BUG+1: learn the sudoku technique step by step at Sudokuen

See the technique in practice

Work through the examples step by step. Each step explains what you see in the puzzle and why the conclusion is valid.

Example:

Look at the whole puzzle. Except for one cell, all empty cells have exactly two candidates left.
The cell at row 8, column 1 stands out: it has three candidates, 2, 3 and 6.
A puzzle where absolutely every empty cell had only two candidates would have multiple valid solutions, which is impossible in a real sudoku. This cell must therefore break that pattern.
Digit 2 appears an even number of times in the cell's row, column and box, while the other two digits appear an odd number of times. Therefore, 2 must go here.

Look at the whole puzzle. Except for one cell, all empty cells have exactly two candidates left.
The cell at row 9, column 1 stands out: it has three candidates, 1, 5 and 8.
A puzzle where absolutely every empty cell had only two candidates would have multiple valid solutions, which is impossible in a real sudoku. This cell must therefore break that pattern.
Digit 8 appears an even number of times in the cell's row, column and box, while the other two digits appear an odd number of times. Therefore, 8 must go here.

Look at the whole puzzle. Except for one cell, all empty cells have exactly two candidates left.
The cell at row 5, column 4 stands out: it has three candidates, 7, 8 and 9.
A puzzle where absolutely every empty cell had only two candidates would have multiple valid solutions, which is impossible in a real sudoku. This cell must therefore break that pattern.
Digit 8 appears an even number of times in the cell's row, column and box, while the other two digits appear an odd number of times. Therefore, 8 must go here.

Look at the whole puzzle. Except for one cell, all empty cells have exactly two candidates left.
The cell at row 6, column 9 stands out: it has three candidates, 1, 4 and 7.
A puzzle where absolutely every empty cell had only two candidates would have multiple valid solutions, which is impossible in a real sudoku. This cell must therefore break that pattern.
Digit 1 appears an even number of times in the cell's row, column and box, while the other two digits appear an odd number of times. Therefore, 1 must go here.

Look at the whole puzzle. Except for one cell, all empty cells have exactly two candidates left.
The cell at row 3, column 2 stands out: it has three candidates, 4, 5 and 7.
A puzzle where absolutely every empty cell had only two candidates would have multiple valid solutions, which is impossible in a real sudoku. This cell must therefore break that pattern.
Digit 7 appears an even number of times in the cell's row, column and box, while the other two digits appear an odd number of times. Therefore, 7 must go here.

BUG stands for Bivalue Universal Grave, a state where absolutely every empty cell has exactly two candidates. Such a puzzle cannot have a unique solution, so a valid sudoku can never end there. BUG+1 occurs when the puzzle is one step away: all empty cells have two candidates except one cell that has three.

That one cell must prevent the puzzle from becoming a Bivalue Universal Grave. Of its three candidates, one digit has a different occurrence count in the cell's row, column and box. That digit must be placed to keep the puzzle from collapsing into a state with multiple solutions. The pattern often appears near the end of hard puzzles.

Check that every empty cell in the puzzle has exactly two candidates, with one exception.
Find the exception, that is, the cell with three candidates.
For each of the three candidates, count how many times the digit appears as a candidate in the cell's row, column and box.
Place the digit that stands out from the other two in the number of occurrences, because without it the puzzle would end in a state with no unique solution.

Using the pattern too early. BUG+1 requires the entire puzzle to be in the state, not just one corner.
Missing another cell with three candidates somewhere else. If there are two such cells, the puzzle is not a BUG+1, and the conclusion does not hold.
Forgetting the unique-solution assumption. The technique relies on the puzzle being a valid Sudoku with exactly one solution.

The hardest puzzles require techniques that follow long logical chains across the entire puzzle. In practice, they work like proofs by contradiction: make an assumption, follow its consequences and identify what cannot hold. Work through the examples below step by step, using the same tools that the solver applies to your own puzzle.

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BUG+1

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How to recognize the pattern

Step-by-step procedure

Common mistakes

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