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Learn Sudoku

One idea at a time, from your first cell to advanced patterns. Each technique has a worked example, and in the game you can practice it on a real board.

The basics

1. Your first SudokuThree rules. No arithmetic. A calm place to begin.
2. Read the board with confidenceCells, houses, coordinates, and what “sees” actually means.
3. Pencil marks that you can trustBuild complete candidate lists before relying on them.
4. Two ways to find a certain answerOne option in a cell versus one home for a digit.
5. Progress without filling a squareLearn why a proved elimination is a useful move.
6. When two cells reserve two digitsUnderstand pairs before meeting triples and quads.
7. Strong and weak links, without jargonTurn two simple promises into a chain you can follow.
8. Make advanced logic feel smallerRead evidence, test every case, and check the exact conclusion.

Foundations

• Full houseOne empty cell in a row, column, or box means just one digit is missing.
• Naked singleOne cell has just one candidate left. Place that digit.
• Hidden singleOne digit has just one remaining location in a house, even if that cell has several pencil marks.

Box and line

• Pointing pairA box needs a digit, and its only two possible locations are on one line. That line cannot contain the digit anywhere outside the box.
• Pointing tripleThe same box-to-line deduction, with three possible locations rather than two.
• Claiming / box-line reductionA line needs a digit and all its available locations are in one box. Remove that digit from the rest of the box.

Subsets

• Naked pair2 cells in one house contain only 2 different candidates between them. They reserve those digits, in some order.
• Hidden pair2 digits are restricted to the same 2 cells in a house. Those cells cannot contain other digits.
• Naked triple3 cells in one house contain only 3 different candidates between them. They reserve those digits, in some order.
• Hidden triple3 digits are restricted to the same 3 cells in a house. Those cells cannot contain other digits.
• Naked quad4 cells in one house contain only 4 different candidates between them. They reserve those digits, in some order.
• Hidden quad4 digits are restricted to the same 4 cells in a house. Those cells cannot contain other digits.

Fish

• X-Wing2 base rows confine a digit to 2 cover columns (or transpose rows and columns). Those columns are reserved for the bases.
• Swordfish3 base rows confine a digit to 3 cover columns (or transpose rows and columns). Those columns are reserved for the bases.
• Jellyfish4 base rows confine a digit to 4 cover columns (or transpose rows and columns). Those columns are reserved for the bases.

Short chains

• SkyscraperTwo two-location rows or columns have linked near ends. At least one far end must hold the digit.
• 2-String KiteA two-location row and a two-location column connect through two distinct cells in one box. At least one remote endpoint must be the digit.
• Turbot fishA four-candidate strong-weak-strong chain. Skyscrapers and kites are recognizable arrangements of this same argument.
• Empty rectangleInside a box a digit lies on two crossing arms. An outside strong link connects one arm to a deduction that attacks the other.

Wings

• XY-Wing / Y-WingA two-candidate pivot XY sees wings XZ and YZ. One wing must be Z, whichever value the pivot takes.
• XYZ-WingThe pivot has XYZ and its wings have XZ and YZ. Z is guaranteed in at least one of these three cells.
• W-WingTwo cells with the same pair are connected through a strong link on one of their digits. Their other digit is guaranteed at one end.

Fish with fins

• Finned X-WingExtra candidates spoil an ordinary fish. A target can still be removed when it is excluded both by the fin case and by the no-fin fish case.
• Sashimi X-WingA finned fish whose no-fin core is incomplete. The same two-case counting proof works even where a base line has just one core position.
• Finned SwordfishExtra candidates spoil an ordinary fish. A target can still be removed when it is excluded both by the fin case and by the no-fin fish case.
• Sashimi SwordfishA finned fish whose no-fin core is incomplete. The same two-case counting proof works even where a base line has just one core position.
• Finned JellyfishExtra candidates spoil an ordinary fish. A target can still be removed when it is excluded both by the fin case and by the no-fin fish case.
• Sashimi JellyfishA finned fish whose no-fin core is incomplete. The same two-case counting proof works even where a base line has just one core position.

Coloring and chains

• Remote pairsA chain of cells sharing the same two candidates alternates their values. Cells seeing two opposite-parity members lose both digits.
• Simple coloring: trapColor one digit along connected strong links using alternating colors. A candidate that sees both color groups cannot be true.
• Simple coloring: wrapIf two same-colored candidates conflict, that color cannot be true anywhere in this connected component.
• X-ChainFollow one digit using alternating strong and weak links, starting and ending strong. One endpoint must be true.
• XY-ChainMove through bivalue cells using their internal strong links and shared-digit weak links. Matching endpoint digits give eliminations.

Expert logic

• Alternating inference chainAn AIC generalizes the strong-weak pattern to multiple digits and both cell and house links. This trainer demonstrates same-digit endpoint eliminations.
• Almost locked sets: ALS-XZAn ALS has one more candidate digit than cells. Connect two such sets with a restricted common digit X; a shared Z is then guaranteed somewhere across them.
• Contradiction forcingTemporarily assume a candidate is true. If explicitly justified consequences make a cell or house impossible, the assumption is false.

Uniqueness

• Unique rectangle: type 1Three corners are the same pair. The fourth must break that pair, or swapping the rectangle would give a second solution.
• Unique rectangle: type 2Two pure-pair corners and two same-line roof corners share a single extra digit. At least one roof must take that extra digit.
• Unique rectangle: type 4A strong link on one rectangle digit between the two roofs forces the other rectangle digit out of both roofs.
• BUG+1A nearly binary grid has one extra candidate that must prevent an ambiguous binary pattern. The exceptional cell takes that candidate.

Specialty reference

• Continuous and discontinuous nice loopsClosed inference paths have additional deduction rules beyond an open endpoint chain. The way links meet determines the rule.
• Grouped AICsA node can mean that a digit occurs somewhere within a defined set of cells. Links must apply to that entire group.
• Multiple coloring componentsInteractions between separate two-color networks can yield further exclusions.
• 3D MedusaTwo-color a graph of candidate nodes. Strong links in bivalue cells connect different digits, extending single-digit coloring.
• ALS-XY-WingA three-ALS chain uses different restricted common digits at its two joins. A shared endpoint digit supplies eliminations.
• Longer ALS chainsLink several almost locked sets through restricted common candidates. Track which digit a missing endpoint forces into the next set.
• Death BlossomEach candidate in a stem cell excludes a digit from a linked ALS petal, locking that petal. A common petal digit may become unavoidable.
• Sue de CoqA constrained box-line intersection combines with disjoint supporting candidate sets in the rest of the line and box.
• Franken fishGeneralized fish can include boxes among the base or cover houses.
• Mutant fishFurther generalized fish mix house types more broadly within base and cover selections.
• Siamese fishRelated fish structures can share a core while using different fins or covers.
• Kraken fishInference chains can connect fish fins to a target that does not directly see every fin.
• Forcing netsConsequences can branch and recombine rather than follow one linear path. The resulting proof is a network.
• Other rectangle variantsUnique-rectangle types 3, 5, and 6, hidden rectangles, and avoidable rectangles use additional subset, link, or solved-value conditions.
• Templates / pattern overlayConsider all placements of one digit that meet the row, column, and box constraints. Their overlaps and incompatibilities can force exclusions.
• Backtracking and exact searchSystematic search enumerates solutions or disproves a candidate by contradiction. This app uses it behind the scenes for validation.