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Strategies for Popular Number Puzzles

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 in 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. There is also an article on Brute Force vs Logic.

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.

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.


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.

I'm pleased to include on this web site the Sudoku Song (MP3 file) by Peter Levy (official web site here). Peter wrote and recorded this song a couple of years ago and managed to capture the essence of the Sudoku craze to great acclaim.

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Thursday 17-Jun-2021

... by: Anonymous

Hello Andrew Stuart,

Please check my comment on the Exocet page, which explains the logic behind rule 1. Adding it to the article would benefit many people.
Andrew Stuart writes:


Tuesday 26-May-2020

... by: Pieter, Newtown, Oz

Hi Andrew
Noticed a minor typo with a major effect in Eric's comment on Monday 27-May-2019 below.
Andrew Stuart writes:
Err, that has always been "this solver"

The link has a stray " in it which makes the link non-functional.

Ciao, Pieter
Andrew Stuart writes:

Fixed thanks!

Article created on 12-April-2008. Views: 1060421
This page was last modified on 23-January-2019.
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