BUG+1
BUG+1 — short for Bi-Value Universal Grave, plus one — is a slick uniqueness technique that often finishes a grid in a single move. Like the Unique Rectangle, it leans on the fact that a proper Sudoku has exactly one solution.
The "grave" idea
A Bi-Value Universal Grave is a hypothetical dead-end: a grid state where every remaining unsolved cell has exactly two candidates, and every candidate digit appears exactly twice in each row, column and box. Such a state is "deadly" — it always has two valid solutions, because you can swap the pairs throughout. A proper puzzle can never reach it.
How BUG+1 works
Now suppose you're solving and you notice the grid is almost a BUG: every unsolved cell is bi-value except one, which has three candidates. Because the fully bi-value state is forbidden, that one extra candidate is exactly what saves the puzzle from being deadly — so it must be the answer for that cell. You place it immediately, and the grid usually cascades to a finish.
The trick to spotting it: for the three-candidate cell, find the digit that appears an odd number of times (three, not two) in that cell's row, column or box. That's the one to place.
Three cells of one unit near the end of a solve. The outer two are bi-value; the green cell has three candidates. Across them digit 2 appears three times (odd) while 5 and 7 appear twice each — so the green cell must be 2.
Step by step
- Check for a near-BUG. Every unsolved cell bi-value except one with three candidates.
- Find the odd digit in the three-candidate cell — the one appearing three times rather than twice in a shared unit.
- Place it. That digit is the solution for the cell.
A word of caution
Like all uniqueness techniques, BUG+1 only works on puzzles guaranteed to have a single solution — which every SudokuStreak puzzle is. It's an endgame tool: you'll reach it only when the grid has boiled down almost entirely to bi-value cells, but when you do, it's one of the most satisfying one-move finishes in Sudoku.
Common mistakes
- More than one three-candidate cell. BUG+1 needs exactly one; two or more and the argument doesn't apply.
- Using it on an unchecked puzzle. Without a guaranteed unique solution, the reasoning can mislead.
Which Sudoku types is this best for?
The same logic applies across variants, but it pays off more in some than others.