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.
BUG+1 is the technique that puts Bivalue Universal Grave reasoning to work. Imagine a grid where every unsolved cell has exactly two candidates — except one cell, which has three. That cell is the +1. Two of its three candidates already appear twice in each of its row, column, and box; the third candidate appears three times. The third candidate must be the answer for that cell. Anything else would leave a true BUG state, and the puzzle's uniqueness forbids it.
How to fire the technique
Three conditions need to hold simultaneously:
- Every unsolved cell on the grid has exactly two candidates, except one cell that has three.
- For each of the three candidates in the +1 cell, count how many times that candidate appears as a pencil mark in the cell's row, column, and box.
- Two of the three candidates appear exactly twice in each unit; one appears three times.
The candidate that appears three times is the answer. Place it.
The reasoning: if the +1 cell took one of the two-times candidates instead, the third occurrence of that candidate elsewhere would still be there, and the third candidate (the three-times one) would have only two cells left. Combined with all other cells being bivalue, the resulting state is a true BUG — two valid solutions. To avoid that, the +1 cell takes the three-times candidate, removing its third occurrence and leaving the grid in a regular bivalue state with a forced solution.
Why solvers find it elegant
BUG+1 is one of the quickest closing moves in the late game. A puzzle that's down to mostly bivalue cells looks intimidating — chain techniques would take many steps to resolve — but if a single 3-candidate cell exists, BUG+1 closes the puzzle in one placement. The eyeball-scan version of the technique is fast: count pencil marks, find the asymmetry, place.
The catch is the same as for unique rectangle and the parent BUG concept: the move depends on the puzzle being uniquely solvable, which is a meta-property rather than a direct rule. Solvers who reject uniqueness-based arguments will solve the same puzzles via longer chain techniques. Solvers who accept the move close their late games faster.
When you'll see it
Master and extreme puzzles often reach near-BUG states in their final moves. A useful habit is, whenever a puzzle's pencil marks compress to almost-all-bivalue, check whether exactly one 3-candidate cell remains. If yes, run the BUG+1 conditions; if all three hold, the placement is immediate.
See also
- 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.
- 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.