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

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.

22 October 2022

by Sanjeev Kumar

by Sanjeev Kumar

RE: Comments and feedback for deadlyPattern

I'm obliged as much clarity as perhaps possible. But I'm still not sure, which candidate we can remove in the blue boxes? In which cases, this theory can help us remove some candidate options?

I'm obliged as much clarity as perhaps possible. But I'm still not sure, which candidate we can remove in the blue boxes? In which cases, this theory can help us remove some candidate options?

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Sudoku Rules and Techniques

Sudoku Rules

Acknowledgments

I would like to acknowledge these sites referenced for strategy ideas and solving techniques.

SudokuWiki.Org by Andrew Stuart

PaulsPages.co.uk by Paul Stevens

Sudoku Rules

Cross Hatching

Counting

Naked Set

Hidden Set

Claiming

Remote Pairs

X Wing

XY Wing

Simple Coloring

Fishy Things

Unique Rectangle

X Chain

Aligned Pair Exclusion

Forcing Chains

Finned Fishy Things

Almost Locked Sets

Counting

Naked Set

Hidden Set

Claiming

Remote Pairs

X Wing

XY Wing

Simple Coloring

Fishy Things

Unique Rectangle

X Chain

Aligned Pair Exclusion

Forcing Chains

Finned Fishy Things

Almost Locked Sets

Acknowledgments

I would like to acknowledge these sites referenced for strategy ideas and solving techniques.

SudokuWiki.Org by Andrew Stuart

PaulsPages.co.uk by Paul Stevens