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Sudoku Technique Visualizer

The Sudoku Technique Visualizer maps base sets, cover sets, and exact candidate eliminations across 5 core 9×9 deduction patterns—starting with a Row-Base X-Wing on digit 7 across Rows 2 and 8 (Columns 3 and 7) that eliminates candidate 7 from 4 peer cells (R4C3, R6C3, R4C7, and R5C7). Explore advanced solving techniques with color-coded base rows, intersecting cover units, and candidate elimination breakdowns.

5 Key TechniquesColor-coded highlightsInteractive elimination

Select Pattern

Advanced Solving Techniques

Base Unit / Pivot Cover Unit / Wing Eliminated Target
Fish Pattern

X-Wing (Row Base)

Candidate 7 appears in exactly two columns across two rows (Row 2 and Row 8 at Cols 3 and 7).

Deduction Principle:

Because 7 must occupy opposite corners of this rectangle (either R2C3 & R8C7, or R2C7 & R8C3), candidate 7 is guaranteed in Columns 3 and 7 within these rows. Therefore, candidate 7 can be eliminated from all other cells in Column 3 and Column 7.

Fish Patterns

How Fish Logic Works (X-Wing & Swordfish)

A "fish" pattern occurs when a single candidate digit is restricted to $N$ cells across $N$ parallel rows (or columns) such that all these cells align in the same $N$ perpendicular columns (or rows). Because each base row must contain exactly one instance of that digit, the $N$ digits fully occupy the $N$ crossing cover columns, eliminating that candidate from every other cell in those columns.

Bivalue Chains

How Wing Logic Works (XY-Wing)

An XY-Wing uses three cells that each have exactly two candidates. A central “pivot” cell ${X,Y}$ sees two “wing” cells ${X,Z}$ and ${Y,Z}$. Regardless of whether the pivot is $X$ or $Y$, one of the two wings is logically forced to be $Z$. Therefore, any cell in the grid that shares a unit with both wings cannot contain $Z$.

Set-Theoretic Formulas & Pattern Comparison

What are the exact elimination rules and coordinates for all 5 visualized Sudoku techniques?

Every advanced Sudoku pattern is a set-cover deduction: when N base constraints restrict a candidate digit (or subset of digits) to at most N cover units, every candidate appearance inside those cover units outside the base cells is logically eliminated.

Plain-Text Candidate Elimination Equations

  • N-Fish Rule (X-Wing N = 2, Swordfish N = 3): Let B = {r_1..r_N} be N base rows and C = {c_1..c_N} be N cover columns. If ∀ r ∈ B: { c : d ∈ Cand(r, c) } ⊆ C, then ∀ r' ∉ B, ∀ c ∈ C: remove d from Cand(r', c).
  • XY-Wing (3-Cell Bivalue Chain): Given pivot cell P with Cand(P) = {X, Y} and two peers W_1 ∈ Peer(P) with Cand(W_1) = {X, Z} and W_2 ∈ Peer(P) with Cand(W_2) = {Y, Z}, any common peer T ∈ Peer(W_1) ∩ Peer(W_2) satisfies Z ∉ Cand(T).
  • Naked Subset (Naked Pair k = 2): If k cells S = {u_1..u_k} within a single unit U satisfy |⋃_{u ∈ S} Cand(u)| = k, then ∀ v ∈ (U \ S): Cand(v) ← Cand(v) \ ⋃_{u ∈ S} Cand(u).
  • Locked Candidates (Pointing Pair): If all candidate positions for digit d inside 3×3 box B_0 lie in a single row R_0 ({ (r, c) ∈ B_0 : d ∈ Cand(r, c) } ⊆ R_0), then ∀ (r, c) ∈ (R_0 \ B_0): d ∉ Cand(r, c).

Worked X-Wing & XY-Wing Examples With Exact Board Coordinates

  1. Preset 1 — X-Wing on Digit 7: In Row 2, candidate 7 appears only at R2C3 {4, 7} and R2C7 {4, 7}. In Row 8, candidate 7 appears only at R8C3 {1, 7} and R8C7 {1, 7}. Because two base rows (`R2, R8`) lock digit 7 into two cover columns (`C3, C7`), candidate 7 is eliminated from 4 target cells: R4C3, R6C3, R4C7, and R5C7.
  2. Preset 3 — XY-Wing on Digit 5: Pivot cell R4C5 has candidates {3, 8}. Wing A at R4C2 (same row) has {3, 5}; Wing B at R8C5 (same column) has {8, 5}. If R4C5 = 3, then R4C2 = 5; if R4C5 = 8, then R8C5 = 5. Cell R8C2 sees both wings (Column 2 and Row 8), so candidate 5 is eliminated from R8C2.

5 Visualized Sudoku Techniques: Metrics, Coordinates & Elimination Table

Technique Name Pattern Category Target Digit(s) Base Set / Pattern Coordinates Cover Set / Intersection Scope Eliminated Candidates (Count & Cells)
X-Wing (Row Base) 2×2 Fish Pattern Digit 7 4 cells in R2 & R8: R2C3, R2C7, R8C3, R8C7 2 Cover Columns: Col 3, Col 7 4 eliminations: 7 removed from R4C3, R6C3, R4C7, R5C7
Swordfish 3×3 Fish Pattern Digit 4 6 cells in R2, R5, R8: R2C2, R2C5, R5C5, R5C8, R8C2, R8C8 3 Cover Columns: Col 2, Col 5, Col 8 4 eliminations: 4 removed from R1C2, R4C5, R7C8, R9C2
XY-Wing 3-Cell Bivalue Chain Digit 5 (Z) Pivot R4C5 {3,8} + Wings R4C2 {3,5}, R8C5 {8,5} Common peer of both wings: Col 2 ∩ Row 8 1 elimination: 5 removed from R8C2
Naked Pair 2-Cell Unit Subset Digits 3, 9 2 cells in Row 3: R3C4 {3,9}, R3C8 {3,9} Remaining 7 cells of Row 3 3 eliminations: 3 at R3C1, 9 at R3C5, 3 at R3C6
Locked Candidates (Pointing) Box-Line Reduction Digit 6 2 cells in Box 1: R2C1 {4,6}, R2C2 {3,6} Row 2 outside Box 1 (R2C4..R2C9) 3 eliminations: 6 removed from R2C5, R2C7, R2C9