Uniqueness
BUG
A Bivalue Universal Grave, or BUG, is a position in which every unsolved cell holds exactly two candidates except one. That shape can't be the finished puzzle: if every cell were a pair, the whole grid would resolve two ways at once, and a proper sudoku has one solution. So the one cell with three candidates must be the extra digit, and it can be placed immediately.
- Level
- Advanced
The pattern
What it does.
The reasoning is the same kind as a unique rectangle, taken to the whole grid. A grid of nothing but two-candidate cells has no logical way to choose between the two readings of each pair, and it therefore has two solutions rather than one.
The single cell with a third candidate is the flaw that breaks the symmetry. It has to take the digit that makes it a pair like everything else, because leaving it free would leave the puzzle ambiguous.
It's the largest pattern on this site and the simplest to apply: you aren't looking for a shape in one unit, you're counting candidates across the grid.
Example
A worked example.
Fill the candidate list completely
This technique reads nothing but the marks, so every empty cell needs its candidates written in before it can be checked. An incomplete list will hide the pattern or invent one.
Count candidates in every empty cell
If every empty cell holds exactly two candidates except for a single cell holding three, the position is a BUG.
Check the exception holds three
The one cell that breaks the pattern must hold exactly three candidates. If two cells hold three, or one holds four, there's no BUG and the technique doesn't apply.
Place the third digit
The exceptional cell must take its third candidate, the one not shared with the pairs around it. Place it, and the grid usually falls to singles from there.
Spotting it
How to spot it.
- Count rather than search. Run your eye over the empty cells and ask whether they are all pairs; the odd one out is the whole technique.
- It appears late in a puzzle, when almost everything is solved and the marks have been trimmed down. It isn't worth looking for early.
- If the exception holds more than three candidates, look for a BUG with one extra candidate, written BUG+1: the same argument applies to the extra digit.
- Always finish the candidate list first. Most missed BUGs are missed because one cell still has stale marks in it.
Where it stops working
It needs exactly one exception, and it rests on the puzzle having one solution, as the unique rectangle does. A grid where the candidate lists aren't complete won't show the pattern at all, and a grid with more than one exception belongs to a different technique. It places a digit rather than removing one, which is why it's worth the counting when it appears.
Keep going
Related topics.
New to sudoku? The rules take two minutes to read, and the first-puzzle walkthrough covers the basics that come before any of these.
Beyond the lessons.
The game's lessons stop at X-Wing, so there's no BUG lesson. The eight it does teach will get you through almost any puzzle; this page is here for when you run into the pattern anyway.