BUG+1

What Is a BUG (Bivalue Universal Grave)?

A BUG is a hypothetical state where every unsolved cell has exactly two candidates, and each digit appears exactly twice in every relevant house. This perfect symmetry means candidates form closed loops resolvable in two ways, guaranteeing multiple solutions. A valid puzzle can never reach this state.

What Is BUG+1 in Sudoku?

BUG+1: every unsolved cell is bivalue except one trivalue cell. Two of its candidates appear exactly twice in every house (BUG candidates). The third (the "extra" digit) breaks the symmetry.

How the BUG+1 Deduction Works

If the extra digit were removed, the board would become a BUG (multiple solutions). Since that is impossible, the extra digit must be the answer. BUG+1 yields a direct placement, not just a candidate elimination.

How to Identify the Extra Digit

Method 1: Count occurrences in houses. Two candidates appear exactly twice everywhere; the extra appears three times in at least one house. Method 2: The removal test. Whichever candidate, if removed, would complete the BUG pattern is the extra digit that must stay.

Why BUG+1 Is a Uniqueness Technique

BUG+1 relies on the assumption that the puzzle has exactly one solution. Other uniqueness techniques include Unique Rectangles and Avoidable Rectangles. BUG+1 is perfectly sound for puzzles from reputable sources.

Difficulty Classification and Rarity

Level 8 (Expert). Relatively uncommon -- requires a very specific near-BUG state late in the solving process. When it appears, it yields a satisfying direct placement.

Tips for Spotting BUG+1

Check when 8-15 unsolved cells remain and most are bivalue. Quick scan: if any cell has more than 3 candidates, stop. If two or more have 3, stop. If exactly one has 3 and all others have 2, verify the BUG+1 conditions. Accurate pencilmarks are essential.

Summary

BUG+1 detects when the board is one cell away from a multi-solution state. By identifying the single trivalue cell and its extra digit, the technique yields a direct placement. Level 8 (Expert), rare but elegant.