3. Human Solvable Patterns

Human solvable patterns rely on logic that is not too complicated and involved to resolve. As expertise in solving puzzles improves, one can resolve more complicated patterns, so it is a matter of personal judgement where to draw the “too complicated” line.

Practically, a point of diminishing returns exists between:

• the complexity of the pattern,

• the complexity of the logic to resolve the pattern, and

• the probability of the pattern’s occurrence.

This text does not claim to be an exhaustive coverage of all possible conditional logic techniques. There is often patterns that can be solved with two or more techniques. An objective of this treatise is to present a set of techniques that can be used to solve any puzzles.

However, as logic techniques get more complex and involve many variables they in turn become too complex and take too long for even the expert mere mortals among us without some high speed computational assistance. Some such techniques are presented, and it is left to the reader to decide for themselves where computer aided logic solving starts, At least the most simplest patterns of these complex techniques can be solved unaided.

Where multiple techniques can resolve a pattern, I favour the most generalised technique or the one with broadest reach, unless it is much more complex than another technique.

Many resources on the internet document the identification and resolution of patterns effectively. I reference all sources, and often, rather than rehashing their information, I, with gratitude, defer to them. descriptions.

• 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