Locked candidates

Also called pointing and claiming. This is the first technique that does not place a digit but removes candidates. The removal then opens a naked or hidden single somewhere else, and a stuck board starts moving again. You need it from 9×9 Hard upward.

Why it works

A box and a line (row or column) overlap in three cells. Suppose every cell in a box that can still take a 5 lies in that overlap, that is, on one line. The box must contain a 5, so the 5 ends up somewhere on that line inside the box. The line then already has its 5, so no cell of the same line outside the box can be 5.

On a real board

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In box 9, 5 can only go in the two circled cells, and both are in column 7. So 5 comes off the rest of column 7 outside the box (red). Play this board →

This is a 9×9 · Hard board, filled as far as naked and hidden singles go. Nothing more can be placed. Candidates are shown for the empty cells of box 9 and column 7.

In box 9, the digit 5 fits only in row 7, column 7 and row 8, column 7.
Both cells are in column 7. So the box's 5 lies on column 7, inside the box.
Therefore remove 5 from row 2, column 7, the part of column 7 outside the box.
That leaves the outlined cell, row 2, column 7, with a single candidate: 9. A naked single fills it, and the board moves again.

Two directions

Name	What you see	Where you remove
Box → line (pointing)	In a box, a digit's candidates all lie in one row or column	That row or column, outside the box
Line → box (claiming)	In a row or column, a digit's candidates all lie in one box	The other cells of that box

The second is the same idea turned around. If every cell of a row that can take a 3 lies inside one box, the row's 3 is in that box. The box can only hold one 3, so its other two rows lose 3 as a candidate.

Spotting it

Pick one digit and, box by box, ask only which line its candidates lie on. When notes sit in fixed spots in each cell, you can see straight away whether the same digit lines up across or down inside a box.
Start with boxes where the digit has only two or three candidates. Widely scattered candidates cannot line up.
After removing, look first at the cells that lost a candidate and the lines they belong to. As in the example, the next move often opens right there.

On 16×16, boxes are 4×4, so a box and a line overlap in four cells. The idea is the same, but locked candidates turn up far more often. On 12×12 the boxes are 3 rows by 4 columns, so a row overlaps a box in four cells and a column in three.

Where you need it

9×9, 12×12 and 16×16 Hard boards were chosen so that they cannot be finished without locked candidates or a naked pair. The first time you try it, open the example board above and find the same spot yourself.