Intermediate Synthesis: Subset Mastery
The intermediate tier is all about subsets: recognizing groups of candidates that lock each other in place. Review your mastery of these elimination techniques before advancing to fish and wing patterns.
Techniques Covered
Box/Line Reduction
Eliminating candidates when they are confined to one box within a row or column.
Naked Pairs
Two cells in a unit sharing exactly two candidates.
Naked Triples
Three cells in a unit whose candidates are a subset of three digits.
Naked Quads
Four cells whose combined candidates contain at most four digits.
Hidden Pairs
Two candidates confined to exactly two cells in a unit.
Hidden Triples & Quads
Three or four candidates confined to three or four cells.
Self-Assessment Checklist
Check each skill you feel confident about. If any items are unclear, revisit the relevant technique lesson.
- ☐Can you find Naked Pairs in under 30 seconds?
- ☐Do you understand the relationship between Naked and Hidden subsets?
- ☐Can you apply Box/Line Reduction consistently?
- ☐Can you find Quads without hints?
- ☐Do you know when to look for hidden subsets vs naked subsets?
- ☐Can you solve Medium-rated puzzles reliably?
What You Should Be Able To Do
Solve Medium-Rated Puzzles Reliably
Medium puzzles require subset techniques. You should be able to work through them without needing advanced patterns like fish or chains.
Recognize All Subset Patterns
Whether it is a Naked Pair or a Hidden Quad, you should be able to identify the pattern and know which candidates to eliminate and from which cells.
Know When to Look for Hidden vs Naked Subsets
Naked subsets jump out when cells share a small set of candidates. Hidden subsets appear when candidates only live in a few cells. Knowing which to scan for first saves time.
Technique Recognition
Test your ability to identify which technique applies in a given situation. These exercises build the pattern-recognition skills that separate reading about techniques from actually using them.