Techniques

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.