Bivalue Universal Grave

Also called BUG, Bivalue Universal Grave (general).

New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.

This technique assumes the puzzle has exactly one solution. It reasons about what would create a second solution, so it is only valid on a properly constructed puzzle. Do not use it to check whether a grid is well formed.

What it means

Say every open square had just two numbers left. And say each number had just two homes in every group. That grid would have two answers. A good puzzle has one. So whatever breaks that tidy pattern must be true.

The exact rule, for stronger players

The rule, stated exactly: A grid state in which every unsolved cell has exactly two candidates and every digit appears exactly twice in every house is a BUG. Such a state has an even number of solutions, so it cannot occur in a uniquely solvable puzzle.

What it removes: Nothing directly. The value comes from being one step away, which is BUG+1 and its relatives.

Why it works: In that state every digit forms conjugate pairs throughout, so the remaining assignment can be flipped wholesale, producing a second solution. This technique is only valid when the puzzle is known to have exactly one solution. It is not a deduction about Sudoku rules, it is a deduction about the puzzle setter's promise. On a grid with multiple solutions it produces wrong answers.

Worked examples

None yet. This pattern does not turn up in our daily boards, so there is no real example to show. We would rather wait than draw a fake one.

Learn these first

Deadly PatternA shape that would give the puzzle two answers if it ever appeared.
Naked PairTwo squares in the same group both hold only the same two digits.

Related uniqueness

BUG-LiteThe pattern applied to part of the grid rather than all of it.
BUG+1Say every open square had two numbers left, and each number had two homes in every group.
BUG+2The same idea when two squares break the pattern instead of one.
BUG+3The same again with three odd squares.
Extended Unique RectangleA bigger version using six squares and three numbers instead of four and two.

How often does it come up?

Our rough estimate: the pure state never appears in a valid puzzle by definition. BUG+1 is what solvers actually meet.

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