BUG Type 1

What is BUG Type 1?

A valid Sudoku has exactly one solution. That guarantee becomes a deduction tool when the grid nears completion and almost every empty cell has exactly two candidates. If every remaining cell were bivalue and every candidate appeared exactly twice in each row, column, and block where it occurs, the grid would have two interchangeable solutions — a deadly pattern called a Bi-value Universal Grave, or BUG.

Type 1 is the simplest case. A single cell breaks the pattern by carrying three candidates instead of two. That cell — the escape cell — cannot hold either of its two "extra" candidates, because doing so would let the rest of the grid collapse into the BUG. So both extra candidates are removed from the escape cell, often leaving it as a naked single with just the one value that prevents the deadly pattern.

How to spot it

BUG Type 1 appears late in a solve, when the grid is nearly complete and most empty cells are bivalue. Scan for a cell that has three candidates while every other unsolved cell has exactly two. Then check whether each candidate digit appears exactly twice in every row, column, and block where it shows up — if so, the grid is one step away from a BUG, and the tri-value cell is the escape. Remove its two extra candidates and the puzzle continues. If two or more cells break the bivalue symmetry, you are looking at a different BUG type (2, 3, or 4) instead.

The logic

If the escape cell held either of its extra candidates, every other empty cell would be bivalue and every candidate would appear exactly twice in each house — the BUG state, which has two interchangeable solutions. A puzzle with a unique solution cannot contain a BUG, so the escape cell must avoid both extra candidates. Removing them is the only safe play, and it follows directly from the uniqueness guarantee without needing to know which of the two BUG configurations is correct.