A BUG is a hypothetical state where every unsolved cell has exactly two candidates, and each digit appears exactly twice in every row, column, and block where it is still unsolved. This perfect symmetry means every candidate is paired with another candidate of the same digit and another candidate in the same cell.

That symmetry creates closed loops that can be resolved in two opposite ways. Both resolutions satisfy the Sudoku constraints, so the grid would have multiple solutions. A valid one-solution puzzle can never be allowed to fall into a pure BUG state.

BUG+1 is the near-miss version of BUG. Every unsolved cell is bivalue except one trivalue cell with three candidates.

Two candidates in the trivalue cell behave like normal BUG candidates: if you removed the third candidate, those two would fit into the global twice-per-house BUG symmetry. The third candidate is the extra digit. It is the only thing preventing the puzzle from becoming a multi-solution BUG.

If the extra digit were removed, the board would become a BUG (multiple solutions). Since that is impossible, the extra digit must be the answer. BUG+1 yields a direct placement, not just a candidate elimination.

Method 1: Count occurrences in houses. For each candidate in the trivalue cell, inspect the cell's row, column, and block. BUG candidates keep the twice-per-house pattern. The extra candidate is the one that creates a third occurrence in at least one of those houses.

Method 2: The removal test. Temporarily remove one candidate from the trivalue cell. If the remaining grid becomes a pure BUG pattern, the removed candidate is the extra digit. Since a valid puzzle cannot enter that BUG state, the extra digit must stay and is the solution for the cell.

BUG+1 relies on the assumption that the puzzle has exactly one solution. Other uniqueness techniques include Unique Rectangles and Avoidable Rectangles. BUG+1 is perfectly sound for puzzles from reputable sources.

Level 8 (Expert). Relatively uncommon -- requires a very specific near-BUG state late in the solving process. When it appears, it yields a satisfying direct placement.

Check when 8-15 unsolved cells remain and most are bivalue. Quick scan: if any cell has more than 3 candidates, stop. If two or more have 3, stop. If exactly one has 3 and all others have 2, verify the BUG+1 conditions. Accurate pencilmarks are essential.

BUG+1 detects when the board is one cell away from a multi-solution state. By identifying the single trivalue cell and its extra digit, the technique yields a direct placement. Level 8 (Expert), rare but elegant.