Uniqueness

Conditional eliminations that use an explicitly stated unique-solution premise: Unique Rectangles, Unique Loops and the Bivalue Universal Grave (BUG).

Unique Rectangle Type 1

One rescue cell contains extra candidates; the deadly pair is removed from it.

Unique Rectangle Type 2

The rectangle's rescue cells share one extra candidate that can be removed from their common peers.

Unique Rectangle Type 3

The extra candidates combine with other cells to form a naked set in a shared house.

Unique Rectangle Type 4

A rectangle digit is locked into two rescue cells, allowing the other rectangle digit to be removed.

Unique Loop Type 1

A longer uniqueness loop has one rescue cell from which the deadly pair can be removed.

Unique Loop Type 2

Rescue cells in a longer loop share an extra candidate that eliminates from common peers.

Unique Loop Type 3

Extra loop candidates form a naked set with other cells in a shared house.

Unique Loop Type 4

One loop digit is locked into the rescue cells, so the other loop digit can be removed there.

BUG Type 1

One guardian candidate prevents the verified BUG state and must be kept.

BUG Type 2

Several BUG exception cells share a guardian digit that can eliminate from their common peers.

BUG Type 3

BUG values combine with nearby cells to form a naked set in a shared house.

BUG Type 4

Two BUG cells lock an additional candidate in their shared house.

How uniqueness-based Sudoku logic works

Uniqueness techniques apply to a properly constructed Sudoku that is guaranteed to have exactly one solution. A deadly construction is an unresolved arrangement that could exchange two digits and produce two valid completions. A Unique Rectangle uses four cells in two rows, two columns and two boxes; a Unique Loop extends the same principle around a longer even loop. Because the deadly form cannot remain in a unique puzzle, at least one cell must break it.

The four types describe different ways those extra candidates provide a rescue. Type 1 removes the deadly pair from a single rescue cell. Types 2 and 4 exploit a shared extra candidate or a conjugate relationship, while Type 3 combines the extras with a subset in a common house. BUG applies the same premise to the all-bivalue endgame state: the cells or candidates that would leave a deadly balanced state are identified and resolved. These are conditional deductions: they should be used only when puzzle uniqueness is known, not as a general substitute for contradiction testing on an arbitrary grid.

← Back to Sudoku Rules