Yet Another Sudoku

Table of Contents

• 1. Introduction
  • 1.1. History
  • 1.2. What is Sudoku
  • 1.3. Sudoku Rule
  • 1.4. Sudoku Facts
  • 1.5. What’s Ahead?
  • 1.6. Intended Audience
  • 1.7. Acknowledgements
• 2. Foundation
  • 2.1. Sudoku Notation
    • 2.1.1. Cells, Ccells, Houses and Chouses
    • 2.1.2. Syntax
      • 2.1.2.1. Cell (Location) Specifiers
      • 2.1.2.2. Ccell Specifiers
      • 2.1.2.3. Ccell Postfixes
      • 2.1.2.4. Pattern Combiners
      • 2.1.2.5. Operators
      • 2.1.2.6. Conditionals
      • 2.1.2.7. Relational Specifiers
      • 2.1.2.8. Candidate Dressing
      • 2.1.2.9. Set Algebra
    • 2.1.3. Symantics
      • 2.1.3.1. Singles
      • 2.1.3.2. (Straight) Subsets
      • 2.1.3.3. Fish
      • 2.1.3.4. Bent Subsets
      • 2.1.3.5. Inference Chains, Loops and Nets
      • 2.1.3.6. Super Human Patterns
    • 2.1.4. Outcomes
    • 2.1.5. Candidate Diagrams
      • 2.1.5.1. Candidate Representation
      • 2.1.5.2. Some Examples
        • 2.1.5.2.1. Locked Exposed Pair
        • 2.1.5.2.2. Y-Wing
        • 2.1.5.2.3. Locked Pointing Single
        • 2.1.5.2.4. XYZ-Wing
        • 2.1.5.2.5. Locked Exposed Triple
        • 2.1.5.2.6. Swordfish
        • 2.1.5.2.7. Finned Swordfish
    • 2.1.6. Other Notations
      • 2.1.6.1. Candidate Grids
      • 2.1.6.2. Sets
      • 2.1.6.3. Chains
  • 2.2. Premises, Inferences and Searching
    • 2.2.1. Premises and Inferences
    • 2.2.2. Searching
  • 2.3. Spatial Representation
  • 2.4. Links and Chains
    • 2.4.1. Weak Links
    • 2.4.2. Strong Links
    • 2.4.3. Chains, Loops, and Nets
      • 2.4.3.1. Chains
      • 2.4.3.2. Loops
      • 2.4.3.3. Nets
    • 2.4.4. Indirect Links
      • 2.4.4.1. Weak Link Patterns
      • 2.4.4.2. Robust Link_patterns
      • 2.4.4.3. Strong Links
    • 2.4.5. Strong Links Masquerading as Weak
    • 2.4.6. Cannibalistic Eliminations
  • 2.5. Truth, Sets and Fish
    • 2.5.1. Truths
    • 2.5.2. Sets
    • 2.5.3. Subsets
      • 2.5.3.1. Exposed or Hidden
      • 2.5.3.2. Straight or Bent
      • 2.5.3.3. Straight Subsets
      • 2.5.3.4. Bent Subsets
        • 2.5.3.4.1. Restricted and Unrestricted Candidates
    • 2.5.4. Nearly Locked Sets
    • 2.5.5. Fish
  • 2.6. Uniqueness
• 3. Human Solvable Patterns
  • 3.1. Singles
    • 3.1.1. Basic Solving Without Pencil Marks
    • 3.1.2. Exposed Singles
    • 3.1.3. Hidden Singles
    • 3.1.4. Locked Singles
      • 3.1.4.1. Pointing Locked Candidates
      • 3.1.4.2. Claiming Locked Candidates
    • 3.1.5. Empty Rectangles
  • 3.2. Subsets
    • 3.2.1. Exposed Pairs
    • 3.2.2. Locked Exposed Pairs
    • 3.2.3. Hidden Pairs
    • 3.2.4. Exposed Triples
    • 3.2.5. Locked Exposed Triples
    • 3.2.6. Hidden Triples
    • 3.2.7. Exposed Quads
    • 3.2.8. Hidden Quads
  • 3.3. Bent Subsets
    • 3.3.1. Bent Exposed Subsets
      • 3.3.1.1. Bent Exposed_Triples
        • 3.3.1.1.1. Y-Wings
        • 3.3.1.1.2. XYZ-Wings
      • 3.3.1.2. Bent Exposed Quads
      • 3.3.1.3. Bent Exposed Quints
      • 3.3.1.4. Bent Exposed Sexts
    • 3.3.2. Grouped Bent Subsets
      • 3.3.2.1. Grouped Bent Pairs
        • 3.3.2.1.1. Exposed Line, Hidden Box Grouped Bent Pairs
        • 3.3.2.1.2. Hidden Line, Exposed Box Grouped Bent Pairs
      • 3.3.2.2. Grouped Bent Triples
        • 3.3.2.2.1. Exposed Line, Hidden Box Grouped Bent Triples
        • 3.3.2.2.2. Hidden Line, Exposed Box Grouped Bent Triples
      • 3.3.2.3. Grouped Bent Quads
        • 3.3.2.3.1. Exposed Line, Hidden Box Grouped Bent Quads
        • 3.3.2.3.2. Hidden Line, Exposed Box Grouped Bent Quads
    • 3.3.3. Bent Hidden Triples
  • 3.4. Fish
    • 3.4.1. Basic Fish
      • 3.4.1.1. X-Wing
      • 3.4.1.2. Swordfish
      • 3.4.1.3. Swordfish
      • 3.4.1.4. Jellyfish
    • 3.4.2. Finned Fish
      • 3.4.2.1. Finned X-Wing
      • 3.4.2.2. Finned Swordfish
      • 3.4.2.3. Finned Jellyfish
      • 3.4.2.4. Algorithmic rules for Finned Fish
    • 3.4.3. Sashimi Fish
      • 3.4.3.1. Sashimi X-Wing
      • 3.4.3.2. Sashimi Swordfish
      • 3.4.3.3. Sashimi Jellyfish
      • 3.4.3.4. Algorithmic rules for Sashimi Fish
    • 3.4.4. Kraken Fish
      • 3.4.4.1. Algorithmic rules for Kraken Finned Fish
      • 3.4.4.2. Algorithmic rules for Kraken Sashimi Fish
      • 3.4.4.3. Kraken Fish Practical issues
      • 3.4.4.4. Kraken Fish Examples
    • 3.4.5. Fraken Fish
    • 3.4.6. Mutant Fish Patterns
  • 3.5. Chains, Loops and Nets
    • 3.5.1. abcd
      • 3.5.1.1. lskdfjs;df
        • 3.5.1.1.1. Broken Wings
        • 3.5.1.1.2. Super Nodes
      • 3.5.1.2. Chained Strong Linked Patterns
    • 3.5.2. Some Chain Examples
      • 3.5.2.1. A Two String Kite
      • 3.5.2.2. A Skyscraper
      • 3.5.2.3. A Strong Linked Net (SLN) Chain
    • 3.5.3. Chain Eliminations and Placements
      • 3.5.3.1. Weak Link Ended Chains (WE-AIC)
      • 3.5.3.2. Strong Link Ended Chains (SE-AIC)
        • 3.5.3.2.1. Type 1: Same end Values
        • 3.5.3.2.2. Type 2: Different End Values
        • 3.5.3.2.3. Type 3: Opposing Exposed Pair Ends
      • 3.5.3.3. Strong Linked Patterns
        • 3.5.3.3.1. Type 1: Same State Nodes See Each Other
        • 3.5.3.3.2. Type 2: All Candidates in a Cell See Same State Nodes
        • 3.5.3.3.3. Type 3: Ccells See Opposing State Nodes
    • 3.5.4. Sub Chains
    • 3.5.5. AI Loops
      • 3.5.5.1. Even AI Loops
      • 3.5.5.2. Strong AI Loops
      • 3.5.5.3. Weak AI Loops
    • 3.5.6. Group Links
      • 3.5.6.1. Characterising Group Links
      • 3.5.6.2. Line Group Link Examples
      • 3.5.6.3. Box Group Link Examples
      • 3.5.6.4. Group Links in Even Loops
  • 3.6. Nearly Locked Sets
  • 3.7. Exotic Patterns
  • 3.8. Base, Link, and Cover Sets
    • 3.8.1. Introduction
      • 3.8.1.1. Some Definitions
      • 3.8.1.2. Base Set Cover Set - X Wing Example
    • 3.8.2. Single Base Set Patterns
      • 3.8.2.1. Hidden Single Example
    • 3.8.3. Multi Base Set Patterns and Rank
      • 3.8.3.1. Rank 0 Patterns
        • 3.8.3.1.1. Rank 0 Exposed Quad Example
        • 3.8.3.1.2. Rank 0 Locked Exposed Triple - Subset Example
        • 3.8.3.1.3. Rank 0 Hidden Pair Subset Example
        • 3.8.3.1.4. Rank 0 Swordfish Example
        • 3.8.3.1.5. Rank 0 Even Loop Example
      • 3.8.3.2. Rank 1 Patterns
        • 3.8.3.2.1. Rank 1 Finned X Wing Example
        • 3.8.3.2.2. Rank 1 Two String Kite Example
        • 3.8.3.2.3. Rank 1 Nearly Locked Set or XY Chain Example
      • 3.8.3.3. Rank ‘r’ Patterns
        • 3.8.3.3.1. Triplets and Rank
          • 3.8.3.3.1.1. Base Triplets
          • 3.8.3.3.1.2. Link Triplets
          • 3.8.3.3.1.3. Rank Regions
          • 3.8.3.3.1.4. Additive Properties of Triplets
        • 3.8.3.3.2. The art of Identifying Rank ‘r’ Patterns
        • 3.8.3.3.3. Rank ‘r’ Examples
  • 3.9. Searching
  • 3.10. Uniqueness
  • 3.11. Last Resort
• 4. Generating Puzzles
• 5. Grading Puzzles
• 6. Software
  • 6.1. Programs
    • 6.1.1. Yet Another Sudoku
    • 6.1.2. Pattern Regression Tester
    • 6.1.3. Batch Puzzle Generator and Grader
    • 6.1.4. Batch Puzzle Solver
  • 6.2. File Formats
  • 6.3. Algorithms
• 7. Glossary and Abbreviations
• 8. References

List of Figures

Figure 2.1: Locked Exposed Pair Pattern

Figure 2.2: Y-Wing Pattern

Figure 2.3: Locked Pointing Single Pattern

Figure 2.4: XYZ-Wing Pattern

Figure 2.5: Locked Exposed Triple Pattern

Figure 2.6: Swordfish

Figure 2.7: Finned Swordfish

Figure 2.8: Links Example

Figure 2.9: Cannibalistic AI Chain Example

Figure 2.10: Truths

Figure 3.1: Empty Rectangle Pattern

Figure 3.2: Y-Wing (Column / Box) Example

Figure 3.3: Y-Wing (Row / Column) Example

Figure 3.4: XYZ-Wing Example

Figure 3.5: Bent Exposed Quad Example 1

Figure 3.6: Bent Exposed Quad Example 2

Figure 3.7: Bent Exposed Quad Example 3

Figure 3.8: Bent Exposed Quint Example

Figure 3.9: Bent Exposed Sext Example

Figure 3.10: Grouped Bent Pair: Exposed Line, Hidden Box Candidate Diagram

Figure 3.11: Group Bent Pair Exposed Row, Hidden Box Example

Figure 3.12: Group Bent Pair Exposed Column, Hidden Box Example

Figure 3.13: Grouped Bent Pair: Hidden Line, Exposed Box Candidate Diagram

Figure 3.14: Group Bent Pair hidden Row, Exposed Box Example

Figure 3.15: Group Bent Pair Hidden Column, Exposed Box Example

Figure 3.16: Grouped Bent Triple: Exposed Line, Hidden Box Candidate Diagram

Figure 3.17: Group Bent Triple Exposed Row, Hidden Box Example

Figure 3.18: Group Bent Triple Exposed Column, Hidden Box Example

Figure 3.19: Grouped Bent Triple: Hidden Line, Exposed Box Candidate Diagram

Figure 3.20: Group Bent Triple Hidden Row, Exposed Box Example

Figure 3.21: Group Bent Triple Hidden Column, Exposed Box Example

Figure 3.22: Grouped Bent Quad: Exposed Line, Hidden Box Candidate Diagram

Figure 3.23: Group Bent Quad Exposed Row, Hidden Box Example

Figure 3.24: Group Bent Quad Exposed Column, Hidden Box Example

Figure 3.25: Grouped Bent Quad: Hidden Line, Exposed Box Candidate Diagram

Figure 3.26: Group Bent Quad Hidden Row, Exposed Box Example

Figure 3.27: Group Bent Quad Hidden Column, Exposed Box Example

Figure 3.28: Bent Hidden Triple Candidate Diagram

Figure 3.29: Group Bent Hidden Triple Example

Figure 3.30: Basic Fish Candidate Diagrams

Figure 3.31: Two String Kite Example

Figure 3.32: Skyscraper Example

Figure 3.33: Chained Strong Linked Net Type 2 Example

Figure 3.34: Robust Link Different Chutes Candidate Diagram

Figure 3.35: Robust Link Same Chutes Candidate Diagram

Figure 3.36: Robust Link Same House Candidate Diagram

Figure 3.37: Robust Link Different Ends Grid Snip Example 1

Figure 3.38: Robust Link Different Ends Grid Snip Example 2

Figure 3.39: Robust Link Opposing Conjugate Pair Ends Grid Snip

Figure 3.40: Strong Linked Net Type 1 Example

Figure 3.41: Strong Linked Net Type 2 Example

Figure 3.42: Strong Linked Net Type 3 Example

Figure 3.43: Group Link Candidate Diagram

Figure 3.44: Group Link 2-String Kite Candidate Diagram

Figure 3.45: Group Link Line Examples

Figure 3.46: Group Link Box Examples

Figure 3.47: Base, Link and Cover Set Example

Figure 3.48: Single Base Set - Hidden Single Example

Figure 3.49: Exposed Quad Pattern

Figure 3.50: Not Quite an Exposed Quad Pattern

Figure 3.51: Locked Exposed Triple

Figure 3.52: Hidden Pair

Figure 3.53: Swordfish

Figure 3.54: Even Loop

Figure 3.55: Finned X-Wing

Figure 3.56: Two String Kite

Figure 3.57: Unlocked Set Chain Candidate Diagram

List of Tables

Table 2.1: Cell Specifiers

Table 2.2: Ccell Specifiers

Table 2.3: Ccell Postfixes

Table 2.4: Pattern Combiners

Table 2.5: Operators

Table 2.6: Conditionals

Table 2.7: Relational Specifiers

Table 2.8: Candidate Dressing

Table 2.9: Set Algebra

Table 2.10: Candidate Diagram Symbols

Table 2.11: Candidate Diagram Expressions

Table 2.12: Weak Link Inference Table

Table 2.13: Strong Link Inference Table

Table 2.10: Candidate Diagram Symbols

Table 2.11: Candidate Diagram Expressions

Table 2.14: Weak Link Ended AIC Inference Table

Table 2.15: Strong Link Ended AIC Inference Table

Table 2.16: Strongly Linked Chain Inference Table

Table 3.1: SE-AIC with Box Group Link Inference Table