BUG+1 (Bivalue Universal Grave)

BUG stands for Bivalue Universal Grave: a position in which every unsolved cell has exactly two candidates and every candidate appears exactly twice in each row, column and box it can still go in. Such a position never has exactly one solution, so a proper puzzle never reaches it. In BUG+1 the board is one candidate away from that grave: every unsolved cell has two candidates except one cell with three, and one of those three digits appears three times in that cell's row, column and box. That digit is the one that keeps the board out of the grave, so the three-candidate cell must be that digit. Like the Unique Rectangle, BUG+1 relies on the puzzle having one solution. It is an Expert technique in Bare Sudoku.

When to use it

Late in a puzzle, when nearly every empty cell is down to two candidates and the usual techniques have stopped. If exactly one cell has three candidates and all others have two, test for BUG+1 before trying chains.

How to spot it

Count candidates: every unsolved cell must have two, except one cell with three. In that cell's row, column and box, count how often each of its three digits appears. Two of them appear exactly twice in each of those units; the third appears three times. That third digit is the answer for the cell. If more than one cell has three candidates, or a cell has four, the simple BUG+1 does not apply.

Example

Bold digits are given, blue digits were placed while solving, small digits are candidates. Highlighted cells form the pattern, crossed-out candidates are removed, and a circled candidate is the digit to place.

1. Every unsolved cell has exactly two candidates except r9c6, which has three: 3, 4, 6.
2. In row 9, column 6 and box 8, digit 4 appears three times as a candidate. Every other candidate appears exactly twice in each unit where it can still go.
3. If r9c6 were not 4, it would have two candidates like every other cell, and the board would be a Bivalue Universal Grave, which never has exactly one solution. The puzzle has one solution, so that cannot happen.
4. So r9c6 is 4. Remove 3, 6 from it, and the cell is solved.

Common mistakes

• Applying it when two cells have three candidates, or one cell has four. BUG+1 needs exactly one extra candidate on the whole board.
• Picking the wrong digit of the three. The answer is the digit that appears three times in the cell's row, column and box.
• Using it on a puzzle that may have several solutions. Like every uniqueness technique, BUG+1 only works when the puzzle has exactly one solution, as every Bare Sudoku puzzle does.

In Bare Sudoku

Needed from level: Expert
In the game, the hint says: BUG+1

Play this puzzle · Play Sudoku · Sudoku solver

Practice puzzles

In these puzzles, BUG+1 is the hardest technique you need. Each link opens the puzzle in the game; the solver link shows every step.

1. Expert 5.6 · Sudoku solver
2. Expert 5.6 · Sudoku solver
3. Expert 5.6 · Sudoku solver
4. Expert 5.6 · Sudoku solver
5. Expert 5.6 · Sudoku solver
6. Expert 5.6 · Sudoku solver
7. Expert 5.6 · Sudoku solver
8. Expert 5.6 · Sudoku solver
9. Expert 5.6 · Sudoku solver
10. Expert 5.6 · Sudoku solver

Frequently asked questions

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Made by Alparslan Selçuk Develioğlu · Updated 2026-10-04