Deadly Pattern

A Deadly Pattern is a pattern of candidates in a group of cells that causes a Sudoku puzzle to have more than one solution.

A deadly pattern cannot exist in a Sudoku puzzle that has a unique solution. There is some debate on the issue of uniqueness in Sudoku puzzles. On one hand there is nothing in the basic Sudoku rule that specifies uniqueness. On the other, there is no logic that can solve a puzzle with multiple solutions so at some point, to get to any one of the solutions you have to guess.

There are Sudoku enthusiasts that do not agree with the premise of uniqueness. If you are one of them then the solving strategies that use deadly, or almost deadly patterns will probably not work for you.

This helper assumes a Sudoku Puzzle should have a unique solution.Figure 1 shows an example of a deadly pattern in the four blue cells. This is the simplest form of a deadly pattern and uses just four cells and allows two possible solutions. If this candidate pattern was allowed to exist in a puzzle there would be multiple solutions for that puzzle.

There is no logic in the example puzzle that would deterministically lead to a solution for the blue cells. A guess of either candidate in one of the blue cells would lead to one of the solutions.

If a puzzle is expected to have a unique solution then all deadly patterns need to be avoided in the solving process. This is the basis of all the "Uniqueness Tests".

An Almost Deadly Pattern is an instance of a deadly pattern with some additional candidates. The only way to avoid the deadly pattern is to make sure that at least one of the additional candidates is used in one of the cells contained in the almost deadly pattern.

Identifying and using an "almost deadly pattern" can lead to candidate removal and is the how the "uniqueness tests" get implemented.

The green cells in Figure 1 are an example of a common mistake in identifying the rectangle deadly pattern. In this case the cells only contain the same two candidates and are contained in just two rows and two columns but are placed in four separate boxes. The solutions to the other cells in the four boxes will affect the solution for the green cells and mean this is not a deadly pattern.