Techniques

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 a digit's only possible cells inside a row or column all sit in the same 3×3 box, that digit can be eliminated from the rest of that box.

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.

In Killer Sudoku, placing the last digit of a cage by subtracting the digits already in it from the cage's sum. The cage's leftover arithmetic does the work.

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.

In Killer Sudoku, when a one-cell cage's sum directly forces the cell's digit. The simplest possible killer deduction — the cage's sum is the cell's value.

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.

Kakuro deduction at the intersection of two runs. The cell shared between a row run and a column run must hold a digit valid in both — usually pinning the cell directly.

The 45 rule applied across two or more units that a cage spans. Sums and the cells that cross unit boundaries balance via the same 45-each-unit constraint.

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 kakuro placement where cross-reference and run constraints together pin a single cell to a single digit. The kakuro equivalent of a hidden single.

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.

Two digits whose only possible cells inside a unit are the same two cells — even if those cells still show other candidates. The digit-first sibling of the naked pair.

A digit with only one possible cell within a unit (row, column, or 3×3 box) — even if that cell could legally hold other digits. The unit-first sibling of the naked single.

Three digits whose only possible cells inside a unit are the same three cells — even if those cells still show other candidates. The digit-first sibling of the naked triple.

In Killer Sudoku, deducing a cell's digit by applying the 45 rule to a unit whose cages partly overlap with — or partly spill out of — that unit.

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.

Two cells in a kakuro run sharing the same two-digit possible set. The two digits are confined to those two cells, eliminating them from every other cell of the run.

The reference table mapping each (cell-count, target-sum) pair to its valid digit combinations. The foundational lookup that anchors most kakuro deduction.

Three cells in a kakuro run sharing the same three-digit possible set — the kakuro analogue of the naked triple. Eliminates those digits from the rest of the run.

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.

In Killer Sudoku, when two cells in the same unit are confined to the same two-digit pair by their cage's arithmetic — eliminating those digits from elsewhere in the unit.

In Killer Sudoku, when three cells in the same unit are confined to the same three-digit set by their cage's arithmetic — eliminating those digits from elsewhere in the unit.

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.

Two cells in the same unit whose candidate sets are identical and contain exactly two digits. Together they claim those digits across that unit and rule them out elsewhere.

A cell on the Sudoku grid that has only one legal candidate left — the simplest deduction in the game, and the one that solves most of an easy puzzle.

Three cells in the same unit whose candidates collectively use only three digits. Together they claim those digits across the unit and rule them out elsewhere.

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.

Killer-Sudoku reasoning where partial information about a cage's digits — eliminations, placements, or external constraints — narrows the cage's combinations to a smaller set.

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

When a digit's only possible cells inside a 3×3 box all share a row or a column, that digit can be eliminated from the rest of that row or column outside the box.

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.

The X-wing's three-row counterpart. When a digit's possible cells across three rows fall in the same three columns, that digit can be eliminated from those columns elsewhere.

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.

In Killer Sudoku, the fact that every row, column, and 3×3 box must sum to 45 — because 1+2+…+9 = 45. The foundational arithmetic identity behind most killer techniques.

In Killer Sudoku, cage sums whose cell count and total leave only one possible digit set. The arithmetic shortcut behind most killer pair and triple deductions.

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 kakuro run whose cell count and target sum together force exactly one valid digit combination — the most direct deductive move in the puzzle.

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.

When a digit's only two cells across two rows form a rectangle in two columns — eliminating that digit from the rest of those columns. Or the same shape rotated 90°.

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.

A three-cell wing pattern where the pivot has three candidates and each wing has two — eliminating the shared candidate from any cell that sees all three.

Three bivalue cells where the pivot shares one candidate with each wing — eliminating the third candidate from any cell that sees both wings.