BUG Type 3

BUG Type 3 handles two escape cells with different extra candidates: together with neighbouring cells they form a naked set in a shared row, column, or block, and the set's values can be removed from any other cell in that house.

What is BUG Type 3?

A valid Sudoku has exactly one solution. Near the end of a solve, the grid can reach a state where 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. Any cell that breaks this symmetry by carrying extra candidates is called an escape cell.

Type 3 is the case where two escape cells break the pattern, and each carries different extra candidates. Because removing all those extra candidates would restore the deadly BUG, at least one of the two escape cells must hold one of them. If a neighbouring cell in the same row, column, or block already carries only those extra-candidate digits, the escape cells plus that neighbour form a naked set — a naked pair, triple, or larger — in that house. The set's values can then be removed from any other cell in the house, exactly as in a standard naked-set elimination.

How to spot it

BUG Type 3 appears late in a solve, when the grid is nearly complete and most empty cells are bivalue. Look for two cells that each have three or more candidates while every other unsolved cell has exactly two. If the two escape cells carry different extra candidates, check whether a neighbouring cell in their shared row, column, or block already holds only those extra digits. If so, the escape cells plus that neighbour form a naked set, and the set's values can be removed from any other cell in that house. If the two escape cells share the same extra candidate, you are looking at Type 2 instead; if a locked digit is involved, it is Type 4.

The logic

If all the extra candidates were removed from both escape cells, 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 at least one of the two escape cells must hold one of the extra candidates. That means the escape cells, together with any neighbour that already carries only those digits, occupy all occurrences of those digits within their shared house — a naked set. Any other cell in that house cannot hold any of the set's values, so they are removed. The deduction combines the uniqueness guarantee with standard naked-set logic.