Sudoku uniqueness techniques use a whole-puzzle premise:
the puzzle is intended to have exactly one solution.
They detect candidate structures that would allow two interchangeable completions if a certain state were reached. Because a proper published Sudoku is expected to have one solution, that deadly state must be prevented.
This family includes Unique Rectangles, Hidden/Avoidable Rectangle ideas, BUG+1, and related patterns.
It is powerful — and conceptually different from ordinary local rules.
Uniqueness is not a fourth Sudoku rule
Classic Sudoku rules constrain rows, columns and boxes.
They do not by themselves state that a partially filled puzzle has exactly one completion.
Uniqueness is a property of a properly constructed puzzle. That matters because a uniqueness deduction is valid only when you are entitled to rely on that property.
If the puzzle may have multiple solutions, uniqueness techniques can remove a candidate that belongs to a valid alternate solution.
What is a deadly pattern?
A deadly pattern is a candidate configuration that would permit two or more solutions without violating row/column/box rules.
The classic example is a four-cell rectangle containing two digits in a swappable arrangement. If both assignments remain possible, the digits can trade places and produce two solutions.
Uniqueness techniques do not solve the deadly pattern after it appears. They reason that a valid unique puzzle must contain something that prevents it.
Unique Rectangles
A Unique Rectangle uses four cells occupying:
- exactly two rows;
- exactly two columns;
- exactly two boxes.
Two digits form the dangerous interchangeable pattern.
Type 1
One corner contains additional candidates. At least one additional candidate must survive to prevent the deadly two-digit rectangle.
Therefore the two UR digits can be eliminated from that corner.
Types 2–6
Other UR types use extra candidates, Strong Links, subsets or different corner arrangements to prove eliminations while preventing the deadly state.
VeyraPlay keeps those types summarized inside the Unique Rectangle Guide for this freeze rather than creating five near-duplicate URLs. If search data later shows strong independent intent, they can become dedicated pages without changing the family model.
Hidden Rectangle
A Hidden Rectangle is a uniqueness pattern where extra candidates obscure the two-digit rectangle more heavily. Strong-link restrictions on the UR digits reveal which corner candidates cannot survive.
It belongs to the same conceptual family: prevent a swappable two-solution state.
Avoidable Rectangle
Avoidable Rectangles involve already solved cells as part of the rectangle.
A crucial condition is whether those solved cells are givens. A fixed given cannot be swapped, so it can destroy the ambiguity on which the technique relies.
That makes Avoidable Rectangles unusually dependent on the distinction between clues and later placements.
BUG and BUG+1
A Bivalue Universal Grave (BUG) is a larger deadly state:
- every unsolved cell is bivalue;
- every candidate appears exactly twice in every row, column and box in which it occurs.
That structure has two completions.
In BUG+1, one cell carries one extra candidate beyond the BUG pattern. That additional candidate must be true to prevent the puzzle from collapsing into the two-solution BUG state.
The BUG conditions must be verified. “Every cell is bivalue except one trivalue cell” is not sufficient.
Why some solvers avoid uniqueness techniques
Uniqueness techniques have a philosophical difference from ordinary candidate logic.
A Naked Single is true because the row/column/box constraints leave one legal value.
A UR elimination may be true because otherwise the puzzle would have multiple solutions.
Some solvers prefer a technique set that derives everything from local constraints without assuming the constructor's uniqueness guarantee.
Both styles are legitimate. VeyraPlay labels the premise explicitly so the solver can choose.
When is the uniqueness premise safe?
Reasonable cases include:
- a published puzzle from a source that guarantees uniqueness;
- a VeyraPlay puzzle whose solution count has been verified;
- a generated puzzle checked by a complete solver.
Avoid uniqueness techniques when:
- the puzzle source is unknown;
- you are testing an unfinished construction;
- the puzzle may intentionally allow multiple solutions;
- the variant has a different solution model you have not verified.
Uniqueness techniques vs contradiction
Both can reject a candidate, but the contradiction differs.
Ordinary contradiction:
this candidate causes a cell or house to violate Sudoku constraints.
Uniqueness contradiction:
this candidate leaves two valid completions, contradicting the puzzle's unique-solution premise.
That distinction is worth preserving in explanations.
Common uniqueness mistakes
Treating uniqueness as a basic rule
It is a puzzle-level assumption.
Ignoring geometry
UR cells must satisfy the required two-row/two-column/two-box structure.
Using a UR on an unverified puzzle
The proof depends on uniqueness.
Applying BUG+1 from cell counts alone
You must verify the candidate occurrence conditions too.
Assuming every rectangle is a Unique Rectangle
The relevant candidate pair and deadly interchangeability must exist.
FAQ
Are uniqueness techniques logically valid?
Yes when the puzzle is known to have one solution and the technique's specific pattern conditions are satisfied.
Do I need uniqueness techniques to solve Sudoku?
No. Many puzzles can be solved without them, and some solver styles deliberately avoid the uniqueness premise.
How many Unique Rectangle types are there?
Common taxonomies describe Types 1–6 plus Hidden and Avoidable Rectangles, with additional variants in expert literature.
Is BUG+1 a Unique Rectangle?
No. BUG+1 is a broader uniqueness pattern, but it relies on the same one-solution premise.
Why does VeyraPlay not create a page for every UR type yet?
The family is covered here and in the main Unique Rectangle Guide. Individual type pages can be split later if real search or product data justifies separate intent.
What to learn next
Use the Unique Rectangle Guide for Type 1 geometry, BUG+1 for the global bivalue structure, and Unique Solutions for the underlying puzzle-validity theory.