Solving Technique - Revision history

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Brute Force

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Rooted: Created page with "These are the methods used to solve a Sudoku. There are many different solving techniques discovered in the last few years, mainly because there is a large community of puzzle..."

2020-05-31T04:31:57Z

Created page with "These are the methods used to solve a Sudoku. There are many different solving techniques discovered in the last few years, mainly because there is a large community of puzzle..."

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These are the methods used to solve a Sudoku. There are many different solving techniques discovered in the last few years, mainly because there is a large community of puzzlers who share their knowledge on the various [[Sudoku Forums]].

Because there are so many, a rough subclassification has been made:

== [[Single]]s ==
; [[Full House]]
: A [[house]] with a single empty [[cell]].

; [[Last Digit]]
: The last instance of a [[digit]].

; [[Hidden Single]] | [[Pinned Digit]]
: A single candidate remaining for a digit in a house.

; [[Naked Single]] | [[Forced Digit]] | [[Sole Candidate]]
: A single candidate remaining in a cell.

== [[Intersection]]s ==
; [[Locked Candidates]] | Intersection Removal | Line-Box Interaction | Pointing (Pair, Triple) | Claiming
: [[Candidate]]s are locked in the [[intersection]] of a [[line]] and a [[box]].

; [[Locked Pair]]
: A [[Naked Pair]] located in a single intersection.

; [[Locked Triple]]
: A [[Naked Triple]] located in a single intersection.

; [[Almost Locked Candidates]]
: A box-line intersection where the line or the box contains an [[Almost Locked Set]], and the remaining cells in the line or box outside the intersection does not contain digits from the Almost Locked Set.

== [[Subset]]s ==
; [[Naked Subset]]
: '''N''' cells with candidates for '''N''' digits.

:; [[Naked Pair]]
:: '''2''' cells with candidates for '''2''' digits.

:; [[Naked Triple]]
:: '''3''' cells with candidates for '''3''' digits.

:; [[Naked Quad]]
:: '''4''' cells with candidates for '''4''' digits.

; [[Hidden Subset]]
: '''N''' digits with candidates in '''N''' cells.

:; [[Hidden Pair]]
: '''2''' digits with candidates in '''2''' cells.

:; [[Hidden Triple]]
: '''3''' digits with candidates in '''3''' cells.

:; [[Hidden Quad]]
: '''4''' digits with candidates in '''4''' cells.

== [[Fish]] ==
; Basic Fish
: Rows and columns only.

:; [[X-Wing]]
:: 2 rows vs. 2 columns

:; [[Swordfish]]
:: 3 rows vs. 3 columns

:; [[Jellyfish]]
:: 4 rows vs. 4 columns

:; [[Squirmbag]]
:: 5 rows vs. 5 columns

; [[Finned Fish]]
: Fish patterns with additional candidates in a single box.

; [[Sashimi Fish]]
: Incomplete basic fish patterns with a [[fin]].

; [[Franken Fish]]
: Fish patterns that include box constraints.

; [[Mutant Fish]]
: Fish patterns with mixed sets of constraints.

; [[Kraken Fish]]
: A fish pattern with indirect connections to a candidate which can be eliminated.

== Single Digit Patterns ==
; [[Skyscraper]]
: Two parallel strong links, weakly connected at the base.

; [[2-String Kite]]
: Two crossing strong links, weakly connected in a box.

; [[Empty Rectangle]]
: A single-digit technique that makes use of a [[box]] whose [[candidates]] for that [[digit]] are contained within the union of a [[boxrow]] and a [[boxcol]].

== [[Coloring]] ==
; [[Simple Colors]]
: Uses only 2 colors to form a single color [[cluster]].

; [[Multi-Colors]] | [[Supercoloring]]
: Uses multiple colors (4, 6 or a higher multiple of 2) to form multiple color clusters.

; [[Weak Colors]]
: Extends Simple-Colors by the use of [[hinge]] linkages.

; [[X-Colors]]
: Uses only 2 colors, but also takes the [[implication]]s for each color into account.

; [[Color Trap]]
: A technique that uses a single cluster to eliminate candidates outside the cluster.

; [[Color Wrap]]
: A technique that uses a single cluster to detect a [[contradiction]] in one of the colors.

; [[Color Wing]]
: A technique that uses multiple clusters to eliminate candidates outside these clusters. Same as Multi-Colors.

; [[3D Medusa]] Coloring | [[Advanced Coloring]] | [[Ultracoloring]]
: A set of techniques that uses colors on multiple digits.

== Uniqueness ==
; [[Uniqueness Test]]
: A set of techniques that avoids the [[Unique Rectangle]] [[deadly pattern]].

; [[Avoidable Rectangle]]
: A set of techniques that avoids the [[Unique Rectangle]] [[deadly pattern]]. Perhaps unique in solving techniques in that it employs solved [[cell]]s as well as those unsolved.

; [[Bivalue Universal Grave]]
: A set of techniques that avoids the [[Bivalue Universal Grave]] [[deadly pattern]].

; [[BUG Lite]]
: A set of techniques that avoids the [[BUG Lite]] [[deadly pattern]].

; [[Uniqueness Controversy]]
: These solving techniques assume that the [[Sudoku]] puzzle has a unique solution. It is not universally accepted that this assumption is a valid one.

== [[Chain]]s and [[Loop]]s ==
; [[Forcing Chain]]
: Generic term for any type of chain.

; [[X-Chain]]
: Single digit chain of cells.

; [[XY-Chain]]
: Chain of [[bivalue]] cells.

; [[Remote Pairs]]
: Simplified form of XY-Chain, involving only two digits.

; [[Fishy Cycle]] | X-Cycle
: Single digit [[continuous]] loop.

; [[Broken Wing]]
: Eliminations caused by loops of odd length.

; [[Nice Loop]]s
: Several types of loops formed by cells following strict rules and a notation system.

; [[Double Implication Chain]] | DIC
: There are 2 interpretations circulating. The first originates from a reliable source [http://www.sudoku.com/forums/viewtopic.php?t=2143].
* A Forcing Chain that has implications in both directions.
* 2 Forcing Chains starting from a bivalue cell or a [[bilocal]] unit showing a [[verity]].

; [[Alternating Inference Chain]] | AIC
: A chain where each node is a candidate, with alternating strong and weak inference.

; [[Oriented Chains]]
: Oriented chains are generalisations of the basic xy-chains. The central idea is that the information collected from previous candidates in a chain (and/or from the target) can be used to select the next candidates. Oriented chains are either 2D or 3D:
:- oriented 2D chains: xyt-chains, xyz-chains and xyzt-chains, together with their "hidden" counterparts: hxyt-chains, hxyz-chains and hxyzt-chains;
:- [[oriented 3D chains]]: nrct-chains, nrcz-chains, nrczt-chains.
:(The original reference to all these chains is the book "The Hidden Logic of Sudoku". Further web references forthcoming)

== Wings ==
; [[XY-Wing]]
: Three [[cell]]s with [[pivot]] cell '''XY''' and two [[pincer]] cells '''XZ''' and '''YZ'''.

; [[XYZ-Wing]]
: Three [[cell]]s with [[pivot]] cell '''XYZ''' and two [[pincer]] cells '''XZ''' and '''YZ'''.

; [[WXYZ-Wing]]
: Four [[cell]]s with [[pivot]] cell '''WXYZ''' and three [[pincer]] cells '''WZ''', '''XZ''' and '''YZ'''.

; [[W-Wing]]
: Four [[cell]]s in a [[chain]]: a cell '''WX''', a cell with '''X''' as a [[candidate]], another cell with '''X''' as a [[candidate]], another cell '''WX''', such that the two cells containing '''X''' as a [[candidate]] have a [[strong link]].

== [[Almost Locked Set]]s ==
; [[ALS-XZ]] rule
: 2 Almost Locked Sets with [[restricted common]] digit '''X''' perform eliminations for common digit '''Z'''.

; [[ALS-XY-Wing]] rule
: 3 Almost Locked Sets with 2 restricted common digits '''Y''' and '''Z''' perform eliminations for common digit '''X'''.

; [[ALS-XY-Chain]]
: Very similar to [[XY-Chain]], except that the [[node]]s in the [[chain]] are Almost Locked Sets.

; [[Death Blossom]]
: A stem cell of N candidates pointing to N petals, each an Almost Locked Set.

== Enumeration on Selected Cells ==
; [[Aligned Pair Exclusion]]
: Checks combinations of [[digits]] in a pair of [[cells]] located in an [[intersection]].

; [[Aligned Triple Exclusion]]
: Checks combinations of [[digits]] in a triple of [[cells]] located in an [[intersection]].

; [[Subset Exclusion]]
: Extension of [[Aligned Pair Exclusion]] to arbitrary sets that need not be aligned.

== Miscellaneous ==
; [[Sue de Coq]]
: Uses two intersecting sets '''A''' and '''B''', where '''A''' is a set of N cells with N candidates in a line, '''B''' is a set of N cells with N candidates in a box, and the sets '''A - B''' and '''B - A''' have no common candidates.

; [[Subset Counting]] | [[Extended Subset Principle]]
: Considers the number of times a digit can be placed in a selected subset of cells.

; [[Braid Analysis]] | [[Braiding]] | [[Traveling Pairs]]
: Analyzes the distribution of digits in a [[chute]], especially how pairs repeat in a chute.

; [[Constraint Subsets]]
: Generalized view of [[subset]] and [[fish]] techniques.

; [[Equivalence Marks]]
: Similar to [[coloring]], but uses marks instead of colors to represent parity.

; [[Gurth's Symmetrical Placement]]
: Technique for puzzles with rotational symmetry.

== Techniques of Last Resort ==
Most of these techniques are controversial. They are either too complex to be used by human solvers, or they require a lot of extra work, or they are not based on logic.

; [[Forcing Net]]
: A general term for techniques that investigate branching chains.

; [[Tabling]] | Trebor's Tables
: All implications for each move are collected in tables.

; [[Graded Equivalence Marks]] | GEM
: A system of marking candidates starting from 2 complementary starting positions.

; [[Bowman Bingo]]
: A systematic approach to investigate implications.

; [[Trial & Error]] | [[Ariadne's Thread]] | [[Bifurcation]]
: The implications for a single move are investigated.

; [[Nishio]]
: Trial & Error limited to single digit.

; [[Templating]] | [[Pattern Overlay Method]] | POM
: All possible ways to place a digit in the remaining candidate space are investigated.

; [[Guess]]ing
: Random moves are made, without any logic behind them.

== Brute Force ==
These are primarily designed for computer solver programs.
* [[Backtracking Algorithms]].

[[Category:Solving Techniques]]

← Older revision		Revision as of 03:32, 21 December 2024
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−	These are the methods used to [https://sudokusolver.net solve a Sudoku]. There are many different solving techniques discovered in the last few years, mainly because there is a large community of puzzlers who share their knowledge on the various [[Sudoku Forums]].	+	These are the methods used to [https://sudokusolver.net solve a Sudoku]. There are many different solving techniques discovered in the last few years, mainly because there is a large community of puzzlers who share their knowledge on the various [[Sudoku Forums]]. For crossword answers and solvers we would recommend [https://xword.com xWord.com]

	Because there are so many, a rough subclassification has been made:		Because there are so many, a rough subclassification has been made:

@@ Line 258: / Line 258: @@
 * [[Backtracking Algorithms]].
-If you are looking for the [https://nytsolver.com New York Times Crossword Answers]. Daily Puzzle games have become quite popular especially after the global phenomenon Wordle. To see all [https://gameanswers.com Daily Puzzle Answers] visit the website linked on this page.
+If you are looking for the [https://nytsolver.com New York Times Crossword Answers]. Daily Puzzle games have become quite popular especially after the global phenomenon Wordle. To see all [https://gameanswers.com Daily Puzzle Answers] visit the website linked on this page. You can now play the Internet's favorite game [https://dailypuzzles.com/games/wordle Wordle online]
 [[Category:Solving Techniques]]

@@ Line 258: / Line 258: @@
 * [[Backtracking Algorithms]].
-If you are looking for the [https://nytsolver.com New York Times Crossword Answers] we recommend [https://nytcrosswordanswers.net NYTCrosswordAnswers.net]
+If you are looking for the [https://nytsolver.com New York Times Crossword Answers]. Daily Puzzle games have become quite popular especially after the global phenomenon Wordle. To see all [https://gameanswers.com Daily Puzzle Answers] visit the website linked on this page.
 [[Category:Solving Techniques]]

@@ Line 258: / Line 258: @@
 * [[Backtracking Algorithms]].
-If you are looking for the New York Times Crossword Answers we recommend [https://nytcrosswordanswers.net NYTCrosswordAnswers.net]
+If you are looking for the [https://nytsolver.com New York Times Crossword Answers] we recommend [https://nytcrosswordanswers.net NYTCrosswordAnswers.net]
 [[Category:Solving Techniques]]

← Older revision		Revision as of 01:33, 25 February 2021
Line 1:		Line 1:
−	These are the methods used to solve a Sudoku. There are many different solving techniques discovered in the last few years, mainly because there is a large community of puzzlers who share their knowledge on the various [[Sudoku Forums]].	+	These are the methods used to [https://sudokusolver.net solve a Sudoku]. There are many different solving techniques discovered in the last few years, mainly because there is a large community of puzzlers who share their knowledge on the various [[Sudoku Forums]].

	Because there are so many, a rough subclassification has been made:		Because there are so many, a rough subclassification has been made: