Naked single
A cell with a single remaining candidate must take it
How to use it
Instead of counting a whole line, count one cell's pencil marks. Keep candidates for each empty cell: the letters not yet in its row or column, the digits not yet in its row or column — then pruned further by the pair rules (see pair elimination). If exactly one candidate survives on a layer, the cell must take it.
Cells with many filled neighbours are the fertile ones: a cell whose row and column are both nearly complete has few candidates left, so scan the intersections of long lines first. A naked single is usually the first move after a batch of givens.
Why it is sound
A cell's candidates are the symbols not yet used in its row or column, further pruned by the pair rules; every excluded symbol would duplicate a peer's value or reuse a used pair, which no valid solution allows. If exactly one candidate survives, every solution assigns it to the cell.
A worked example
Look at the digit layer of r4c1: its row already carries 3 and 2, its column carries 1 and 2 — so the digits 1, 2, 3 are all excluded and only 4 remains. The cell takes 4. That is the whole move: one cell, one layer, all other candidates crossed out by the crossing lines. The placement then strips 4 from row 4 and column 1, often handing the next move to a neighbour.