BUG, which stands for Bivalue Universal Grave, is a uniqueness-based Sudoku technique that leverages the fundamental principle that every valid Sudoku puzzle has exactly one solution. A BUG state occurs when nearly all unsolved cells in the grid have been reduced to exactly two candidates each. If every remaining cell had exactly two candidates, the puzzle would have multiple solutions — a contradiction for a valid puzzle. Therefore, if all unsolved cells have two candidates except for one cell that has three, the extra candidate in that cell must be the correct value.
The reasoning behind BUG is elegant: in a true BUG state (all bivalue cells), every candidate would appear exactly twice in each row, column, and box among the unsolved cells. This symmetric distribution would allow you to swap candidates freely, producing multiple valid solutions. Since a proper Sudoku must have a unique solution, this state is impossible. The cell with three candidates breaks this symmetry — removing one of its candidates would create the forbidden BUG state, so the extra candidate (the one that appears three times in a row, column, or box rather than twice) must be the correct digit for that cell.
BUG is most commonly encountered in its simplest form — BUG+1 — where exactly one cell has more than two candidates. However, variations exist (BUG+2, BUG+3, and so on) that require additional reasoning such as forcing chains to resolve. Recognizing a BUG situation requires careful candidate management throughout the solve. When you notice that your puzzle is approaching a state where almost every cell has exactly two candidates, check for the BUG pattern. It is closely related to the Unique Rectangles technique, as both exploit the uniqueness constraint, and it pairs well with Naked Pairs analysis that helps reduce candidates to the bivalue state.
Try It Yourself
Walk through each step of the bug (bivalue universal grave) technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Examine the current state of the grid. Most unsolved cells have been reduced to exactly two candidates through earlier techniques. Count the candidates in each empty cell carefully.
Step-by-Step Guide
Reduce the puzzle as far as possible using all available techniques until progress stalls.
Examine all remaining unsolved cells and count how many candidates each contains.
Check if every unsolved cell has exactly two candidates — except for exactly one cell with three candidates.
If this pattern holds, you have identified a BUG+1 situation.
In the cell with three candidates, determine which candidate appears three times in its row, column, or box (rather than the expected two).
That over-represented candidate is the solution for the BUG cell — place it immediately.
Verify the placement resolves the grid correctly without contradictions.
Imagine a group of people where everyone has exactly two possible seats. They could swap endlessly and all arrangements would work -- that is a graveyard of ambiguity. One person holding a third option is the tiebreaker who forces a single valid seating chart.
BUG is mathematically sound because a state where every unsolved cell has exactly two candidates means each candidate appears exactly twice per unit among the remaining cells, creating a perfectly symmetric system with multiple valid assignments. This violates the unique-solution constraint of a valid Sudoku. The cell with three candidates is the only asymmetry in the system, and the candidate that appears three times in a unit (rather than the expected two) is the one that breaks the symmetry and must be placed to collapse the grid to a single solution.
When to use: Use BUG when most unsolved cells have exactly two candidates and only one cell has three. This typically appears near the end of a difficult solve after extensive candidate elimination.
Common Mistakes to Avoid
Applying BUG+1 logic when more than one cell has three or more candidates.
BUG+1 only applies when exactly one cell has more than two candidates. If multiple cells have three or more, you need BUG+N analysis or a different technique entirely.
Selecting the wrong candidate as the solution -- picking one that appears twice instead of three times in the relevant units.
The correct value is the candidate that appears three times (not two) in at least one of the cell's row, column, or box. This is the digit that breaks the BUG symmetry.
More Examples
See bug (bivalue universal grave) applied in different puzzle configurations to strengthen your pattern recognition.
BUG+1 with one trivalue cell
Highlighted cells show the bug (bivalue universal grave) pattern
Practice Puzzles
Apply the bug (bivalue universal grave) technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- All unsolved cells have exactly two candidates except one cell with three
- Action:
- Place the candidate that appears three times in the trivalue cell's units
- Look for:
- A grid where almost every cell has exactly two candidates