Bivalue Universal Grave (BUG)
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.
A Bivalue Universal Grave is a hypothetical puzzle state where every remaining unsolved cell has exactly two candidates and every digit appears exactly twice in every unit. Like the deadly pattern of a unique rectangle, a BUG configuration has two valid solutions — the candidates can be swapped in pairs throughout the grid without breaking any constraints. Sudoku's uniqueness rules out a BUG, so any move that would lead to one is forbidden.
How a BUG looks
In a true BUG, every cell carries exactly two pencil marks. Every digit has exactly two candidate cells in every row, column, and box. The candidate graph is a "perfect" bipartite structure — and exactly that perfect structure is what makes the configuration ambiguous. A solver that arrives at a BUG state has, by definition, lost track of which solution applies, because both colourings of the bipartite graph are valid.
Real puzzles never enter this state. What real puzzles enter is a state one move away from BUG: nearly every cell is bivalue, but one cell has three candidates instead of two. That's the BUG+1 configuration, and it's where the technique fires.
Why this is the same family as unique rectangle
Both unique rectangle and BUG exploit the puzzle's uniqueness — they reason about what the puzzle cannot look like and use that constraint to force a move. Some solvers accept both as legitimate techniques; others consider both controversial because they aren't strictly derived from the no-repeats rule. The same pragmatic position applies: every published Sudoku has been checked for uniqueness, so the BUG argument is sound on any puzzle a solver actually encounters.
The conceptual link to BUG+1 is what makes BUG a useful idea in practice. The grave state itself is a hypothetical; the move that prevents reaching it is the technique.
When you'll see it
BUG patterns appear on master and extreme puzzles in their late-game state, when most cells are already bivalue. The clue is usually visual: scanning a partially-solved grid and noticing that almost every remaining cell has only two candidates. If exactly one cell stands out with three, BUG+1 is alive and it's worth checking the candidate-frequency conditions before reaching for harder chain techniques.
See also
- BUG+1— 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.
- Unique rectangle— 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.
- Candidate— A digit (1–9) a cell could still legally hold — one not yet ruled out by anything in its row, column, or 3×3 box. Every empty cell has between one and nine.
Read more
- Which technique is this puzzle asking for
How to read a fresh hard Sudoku and predict which intermediate technique will break it open before you've placed a single digit.