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Techniques

Level 1 · White Belt

Full House99.88%

Full House is the most fundamental Sudoku solving technique. It applies when a house (row, column, or block) has exactly eight cells filled, leaving only one empty cell. The missing digit is the only possibility for that cell.

Level 2 · White Belt (Yellow Stripe)

Hidden Single90.54%

A Hidden Single occurs when a digit can only go in one cell within a house (row, column, or block), even though that cell may have other candidates. The digit is "hidden" among other possibilities but is forced by the constraint of its house.

Naked Single98.65%

A Naked Single is the simplest pencilmark technique. When a cell has only one candidate remaining (after all eliminations from its row, column, and block), that candidate must be the solution.

Level 3 · Yellow Belt

Hidden Pair9.35%

A Hidden Pair occurs when two candidates appear in exactly two cells within a house, even though those cells may contain other candidates. Since those two digits must go in those two cells, all other candidates can be eliminated from them.

Naked Pair26.55%

A Naked Pair consists of two cells in the same house that contain exactly the same two candidates and nothing else. Since those two digits must occupy those two cells, they can be eliminated from all other cells in the house.

Locked Candidates25.65%

Locked Candidates occurs when candidates in a block are restricted to a single row or column. This allows elimination of that candidate from the rest of that row or column outside the block.

Unique Rectangle Type 11.79%

Unique Rectangle Type 1 prevents a deadly pattern where four cells with identical candidate pairs would create multiple solutions. When three corners have only the pair and one has extras, the pair can be eliminated from the fourth.

Level 4 · Yellow Belt (Orange Stripe)

Hidden Triple1.03%

A Hidden Triple extends the Hidden Pair concept to three cells and three candidates. When three candidates appear only in three cells within a house, all other candidates can be eliminated from those cells.

Naked Triple2.35%

A Naked Triple consists of three cells in a house that together contain exactly three candidates. These three digits must go in these three cells, so they can be eliminated elsewhere in the house.

X-Wing is a fish pattern using two rows and two columns. When a candidate appears in exactly two cells in two different rows, and these four cells share the same two columns, the candidate can be eliminated from other cells in those columns.

BUG (Bivalue Universal Grave) is a state where all cells have exactly two candidates and each appears twice per unit - creating multiple solutions. BUG+1 has one cell with three candidates; the extra candidate must be the solution.

Level 5 · Orange Belt

Naked Quad0.12%

A Naked Quad consists of four cells in a house that together contain exactly four candidates. These four digits must occupy these four cells, allowing elimination from other cells.

Skyscraper10.75%

Skyscraper is a single-candidate pattern using two conjugate pairs. When two rows each have exactly two cells with a candidate, sharing one column but not the other, eliminations are possible from cells seeing both "roof" cells.

Two-String Kite7.42%

Two-String Kite uses two conjugate pairs for a single digit, with one pair in a row and one in a column, linked through a shared box. The candidate can be eliminated from cells seeing both string endpoints.

Empty Rectangle

Empty Rectangle uses the absence of a candidate in a rectangular area within a box. When four cells form an empty rectangle for a candidate, combined with a strong link, eliminations become possible.

Simple Coloring1.19%

Simple Coloring (Singles Chains) uses two colors to track conjugate pairs of a single digit. By alternating colors along chains, contradictions or eliminations can be found.

Crane uses two conjugate pairs of the same digit: one in a box and one in a line. The pairs connect through a shared cell, forming a pattern where one of the two tail cells must contain the digit.

Level 6 · Orange Belt (Green Stripe)

Swordfish extends X-Wing to three rows and three columns. When a candidate appears 2-3 times in each of three rows, and all occurrences fall within the same three columns, eliminations can be made.

XY-Wing uses three bi-value cells arranged so each pair shares a candidate. The pivot cell sees both wing cells, and the common candidate of the wings can be eliminated from cells that see both wings.

W-Wing consists of two identical bi-value cells connected by a strong link on one of their candidates. The other candidate can be eliminated from cells that see both bi-value cells.

Unique Rectangle Type 20.40%

Unique Rectangle Type 2 is similar to Type 1, but two cells (on the same side) share an additional candidate. That extra candidate must be placed in one of them, so it can be eliminated elsewhere.

Unique Rectangle Type 50.01%

Unique Rectangle Type 5 occurs when two diagonal cells of the rectangle share an extra candidate beyond the deadly pair. To avoid the deadly pattern, one of these diagonal cells must contain the extra candidate.

Avoidable Rectangle0.04%

Avoidable Rectangle is similar to Unique Rectangle but involves solved cells. When three cells of a rectangle are already solved with two alternating values, the fourth cell must avoid completing the deadly pattern.

Firework uses a pivot cell at the intersection of a row and column, where a digit has strong links along both the row and column. The pattern forces the digit into specific cells, allowing eliminations elsewhere.

Level 7 · Green Belt

Finned X-Wing3.20%

A Finned X-Wing is an X-Wing with extra candidates (the "fin") in one of the base rows/columns. The fin restricts eliminations to cells that see both the fin and the normal elimination zone.

XYZ-Wing extends XY-Wing by having the pivot cell contain three candidates. The pivot has {X,Y,Z}, while wings have {X,Z} and {Y,Z}. Z can be eliminated from cells seeing all three.

Remote Pairs uses a chain of bi-value cells all containing the same two candidates. Cells at opposite ends of an even-length chain have opposite values, allowing eliminations.

Unique Rectangle Type 30.34%

Unique Rectangle Type 3 has two floor cells with only the deadly pair and two roof cells with extra candidates. The extras in the roof cells form a pseudo-locked set with other cells in their shared house, allowing eliminations.

Unique Rectangle Type 41.62%

Unique Rectangle Type 4 occurs when one of the deadly pair digits forms a conjugate pair in the roof cells' shared house. Since that digit is locked in the roof, the other deadly pair digit can be eliminated from both roof cells.

Sashimi X-Wing is a variant of Finned X-Wing where one of the base cells is missing. The pattern still allows eliminations in cells that see both the fin and the expected elimination zone.

Level 8 · Blue Belt

Hidden Quad0.01%

A Hidden Quad is the four-cell extension of Hidden Pairs and Triples. When four candidates appear exclusively in four cells within a house, all other candidates can be eliminated from those cells.

Jellyfish is the four-row, four-column extension of fish patterns. When a candidate in four rows is restricted to the same four columns, it can be eliminated from other cells in those columns.

Finned Swordfish1.90%

A Finned Swordfish is a Swordfish pattern with extra candidates forming a fin. Eliminations are limited to cells seeing both the fish and the fin.

Finned Jellyfish0.16%

A Finned Jellyfish is a Jellyfish pattern with a fin. Eliminations are restricted to cells seeing both the fish columns and the fin.

WXYZ-Wing uses four cells with candidates forming a restricted pattern. When properly configured, a common candidate can be eliminated from cells seeing all pattern cells.

Hidden Unique Rectangle

Hidden Unique Rectangle identifies a deadly pattern where the UR digit is 'hidden' in the roof cells' shared house. If the digit appears only in the roof cells within that house, it can be eliminated to prevent the deadly pattern.

Level 9 · Purple Belt

Squirmbag (or Sixfish) is a five-row, five-column fish pattern. It's extremely rare and only appears in very difficult puzzles.

Almost Locked Sets7.03%

An Almost Locked Set (ALS) is a group of N cells containing N+1 candidates. If one candidate is removed, the remaining N candidates are locked into the N cells.

Sue de Coq1.28%

Sue de Coq uses cells at the intersection of a box and line, combined with companion sets in the line and box. When candidates partition correctly, multiple eliminations become possible.

X-Chain is a single-digit chain technique that connects cells through alternating strong and weak links. When both endpoints are on strong links, the digit can be eliminated from cells that see both endpoints.

Sashimi Swordfish

Sashimi Swordfish is a Swordfish variant where one or more base cells are missing, compensated by fin cells. Eliminations target cells seeing both the fin and the cover set.

Sashimi Jellyfish

Sashimi Jellyfish is the four-row variant of sashimi fish. A Jellyfish pattern with missing base cells, compensated by fins, allows restricted eliminations.

Level 10 · Brown Belt

ALS-XZ is the simplest ALS chain technique. Two Almost Locked Sets share a restricted common candidate (X), allowing elimination of any other common candidate (Z) from cells seeing all Z's in both sets.

X-Cycles are chains of strong and weak links for a single digit that form loops. Depending on link arrangement, eliminations or placements can be determined.

XY-Chain links bivalue cells (cells with exactly 2 candidates) through shared candidates. Each consecutive pair of cells shares a candidate, creating alternating strong and weak inferences that force eliminations.

VWXYZ-Wing5.93%

VWXYZ-Wing uses five cells whose combined candidates total exactly five digits. When properly configured with a pivot and wings, a restricted common candidate can be eliminated from cells seeing all pattern members.

UVWXYZ-Wing2.37%

UVWXYZ-Wing is a six-cell wing pattern with six combined candidates. It extends the wing family to larger sets, using ALS-like logic for eliminations.

Franken X-Wing100.00%

Franken X-Wing extends the basic X-Wing by allowing boxes as base or cover sets alongside rows and columns. This mixed use of houses creates fish patterns impossible with standard rows/columns alone.

Franken Swordfish0.08%

Franken Swordfish is a 3-house Franken fish that mixes boxes with rows and columns. The base and cover sets each use three houses, with at least one box included.

Level 11 · Red Belt

Finned Squirmbag0.01%

A Finned Squirmbag is a Squirmbag (5-fish) pattern with extra candidates forming a fin. This is one of the rarest patterns in Sudoku solving.

ALS-Chain links multiple ALS groups through restricted common candidates. When ALS groups share candidates in specific ways, powerful eliminations become possible.

TUVWXYZ-Wing0.55%

TUVWXYZ-Wing is a seven-cell wing pattern, extending the wing family further. Seven cells with seven combined candidates allow elimination of a restricted candidate.

STUVWXYZ-Wing0.05%

STUVWXYZ-Wing is the largest wing pattern, using eight cells with eight combined candidates. This is the theoretical maximum for the wing family in a 9x9 Sudoku.

Death Blossom0.02%

Death Blossom uses a stem cell connected to multiple Almost Locked Sets (petals) through restricted common candidates. Each candidate in the stem links to a different petal ALS, and common candidates across all petals can be eliminated.

Franken Jellyfish0.03%

Franken Jellyfish is a 4-house Franken fish combining boxes with rows and columns. This is among the rarest fish patterns used in solving.

Grouped X-Cycles98.61%

Grouped X-Cycles extend X-Cycles by allowing grouped nodes - where multiple cells in a box-line intersection act as a single node. This enables stronger chains and more elimination opportunities.

Level 12 · Black Belt

Forcing Chains0.35%

Forcing Chains explore what happens when a cell is assumed to be each of its candidates. If all assumptions lead to the same conclusion, that conclusion must be true.

Medusa Coloring

Medusa Coloring (3D Medusa) extends Simple Coloring to multiple digits by using strong links within bi-value cells. This builds larger color clusters with more elimination opportunities.

Alternating Inference Chain (AIC) is a powerful chain technique that links candidates through alternating strong and weak inferences, potentially spanning multiple digits. When a chain forms a loop or returns to its start, eliminations or placements follow.

Forcing Net extends Forcing Chains by following all implications from each candidate simultaneously, not just single chains. This creates a branching implication network that can find deeper contradictions and common outcomes.

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