Peak Sudoku

BUG+1

All unsolved cells are bivalue except one – that cell's odd digit is forced.
All techniques

Overview

Tier 4
Fish, wings, chains & uniqueness
Typical difficulty
Peak Score 65–75
Also known as
Bivalue Universal Grave + 1, BUG Type 1

When every unsolved cell in the entire grid has exactly two candidates except for one single cell that has three candidates, that three-candidate cell must take the digit that appears 3 times in its houses.

BUG stands for Bivalue Universal Grave. If every unsolved cell in a Sudoku grid has exactly two candidates, and every digit appears exactly twice in every row, column, and box, the grid has two solutions—a fatal flaw. If you find a grid where every remaining cell is bivalue EXCEPT for one cell that contains three candidates, that cell must break the deadly pattern. It immediately takes whichever candidate appears an odd number of times (three times) across its containing row, column, and box.

Worked examples

1 / 5
Every empty cell has two candidates except R2C3, which holds {2,8,9}. Of these, only 9 appears an odd number of times in R2C3's row, column and box, so it is the extra candidate. Without it, the board would be a pattern of pairs that never has exactly one solution, so R2C3 must be 9.
Places 9 in R2C3

How to apply it

Spotting the pattern and making the deduction, in order.

  1. Scan the board when almost all unsolved cells have been reduced to exactly two pencil marks.
  2. Identify the single cell on the board that has three candidates instead of two.
  3. Count how often each of its three candidates appears across its containing row, column, and 3×3 box.
  4. Notice that two of the candidates appear twice in those units, while one candidate appears three times.
  5. To prevent an invalid puzzle state with multiple solutions, the cell must take the candidate with the odd count.
  6. Directly place that odd-count number into the cell to break the deadlock.

Common mistakes

  • Using BUG+1 when there are two or more cells with three candidates (that requires BUG+2 or standard chains).
  • Miscounting the candidate occurrences in the containing row, column, or box.
  • Applying BUG logic on an improperly penciled board with missing candidates.

Frequently asked questions

Does BUG+1 place a digit immediately?
Yes! BUG+1 is unique among advanced techniques because it directly places a number into the cell rather than merely eliminating candidates.
Peak Score 55–70Unique RectangleA pattern that would create two solutions – logic forces it to break.Peak Score 70–85XY-ChainA chain of bivalue cells that forces a digit at both endpoints.

Put BUG+1 into practice

Try a puzzle from the Tough tier (Peak Score 61–70).

Play a Tough puzzleAll 25 techniques