# Binary Universal Grave (BUG)

## Difficulty

## 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.)