Strategy Families

There are two ways one can group all the strategies for Sudoku: by difficulty and by family. Difficulty is rather subjective but necessary, for example, when selecting the order in which strategies are tried by the solver. Some strategies will always be easier for some people to spot than others, but I believe I have chosen an ordering which is not too controversial. So the main documentation has a side menu organised by difficulty.

Below are these strategies organised into themes.

There is a new Introduction to Sudoku and an article on Brute Force vs Logic for those curious.

With chaining strategies, there is definitely a theme going through them. This theme is all about bi-value (only two candidates left in the same cell) and bi-location (only two occurrences of a particular candidate left in the same unit) pairs and the incredible number of deductions one can make from them. You will find, if you read through this group, that earlier strategies become part of a more general theory as the theme develops. Thus, for example, Remote Pairs are a subset of XY-Chains; that is, XY-Chains is a more general approach of which Remote Pairs are a specific instance. Do read the introductory articles Introducing Chains and Links and Weak and Strong Links.

Exotic strategies do overlap with chaining ones, but they have a peculiar flavour of their own and some wonderful, if obscure, logic. They are definitely worth presenting as a demonstration of people's ingenuity but you will only need to have recourse to them on the extreme puzzles.

There are naturally special strategies for Jigsaw and Killers because of their differences. These are now included for the first time on this site.

This strategy list is by no means complete. Many strategies can be further extended and we do not have a complete theory of all Sudoku puzzles. If you are interested in the concepts behind creation and grading, there is a PDF document here called Sudoku Creation and Grading. With the community's help I hope to extend the documentation here.

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For those people wondering why "Escargot" cannot be solved by the solver, there is an article on this special Sudoku here. This is an early 'ultimate puzzle' but this crown has been usurped by the puzzle created by Arto Inkala, which is also in the example list.

I've been looking at a new idea for measuring the difficulty of very hard puzzles - ones that can't use the standard scoring because they don't complete.

Interesting Sudokus for other reasons.

Article: The Relative Incidence of Sudoku Strategies

Article: The 17 Clue 'Proof' - my take on the January 2012 computerised exhaustive search proof.

Article: The Chaos Within Sudoku - A Richter Scale on a paper by Maria Ercsey-Ravasz and Zoltan Toroczkai at the Faculty of Physics, Babes-Bolyai University, Romania. Very interesting paper.

Article: Generalizing Sudoku Strategies by Kevin Gromley, March 2014

My response to Crooks Algorithm is here.

James Pike's articles on Related Sets Algorithm and Multiples

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Interesting video on Zero Knowledge Proofs tying Sudoku to graphs:

A little nugget of Sudoku lore. In 2014 the first minimal Sudoku puzzle with the most clues was discovered. A minimal Sudoku is one where no clue can be removed without breaking the puzzle by introducing multiple solutions. The property of minimal gets harder and harder as more clues are assumed. There no 41 minimal Sudoku puzzles but many with 39. A single variation of the orginal find is all we have:
Load in solver: ..........12.34567.345.6182..1.582.6..86....1.2...7.5...37.5.28.8..6.7..2.7.83615
Load in solver: ..........12.34567.345.6182..1.582.6..86....1.2...785...37.5.2..8..6.7..2.7.83615

There are a couple of definition files that I use for calibrating and testing mine. These were created a long time ago and were very popular but people may have forgotten about them. Happy to host the files here:

1. Ruud's top 50,000 Most very hard
2. Just17.zip 31,513 17 clue puzzles. Hard to make these