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A digit's strong link in a row meets a strong link in a column, with the two cells sharing a box at the corner. Eliminates the digit from cells seeing both far ends.

An advanced colouring technique that two-colours every digit's strong-link graph at once, finding cross-digit eliminations that single-coloured chains miss.

Three Almost Locked Sets in a Y-wing-like configuration. Generalises ALS-XZ to a longer chain and surfaces eliminations that a single-pair ALS interaction would miss.

An interaction between two Almost Locked Sets sharing a common candidate. Eliminates a second shared candidate from cells outside both sets that see all instances.

The general-purpose chain technique. Alternates strong and weak links along a sequence of candidates, eliminating a digit from any cell that sees both endpoints' candidates.

A near-final puzzle state where every unsolved cell has exactly two candidates. The puzzle's uniqueness rules out reaching this state, so the move that prevents it is forced.

When the grid is one cell away from a Bivalue Universal Grave, the digit appearing three times in that cell must be the answer — placing anything else closes the deadly state.

Killer-Sudoku reasoning across cages that share cells with units. The shared cells must satisfy both the cage's sum and the unit's 45 rule, surfacing eliminations.

Decomposing a large killer cage into smaller sub-deductions using the 45 rule across the units the cage passes through.

A killer-Sudoku move that uses the puzzle's uniqueness guarantee against the cage's possible digit combinations to rule out configurations that would imply two solutions.

A box where a digit's candidates sit in one row and one column intersecting inside the box. Combined with a strong link, eliminates the digit elsewhere on the matching axis.

An X-wing where one of the four corners has an extra candidate cell — a fin — in its row or column. The eliminations restrict to cells that see both the X-wing and the fin.

A trial-and-converge technique. Pick a candidate, try both values, follow each through the puzzle. Anything that ends up the same in both branches is forced and can be placed.

The four-row, four-column generalisation of swordfish. A digit confined to the same four columns across four rows lets you eliminate it elsewhere in those columns.

Fish patterns adapted for killer Sudoku. The same X-wing or swordfish argument runs on candidate cells, with cage-sum constraints sometimes tightening the elimination set.

An extension of simple coloring to two or more disjoint chains on the same digit, finding eliminations that fire when the chains interact at a distance.

A trial-and-contradiction technique. Pick a candidate, assume it's the answer, propagate the consequences for that digit alone — if a contradiction lands, eliminate.

An exhaustive technique that enumerates every legal placement-pattern of a single digit, then eliminates candidates that don't appear in any pattern.

A technique that two-colours the strong-link graph of a single digit, then eliminates candidates that see both colours — the entry point into chain reasoning.

Two strong links on the same digit, sharing a column on one end and not the other — eliminates the digit from any cell that sees both 'roof' cells of the pattern.

A pattern crossing two Almost Locked Sets in a row-and-box (or column-and-box) intersection. Niche, distinctive, and surprisingly common once you know to look.

A killer-Sudoku reasoning pattern. Multiple cages whose sums constrain each other through shared cells or units, propagating arithmetic deductions across the chain.

A close cousin of Pattern Overlay. Enumerates valid placement-templates for a digit, then uses pairwise incompatibility to surface eliminations a single template wouldn't catch.

A pattern where four cells across two rows and two columns share the same two candidates — a configuration that would imply two solutions, so it cannot be allowed to complete.

A four-cell wing pattern. Three pivot cells share a fourth candidate that all see the wing cell, eliminating that fourth candidate from any cell that sees all four.

A chain of bivalue cells linked by shared candidates. Eliminates a digit from any cell that sees both endpoints — the workhorse intermediate-to-advanced chain technique.

A closed XY-chain — the endpoints meet rather than going off into eliminations. Every step in the loop is constrained from both sides at once, surfacing extra eliminations.