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Description
A Binary Universal Grave (BUG) is an invalid state of a Sudoku in which there is more than one solution, making the Sudoku not uniquely solvable.
A proper Sudoku should always be uniquely solvable, and there are some techniques that make use of that assumption, BUG being one of them.
What is a BUG?
This is the simplest example for a BUG. This Sudoku is definitely not uniquely solvable.
See how each cell contains only two candidates? And see how each of these candidates occurs no more than twice within its respective regions? That is what defines a Binary Universal Grave. ("bi" meaning "two")
This is also a BUG, making the Sudoku not uniquely solvable.
There are, as before,
- only two candidates per cell and
- each candidate occurs no more than twice in its regions.
So you would never find one of these examples in a real Sudoku.
What to do with that info?
Now that we know that a BUG is always an invalid state, we can conclude that we must not end up there.
This is an example potentially leading up to the previous BUG example. This is from a real Sudoku.
We can see that we are tremendously close to having a BUG, which should get our spider senses tingling.
If the 3 were not there, we would have that invalid BUG state from before, so we know that 3 must be the solution.
When and how to look for BUGs
The BUG technique can be rarely used, but checking can be done so quickly that it is worth looking for regardless.
Basically, whenever all cells except one contain only two candidates, check if removing a candidate from the cell with three candidates would result in a BUG (where no region would have more than two candidates).
The candidate that would, if removed, lead to a BUG is the solution.
(It is the one candidate, that occurs more than twice in its regions.)