Eliminate first, then fill
2-step reasoning
When no cell can be filled directly, you need an intermediate step: prove that a digit cannot be in certain cells. Step one is finding a locked structure — a digit trapped in the intersection of a box and a line, or a group of digits that takes over a group of cells. Step two is using that elimination to open up a new placement.
From this level on, write in the candidates (pencil marks) for every empty cell. These patterns only show up when you can see every possibility of every cell.
Where is this digit trapped?
If a digit in a box lies on only one line (or the reverse), it claims that line: locked candidates.
Which cells are already taken?
N cells holding only N digits (naked set), or N digits living in only N cells (hidden set): those digits cannot appear anywhere else.
When to use it: When you have exhausted hidden and naked singles and the board still won't move.
6 techniques
Locked Candidates: Pointing
Pointing Pair/Triple · Locked Candidates Type 1
In a box, digit d lies on a single row (or column), so d is removed from the rest of that row (column).
Difficulty
Locked Candidates: Claiming
Box/Line Reduction · Locked Candidates Type 2
In a row (column), digit d lies inside a single box, so d is removed from the other cells of that box.
Difficulty
Naked Pair
Naked Pair · Locked Pair
Two cells in a unit have the same two candidates only, so those digits are removed from the rest of the unit.
Difficulty
Hidden Pair
Two digits can only go in the same two cells of a unit, so every other candidate is cleared from those cells.
Difficulty
Naked Triple
Three cells in a unit share just three candidates between them, so those digits are removed from the rest of the unit.
Difficulty
Hidden Triple
Three digits appear in only the same three cells of a unit, so every other candidate is cleared from those cells.
Difficulty