swap rows and columns and the pattern works the same way. Full guide: the X-wing.

Skyscraper

Take two strong links for one digit (a strong link is a unit with exactly two homes for it) running in parallel lines, with one end of each in the same crossing line. Those two base ends cannot both be true, so at least one of the far ends is, and cells seeing both far ends lose the digit. One of the friendlier expert patterns to spot. Full guide: the skyscraper.

XY-wing

A pivot cell holds candidates X and Y. One wing shares X with it and holds Z; the other shares Y and holds Z. Either way the pivot resolves, one wing becomes Z, so cells seeing both wings drop Z. An XYZ-wing adds Z to the pivot itself, tightening the elimination to cells that see all three. Full guide: the XY-wing.

Simple coloring

For one digit, follow every strong link and paint alternating cells in two colors. All cells of one color stand or fall together. A cell outside the chain that sees both colors loses the digit, and a color that collides with itself inside one unit is false everywhere at once. Full guide: simple coloring.

Swordfish

The X-wing’s big sibling: three rows in which one candidate is confined to a shared set of three columns. The digit lands once per column inside those rows, clearing it from the columns elsewhere. Slow to scan for, satisfying to land, and a defining move of expert play. Full guide: the swordfish.

Forcing chains

The summit of the ladder and the signature of master puzzles. Assume a candidate and follow the consequences from cell to cell. A branch that forces a contradiction kills the candidate that started it; two branches that force the same result prove it. Chains of bivalue cells, where every step has only one alternative, are the practical entry point. Every named pattern above is a forcing chain somebody compressed; the chain is the general tool. Full guide: forcing chains.

Where to start

If the ladder is new to you, play easy until scanning is a reflex, then climb one tier at a time. Each play page teaches its own tier’s techniques with worked boards, and the puzzles there are guaranteed to need nothing beyond them.