2. Foundation

This section is my attempt to organise the collective body of foundational material found on the Internet and other sources into a logical consistent flow explaining concepts and how they are related. This section focuses more developing the theory of logic involved in solving puzzles, mostly leaving the practical application of this theory to the next chapter on Human Solvable Patterns.

In the effort to be consistent and unambiguous, some terms have been refined or renamed to be:

• less overloaded,

• more consistent,

• more self descriptive, and

• relate better within the context that they are described.

To keep the reach of this text as wide as possible, verbal or algorithmic descriptions are favoured over using less common algebraic symbols and esoteric formulae.

• 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