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A cell whose row, column, and box between them already contain eight different digits has only one candidate left — and that digit must go in.

Within one house, a digit has only a single cell it can legally occupy — even though that cell may still show other candidates.

The habit of sweeping the board for one digit at a time, using its existing placements to project elimination lines into empty regions.

Disciplined scanning aimed at one box: use the rows and columns crossing it to eliminate cells until a digit has exactly one home.

When a house has just one empty cell, the single missing digit drops straight in — no candidate analysis required.

When a candidate inside a box is confined to a single row or column, it 'points' outward, letting you eliminate it from the rest of that line.

The mirror of a pointing pair. When a line confines a candidate to one box, the line 'claims' it, clearing it from the rest of that box.

The umbrella term for pointing and claiming: a candidate locked to the intersection of a box and a line can be removed from the rest of whichever region it doesn't need.

Two cells in a house showing the identical two candidates. Those digits are reserved for those cells and can be cleared from the rest of the house.

Two digits that can only appear in the same two cells of a house, disguised by extra candidates. Those extras can be stripped away.

Three cells in a house whose candidates together use only three digits. Those digits lock to the trio and clear from the rest of the house.

Three digits confined to the same three cells of a house, buried among other candidates that can then be removed.

A named case of locked candidates where a line restricts a digit to one box, eliminating it from that box's other cells. The backbone of hard-level pruning.

A candidate forming a rectangle across two rows and two columns lets you eliminate it from the rest of those columns (or rows).

An X-Wing scaled to three rows and three columns. A candidate confined to three shared columns across three rows is eliminated elsewhere in those columns.

The four-line fish. A candidate confined to four columns across four rows is eliminated from the rest of those columns.

A pivot cell {X,Y} sees two pincers {X,Z} and {Y,Z}. Whatever the pivot becomes, one pincer must be Z — so Z is eliminated from cells both pincers see.

An XY-Wing whose pivot carries three candidates {X,Y,Z}. Because the pivot could also be Z, eliminations apply only to cells seen by all three cells.

A single-digit chain: two rows each have the candidate in exactly two cells, sharing one column. The far ends eliminate the candidate from cells that see both.

A single-digit pattern using one row conjugate pair and one column conjugate pair that meet in a shared box. The two loose ends eliminate the digit from the cell they both see.

Exploits the single-solution guarantee: four cells forming a rectangle across two boxes with the same pair would allow two solutions, so the deadly pattern must be broken.

A chain of bi-value cells all sharing the same pair {X,Y}. Alternating X/Y along the chain means the two ends are opposite, so any cell seeing both loses both candidates.

For one candidate, colour the ends of conjugate pairs alternately and propagate. Contradictions in the colouring drive eliminations.

Alternating strong and weak links in a single candidate. Following the chain yields eliminations wherever both endpoints see a common cell.

Chains that close into a loop. A fully alternating loop forces eliminations along every weak link around it, often several at once.

Assume each candidate of a cell in turn and follow the forced consequences. If every assumption forces the same result somewhere, that result is certain.