Sudoku techniques
45 techniques, 31 of which the solver can spot for you as a Smart Hint. Each one has a worked example.
Easy
Naked Single
Only one candidate remains for a cell — place it.
Hidden Single
A digit has only one possible cell left in a row, column, or box, even though that cell has other candidates too.
Medium
Pointing Pair/Triple
All of a digit's candidates in a box line up in one row or column, so it can be eliminated from the rest of that line.
Box-Line Reduction
All of a digit's candidates in a row or column fall inside one box, so it can be eliminated from the rest of that box.
Naked Pair
Two cells in a unit share the exact same two candidates — those digits can be removed from every other cell in the unit.
Hard
Naked Triple
Three cells in a unit whose candidates combine to exactly three digits — eliminate those digits from the rest of the unit.
Hidden Pair
Two digits appear as candidates in only the same two cells of a unit — strip those cells down to just those two digits.
Hidden Triple
Same idea as Hidden Pair, but three digits are confined to the same three cells.
Naked Quad
Four cells in a unit whose candidates combine to exactly four digits — eliminate those digits elsewhere in the unit.
Hidden Quad
Four digits confined to the same four cells in a unit — strip those cells down to just those four digits.
X-Wing
A digit's candidates in two rows fall in the exact same two columns, forming a rectangle — eliminate it from the rest of those columns.
Expert
XY-Wing
A pivot cell and two "wing" cells, each sharing one candidate with the pivot, corner a shared digit out of any cell both wings can see.
W-Wing
Two cells with the same candidate pair, linked by a strong chain on one digit elsewhere on the board.
XYZ-Wing
Like XY-Wing, but the pivot keeps a third candidate, which tightens where the elimination applies.
Swordfish
X-Wing's three-line cousin: a digit's candidates across three rows fit inside the same three columns (or vice versa).
Gurth's Theorem
On a puzzle built with 180°-rotational symmetry, the digit that would land on a cell's mirror-image partner must be its complement — narrowing candidates without touching any other unit.
Chute Remote Pairs
Two rows (or columns) in the same "chute" (a 3-box band) sharing the same candidate pair in matching columns let you eliminate that pair from the chute's third row.
Rectangle Elimination
A near-Unique-Rectangle pattern where a strong link on one corner forces a contradiction if a second corner (the "wing") holds the shared digit — eliminating it there.
Extreme
Jellyfish
The four-line version of X-Wing and Swordfish — a digit's candidates across four rows fit inside the same four columns.
Simple Coloring
Chain every cell where a digit has just two possible spots in its unit, alternating two colors — a contradiction or a shared sight line lets you eliminate.
X-Chain / XY-Chain
A longer alternating chain of links that traces a digit (or a sequence of digit pairs) across the board to find a single elimination.
X-Cycles
A single digit's strong and weak links are traced into a closed loop — a continuous loop yields eliminations at its weak links, a discontinuous one pins or clears its meeting cell outright.
3D Medusa
Simple Coloring extended across multiple digits at once — bivalue cells link candidates of different digits into the same two-color chain, unlocking more elimination rules.
Extended Unique Rectangles
A Unique Rectangle's "deadly pattern" idea stretched across three rows, columns, and boxes instead of two, built around a locked triple of candidates.
Hidden Unique Rectangles
A Unique Rectangle deadly pattern hidden behind extra candidates, uncovered via strong links on one of the pattern's two digits instead of bare bivalue corners.
Aligned Pair Exclusion
Two cells that don't share a unit are checked against every "almost locked" set nearby — any combination of their candidates that would leave one of those sets with no valid completion is ruled out.
Grouped X-Cycles
X-Cycles generalized so a "node" can be a group of cells confined to one row-and-box or column-and-box intersection, not just a single cell.
Alternating Inference Chains (AIC)
The most general chaining technique: follow a chain of candidates that alternates "at least one of these is true" with "at most one of these is true", hopping between digits as it goes. Whichever way it resolves, one of the two chain ends must be true.
Exocet
Two "base" cells constrain two "target" cells elsewhere on the board so tightly that the targets' candidates must come entirely from the base cells' digits.
Death Blossom
A "stem" cell's candidates are each matched to their own Almost Locked Set (a "petal") — a digit common to every petal can be eliminated from any cell all the petals can see.
Finned X-Wing / Finned Swordfish
An almost-fish pattern with one or more extra "fin" candidates confined to a single box — eliminations still hold, just narrowed to that box.
Forcing Nets
Forcing Chains generalized into a branching tree instead of a single line — every branch from an assumption is followed, and any conclusion every branch agrees on holds.
Nishio Forcing Chains
Proof by contradiction on a single candidate: tentatively assume it's true, chain the consequences forward, and if that breaks the board, it was false all along.
Forcing Chain Variants (Digit, Cell, Unit, Quad)
Named by what's exhaustively tested — every candidate of one digit, every candidate of one cell, every cell of one unit, or every cell across four related units — each variant follows every branch to see if they all agree on some outcome.
Pattern Overlay Method
Every way a single digit could legally fill the whole board is enumerated as a "pattern"; a candidate present in none of the surviving patterns can be eliminated.
Bowman's Bingo
Last Resort: guess a candidate and manually trace forced Naked/Hidden Singles as far as they go — a contradiction eliminates the guess, same idea as Trial and Error but tracked by hand.
Unique Rectangle
Uses the fact that a proper Sudoku has exactly one solution to rule out candidate patterns that would create a second, deadly duplicate.
Unique Rectangle Types 2-6
The rest of the Unique Rectangle family: when only two corners are a bare pair, what the other two carry still gives the deadly pattern away.
ALS-XY-Wing
Three Almost Locked Sets in a row: two outer sets hang off a middle "bridge" set, and a digit shared by the outer two must land in one of them.
BUG (Bivalue Universal Grave)
If every empty cell has exactly two candidates except one with three, that one cell must hold whichever digit appears an odd number of times.
WXYZ-Wing
XYZ-Wing stretched to four cells: a pivot plus three wings whose combined candidates match the pivot's exactly.
Almost Locked Sets (ALS)
Groups of cells just one candidate away from being "locked" are paired up to find eliminations that simpler subset techniques miss.
Sue de Coq
An advanced intersection technique that combines naked and hidden subsets across a box and one of its lines at the same time.
Forcing Chains
Follows the consequences of both options in a bivalue cell until they force the same outcome somewhere else on the board.
Trial and Error
When no other technique applies, suppose a candidate and follow it through — if that leads to an impossible board, the candidate is ruled out for good.