What Is a BUG in Sudoku

The name, unpacked

BUG stands for Bivalue Universal Grave. A grave is a position where every remaining cell has exactly two candidates and every candidate appears exactly twice in each of its units. Such a position has more than one solution, so a proper puzzle can never actually reach it. It is a grave the puzzle must avoid.

Spotting the BUG plus one

The useful case is when the board is one step from that grave. Every unsolved cell has two candidates except a single cell that has three. That one extra candidate is what saves the puzzle from a second solution. So it must be true.

The move

1. Notice that all unsolved cells are pairs except one cell with three candidates.
2. In that three-candidate cell, find the value that appears an odd number of times across its row, column and box.
3. That value is the solution for the cell. Place it.

Use it only on proper puzzles

Like the Unique Rectangle, the BUG leans on the promise that the puzzle has exactly one answer. Every Shapedoku board is validated for a single solution, so the argument holds here. On an untrusted grid, treat uniqueness tricks with caution.