- Every empty cell starts with up to 9 candidates; your goal is to eliminate all but one
- The simplest elimination: a digit already in a shared row, column, or box removes it as a candidate
- Naked and Hidden subsets eliminate candidates across groups of cells simultaneously
- Locked candidates eliminate a digit from an entire row or column based on box constraints
- More eliminations = fewer candidates = more forced cells = faster solving
Level 1: Direct Elimination
The most basic elimination: if digit 5 already appears in row 3, then 5 is not a valid candidate for any other empty cell in row 3. Apply this across all three unit types (row, column, box) for every given digit, and you have the foundation of all Sudoku solving.
After direct elimination, any cell with only one candidate remaining is a Naked Single — fill it in immediately and propagate its elimination to its peers.
Level 2: Cross-Hatch Scanning
Pick a digit. For each box, use the rows and columns that already contain that digit to eliminate cells within the box. If only one cell remains in the box, that is a placement. If the digit is confined to one row or column within the box, that is a locked candidate — the digit cannot appear elsewhere in that row or column.
Level 3: Naked Subsets
When N cells in a unit share exactly N candidates between them, those N candidates cannot appear in any other cell of that unit. Common examples:
- Naked Pair: Two cells with the same two candidates — eliminates both from the rest of the unit
- Naked Triple: Three cells sharing three candidates — eliminates all three from the rest of the unit
Level 4: Hidden Subsets
When N candidates in a unit can only go in N cells, those cells cannot hold any other candidates. The distinction from naked subsets: you look at where candidates can go rather than what candidates cells have.
- Hidden Single: One candidate confined to one cell in a unit — place it immediately
- Hidden Pair: Two candidates confined to two cells — remove all other candidates from those two cells
Level 5: Intersection Eliminations
When a candidate in a box is confined to one row or column, it can be eliminated from the rest of that row or column outside the box. This works in both directions: if a candidate in a row is confined to one box, it can be eliminated from the rest of that box.
Building a Habit
The key to fast, accurate solving is applying these eliminations systematically rather than randomly. A good workflow: fill pencil marks → apply naked singles → apply hidden singles → check locked candidates → look for pairs → repeat. The full techniques library has worked examples for every level. Practice in a live Hard puzzle where all five levels are typically required.