BUG Plus One Sudoku: How One Cell Cracks the Grid

What a BUG Is

BUG stands for bivalue universal grave, a grid state to be both feared and welcomed. In a pure BUG, every unsolved cell has exactly two candidates, and every candidate appears exactly twice in each row, column, and box. Such a grid would have an even number of solutions, at least two, so a proper puzzle with one answer can never actually reach it. That impossibility is the foundation of bug plus one sudoku.

Think of a BUG as a perfectly balanced deadlock. Because balance means multiple solutions, the real grid must break the balance somewhere, and that break is exactly what you learn to read.

The Plus One Cell in BUG Plus One Sudoku

In bug plus one sudoku, the grid is a BUG in every respect except one cell, which carries three candidates instead of two. That extra candidate is the crack in the balance. To avoid the forbidden all-twos state, the tri-value cell must take the digit that would otherwise appear an odd number of times in its houses.

The recipe is quick. Look at the cell with three candidates, and for each candidate count how often it shows up in that cell's row, column, or box. Two of them appear twice; one appears three times. The digit that appears three times is the answer, and placing it resolves the puzzle.

How to Apply It Step by Step

1. Reach a stage where nearly every empty cell is down to two candidates.
2. Confirm each candidate appears twice in its row, column, and box, except at one cell.
3. Locate the single cell holding three candidates.
4. Choose the candidate there that appears three times in one of its houses.
5. Place it, then finish with straightforward singles.

Why It Works and When to Look

The logic of bug plus one sudoku is pure uniqueness reasoning. If you picked either of the twice-appearing candidates for the odd cell, the grid would collapse into a true BUG with multiple solutions, contradicting the puzzle's single answer. So the third digit is forced. It feels like magic, but it is airtight for any properly made puzzle.

Watch for the pattern late in a solve, when the board is almost all pairs. That near-uniform sea of two-candidate cells is the tell.

Finding It in Shapedoku

Because bug plus one sudoku depends on counting candidates, clean pencil Notes are everything, and Shapedoku keeps them readable with distinct glowing shapes and smart Notes cleanup. When the board thins out to mostly pairs, scan for the lone cell with three shapes and count. The technique appears most on Hard and Extreme grids, so it is a fine goal as you climb the difficulties.

Master it once and you will grin every time a puzzle sets up the pattern, because bug plus one sudoku turns a daunting endgame into a single confident move.