BUG, the bivalue universal grave, is a late-puzzle uniqueness argument. It only fires when the grid is almost solved and nearly every empty cell has two candidates. When the right conditions appear, BUG ends the puzzle in a single placement.
How it works
Imagine reaching a state where every empty cell has exactly two candidates and every unplaced digit appears exactly twice in each of its rows, columns and boxes. That configuration has two valid solutions, because you can swap digit pairs across the grid and end up with another correct completion.
Valid sudoku has one solution. So that state is impossible. The cell that prevents it is the one cell with three candidates instead of two. Whatever digit, when removed, would leave a bivalue universal grave behind, must be the digit that goes in that trivalue cell.
In practice: look at the trivalue cell. Pick the candidate that appears three times (not twice) in the cell's row, column or box. That is the digit that has to go there.
When to look for it
Late in evil puzzles when most cells are placed. If you scan the remaining empty cells and find that almost all of them carry exactly two candidates, with one cell holding three, check BUG immediately.
The pattern is satisfying because the rest of the puzzle has already done the work. BUG just provides the last step.
Step-by-step example
- Confirm every empty cell has exactly two candidates except for one cell with exactly three.
- Look at the trivalue cell. Identify its row, column and box.
- For each of the three candidates, count how many times it appears in the cell's row, column and box (as a candidate, not a placed digit).
- The candidate that appears three times in one of those units (instead of two) is the digit that goes in the trivalue cell.
- Place it. The rest of the puzzle collapses into singles.
Tips for spotting it
- BUG only fires when the grid is almost solved. Do not waste time on it earlier.
- One trivalue cell among bivalues is the signature. Scan candidate-set sizes first.
- Pencil marks must be flawless. A drifted candidate kills the pattern silently.
- BUG often ends a puzzle in one move. Worth checking every late-game position.
Common mistakes
- Applying BUG before the pattern fully forms. Every cell other than the trivalue one must be exactly bivalue.
- Picking the wrong digit. The right one appears three times in the trivalue cell's row, column or box, not two.
- Using the technique on puzzles without guaranteed uniqueness.
- Skipping the check because the grid still has a few placements left. BUG is the last move, not earlier.
Practise it
End-of-game positions on evil sudoku regularly form BUG patterns. When you reach a point where every empty cell looks bivalue, scan for the one that is not. BUG pairs naturally with unique rectangle; both rely on the puzzle having a single solution and both clean up the last few placements.