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Sudoku technique library

Learn 12 Sudoku topics backed by 10 proof techniques.

Follow 12 learning topics from Last Remaining Cell and Candidate Notes through Singles, Locked Candidates, Pairs, Triples, X-Wing, XY-Wing, and Swordfish. The current proof engine executes 10 ranked techniques; the alias and candidate concept make those proofs easier to learn.

Learning order

How the topics connect

Follow all 12 topics in learning order, while keeping the 10 ranked proof techniques distinct from the alias and candidate concept.

Four topic roles

  • Teaching alias1 topic

    A learner-friendly pattern that maps to existing placement proofs.

  • Placement proof2 topics

    A proof that places a forced digit in one cell.

  • Candidate concept1 topic

    The candidate notation shared by every ranked proof technique.

  • Candidate-elimination proof8 topics

    A proof that removes candidates without guessing a digit.

Proof-engine priority

  1. Rank 1Naked Single
  2. Rank 2Hidden Single
  3. Rank 3Locked Candidates
  4. Rank 4Naked Pair
  5. Rank 5Hidden Pair
  6. Rank 6Naked Triple
  7. Rank 7Hidden Triple
  8. Rank 8X-Wing
  9. Rank 9XY-Wing
  10. Rank 10Swordfish

Learning order

  1. Last Remaining CellTeaching alias
  2. Naked SinglePlacement proofRank 1
  3. Hidden SinglePlacement proofRank 2
  4. Candidate NotesCandidate concept
  5. Locked CandidatesCandidate-elimination proofRank 3
  6. Naked PairCandidate-elimination proofRank 4
  7. Hidden PairCandidate-elimination proofRank 5
  8. Naked TripleCandidate-elimination proofRank 6
  9. Hidden TripleCandidate-elimination proofRank 7
  10. X-WingCandidate-elimination proofRank 8
  11. XY-WingCandidate-elimination proofRank 9
  12. SwordfishCandidate-elimination proofRank 10

R1C1 · Verified example

Teaching alias

Last Remaining Cell

Fill the only empty cell in a row, column, or box by identifying its missing digit.

Learn this technique

R5C5 · Verified example

Placement proof · Rank 1

Naked Single

Spot a cell whose legal candidate list has been reduced to one digit.

Learn this technique

R1C7 · Verified example

Placement proof · Rank 2

Hidden Single

Find the only cell in a row, column, or box that can contain a chosen digit.

Learn this technique

R9C1 · Verified example

Candidate concept

Candidate Notes

Record and update only legal candidates so forced moves become easier to see.

Learn this technique

R1C6 · Verified example

Candidate-elimination proof · Rank 3

Locked Candidates

When a candidate is confined to one line inside a box—or one box along a line—remove it from the intersecting peers.

Learn this technique

R4C7 · Verified example

Candidate-elimination proof · Rank 4

Naked Pair

Two cells in one unit share the same two candidates, so those digits can be removed from the unit’s other cells.

Learn this technique

R8C7 · Verified example

Candidate-elimination proof · Rank 5

Hidden Pair

Two digits can appear in only the same two cells of a unit, so every other candidate can be removed from those cells.

Learn this technique

R3C1 · Verified example

Candidate-elimination proof · Rank 6

Naked Triple

Three cells contain non-empty subsets of the same three digits, so those digits can be removed from the unit’s other cells.

Learn this technique

R3C2 · Verified example

Candidate-elimination proof · Rank 7

Hidden Triple

Three digits can appear only across the same three cells, so extra candidates can be removed from those pattern cells.

Learn this technique

R3C6 · Verified example

Candidate-elimination proof · Rank 8

X-Wing

For one digit, two rows or columns place their candidates in the same two crossing lines, so that digit can be removed elsewhere on those lines.

Learn this technique

R1C1 · Verified example

Candidate-elimination proof · Rank 9

XY-Wing

A two-candidate pivot links XZ and YZ wings, allowing Z to be removed from every other cell that sees both wings.

Learn this technique

R2C7 · Verified example

Candidate-elimination proof · Rank 10

Swordfish

For one digit, three base rows or columns confine their candidates to the same three crossing lines, creating exact deletions outside the pattern.

Learn this technique

Review information

What is verified here

Every page derives its coordinates and candidate sets from a fixed or replayed board state. Placement and candidate-elimination steps additionally pass independent proof checks. Logic Coach on the game board remains Singles-only.

Technique terminology and examples are tied to the published engine version. See the review information below for scope and dates.Last updated: 2026-07-19