https://www.sudopedia.org/index.php?title=Solving_technique&feed=atom&action=historySolving technique - Revision history2021-05-07T15:23:05ZRevision history for this page on the wikiMediaWiki 1.34.1https://www.sudopedia.org/index.php?title=Solving_technique&diff=26&oldid=prevRooted: 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..."2020-05-31T04:40:22Z<p>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..."</p>
<p><b>New page</b></p><div>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]].<br />
<br />
Because there are so many, a rough subclassification has been made:<br />
<br />
== [[Single]]s ==<br />
; [[Full House]]<br />
: A [[house]] with a single empty [[cell]].<br />
<br />
; [[Last Digit]]<br />
: The last instance of a [[digit]].<br />
<br />
; [[Hidden Single]] | [[Pinned Digit]]<br />
: A single candidate remaining for a digit in a house.<br />
<br />
; [[Naked Single]] | [[Forced Digit]] | [[Sole Candidate]]<br />
: A single candidate remaining in a cell.<br />
<br />
== [[Intersection]]s ==<br />
; [[Locked Candidates]] | Intersection Removal | Line-Box Interaction | Pointing (Pair, Triple) | Claiming<br />
: [[Candidate]]s are locked in the [[intersection]] of a [[line]] and a [[box]].<br />
<br />
; [[Locked Pair]]<br />
: A [[Naked Pair]] located in a single intersection.<br />
<br />
; [[Locked Triple]]<br />
: A [[Naked Triple]] located in a single intersection.<br />
<br />
; [[Almost Locked Candidates]]<br />
: 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.<br />
<br />
== [[Subset]]s ==<br />
; [[Naked Subset]]<br />
: '''N''' cells with candidates for '''N''' digits.<br />
<br />
:; [[Naked Pair]]<br />
:: '''2''' cells with candidates for '''2''' digits.<br />
<br />
:; [[Naked Triple]]<br />
:: '''3''' cells with candidates for '''3''' digits.<br />
<br />
:; [[Naked Quad]]<br />
:: '''4''' cells with candidates for '''4''' digits.<br />
<br />
; [[Hidden Subset]]<br />
: '''N''' digits with candidates in '''N''' cells.<br />
<br />
:; [[Hidden Pair]]<br />
: '''2''' digits with candidates in '''2''' cells.<br />
<br />
:; [[Hidden Triple]]<br />
: '''3''' digits with candidates in '''3''' cells.<br />
<br />
:; [[Hidden Quad]]<br />
: '''4''' digits with candidates in '''4''' cells.<br />
<br />
== [[Fish]] ==<br />
; Basic Fish<br />
: Rows and columns only.<br />
<br />
:; [[X-Wing]]<br />
:: 2 rows vs. 2 columns<br />
<br />
:; [[Swordfish]]<br />
:: 3 rows vs. 3 columns<br />
<br />
:; [[Jellyfish]]<br />
:: 4 rows vs. 4 columns<br />
<br />
:; [[Squirmbag]]<br />
:: 5 rows vs. 5 columns<br />
<br />
; [[Fish and Subsets]]<br />
: general relationship between Fish and Subsets.<br />
<br />
; [[Finned Fish]]<br />
: Fish patterns with additional candidates in a single box.<br />
<br />
; [[Sashimi Fish]]<br />
: Incomplete basic fish patterns with a [[fin]].<br />
<br />
; [[Franken Fish]]<br />
: Fish patterns that include box constraints.<br />
<br />
; [[Mutant Fish]]<br />
: Fish patterns with mixed sets of constraints.<br />
<br />
; [[Kraken Fish]]<br />
: A fish pattern with indirect connections to a candidate which can be eliminated.<br />
<br />
== Single Digit Patterns ==<br />
; [[Skyscraper]]<br />
: Two parallel strong links, weakly connected at the base.<br />
<br />
; [[2-String Kite]]<br />
: Two crossing strong links, weakly connected in a box.<br />
<br />
; [[Empty Rectangle]]<br />
: 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]].<br />
<br />
== [[Coloring]] ==<br />
; [[Simple Colors]]<br />
: Uses only 2 colors to form a single color [[cluster]].<br />
<br />
; [[Multi-Colors]] | [[Supercoloring]]<br />
: Uses multiple colors (4, 6 or a higher multiple of 2) to form multiple color clusters.<br />
<br />
; [[Weak Colors]]<br />
: Extends Simple-Colors by the use of [[hinge]] linkages. <br />
<br />
; [[X-Colors]]<br />
: Uses only 2 colors, but also takes the [[implication]]s for each color into account.<br />
<br />
; [[Color Trap]]<br />
: A technique that uses a single cluster to eliminate candidates outside the cluster.<br />
<br />
; [[Color Wrap]]<br />
: A technique that uses a single cluster to detect a [[contradiction]] in one of the colors.<br />
<br />
; [[Color Wing]]<br />
: A technique that uses multiple clusters to eliminate candidates outside these clusters. Same as Multi-Colors.<br />
<br />
; [[3D Medusa]] Coloring | [[Advanced Coloring]] | [[Ultracoloring]]<br />
: A set of techniques that uses colors on multiple digits.<br />
<br />
== Uniqueness ==<br />
; [[Uniqueness Test]]<br />
: A set of techniques that avoids the [[Unique Rectangle]] [[deadly pattern]].<br />
<br />
; [[Avoidable Rectangle]]<br />
: 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.<br />
<br />
; [[Bivalue Universal Grave]]<br />
: A set of techniques that avoids the [[Bivalue Universal Grave]] [[deadly pattern]].<br />
<br />
; [[BUG Lite]]<br />
: A set of techniques that avoids the [[BUG Lite]] [[deadly pattern]].<br />
<br />
; [[Reverse BUG]]<br />
: While [[BUG]] looks at [[candidate]]s of unsolved cells, [[Reverse BUG]] looks at solved cells instead.<br />
<br />
; [[Reverse BUG Lite]]<br />
: While [[BUG Lite]] looks at [[candidate]]s of unsolved cells, [[Reverse BUG Lite]] looks at solved cells instead.<br />
<br />
; [[Uniqueness Clue Cover]]<br />
: Eliminates candidates by making the [[uniqueness assumption]].<br />
<br />
; [[Uniqueness Controversy]]<br />
: These solving techniques assume that the [[Sudoku]] puzzle has a unique solution. It is not universally accepted that this assumption is a valid one.<br />
<br />
== [[Chain]]s and [[Loop]]s ==<br />
; [[Forcing Chain]]<br />
: Generic term for any type of chain.<br />
<br />
; [[X-Chain]]<br />
: Single digit chain of cells.<br />
<br />
; [[XY-Chain]]<br />
: Chain of [[bivalue]] cells.<br />
<br />
; [[Remote Pairs]]<br />
: Simplified form of XY-Chain, involving only two digits.<br />
<br />
; [[Fishy Cycle]] | X-Cycle<br />
: Single digit [[continuous]] loop.<br />
<br />
; [[Generalized Fishy Cycles]]<br />
: Strong generalization of Fishy Cycles and several other techniques. More difficult to apply.<br />
<br />
; [[Broken Wing]]<br />
: Eliminations caused by loops of odd length.<br />
<br />
; [[Nice Loop]]s<br />
: Several types of loops formed by cells following strict rules and a notation system.<br />
<br />
; [[Double Implication Chain]] | DIC<br />
: There are 2 interpretations circulating. The first originates from a reliable source [http://www.sudoku.com/forums/viewtopic.php?t=2143].<br />
* A Forcing Chain that has implications in both directions.<br />
* 2 Forcing Chains starting from a bivalue cell or a [[bilocal]] unit showing a [[verity]].<br />
<br />
; [[Alternating Inference Chain]] | AIC<br />
: A chain that connects nodes of one or more candidates using alternating weak and strong [[inference]]s.<br />
<br />
; [[Oriented Chains]] <br />
: 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:<br />
:- oriented 2D chains: xyt-chains, xyz-chains and xyzt-chains, together with their "hidden" counterparts: hxyt-chains, hxyz-chains and hxyzt-chains;<br />
:- [[oriented 3D chains]]: nrct-chains, nrcz-chains, nrczt-chains.<br />
:(The original reference to all these chains is the book "The Hidden Logic of Sudoku". Further web references forthcoming)<br />
<br />
== Wings ==<br />
; [[XY-Wing]]<br />
: Three [[cell]]s with [[pivot]] cell '''XY''' and two [[pincer]] cells '''XZ''' and '''YZ'''.<br />
<br />
; [[XYZ-Wing]]<br />
: Three [[cell]]s with [[pivot]] cell '''XYZ''' and two [[pincer]] cells '''XZ''' and '''YZ'''.<br />
<br />
; [[WXYZ-Wing]]<br />
: Four [[cell]]s with [[pivot]] cell '''WXYZ''' and three [[pincer]] cells '''WZ''', '''XZ''' and '''YZ'''.<br />
<br />
; [[W-Wing]]<br />
: 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]].<br />
<br />
== [[Almost Locked Set]]s ==<br />
; [[ALS-XZ]] rule<br />
: 2 Almost Locked Sets with [[restricted common]] digit '''X''' perform eliminations for common digit '''Z'''.<br />
<br />
; [[ALS-XY-Wing]] rule<br />
: 3 Almost Locked Sets with 2 restricted common digits '''Y''' and '''Z''' perform eliminations for common digit '''X'''.<br />
<br />
; [[ALS-XY-Chain]]<br />
: Very similar to [[XY-Chain]], except that the [[node]]s in the [[chain]] are Almost Locked Sets.<br />
<br />
; [[Death Blossom]]<br />
: A stem cell of N candidates pointing to N petals, each an Almost Locked Set.<br />
<br />
; [[Almost ALS]]<br />
: An almost locked set with 1 extra digit.<br />
<br />
== Enumeration on Selected Cells ==<br />
; [[Aligned Pair Exclusion]]<br />
: Checks combinations of [[digits]] in a pair of [[cells]] located in an [[intersection]].<br />
<br />
; [[Aligned Triple Exclusion]]<br />
: Checks combinations of [[digits]] in a triple of [[cells]] located in an [[intersection]].<br />
<br />
; [[Subset Exclusion]]<br />
: Extension of [[Aligned Pair Exclusion]] to arbitrary sets that need not be aligned.<br />
<br />
== Miscellaneous ==<br />
; [[Sue de Coq]]<br />
: 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.<br />
<br />
; [[Subset Counting]] | [[Extended Subset Principle]]<br />
: Considers the number of times a digit can be placed in a selected subset of cells.<br />
<br />
; [[Braid Analysis]] | [[Braiding]] | [[Traveling Pairs]]<br />
: Analyzes the distribution of digits in a [[chute]], especially how pairs repeat in a chute.<br />
<br />
; [[Constraint Subsets]]<br />
: Generalized view of [[subset]] and [[fish]] techniques.<br />
<br />
; [[Equivalence Marks]]<br />
: Similar to [[coloring]], but uses marks instead of colors to represent parity.<br />
<br />
; [[Gurth's Symmetrical Placement]]<br />
: Technique for puzzles with rotational symmetry.<br />
<br />
== Techniques of Last Resort ==<br />
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.<br />
<br />
; [[Forcing Net]]<br />
: A general term for techniques that investigate branching chains.<br />
<br />
; [[Tabling]] | Trebor's Tables<br />
: All implications for each move are collected in tables.<br />
<br />
; [[Graded Equivalence Marks]] | GEM<br />
: A system of marking candidates starting from 2 complementary starting positions.<br />
<br />
; [[Bowman Bingo]]<br />
: A systematic approach to investigate implications.<br />
<br />
; [[Trial & Error]] | [[Ariadne's Thread]] | [[Bifurcation]]<br />
: The implications for a single move are investigated.<br />
<br />
; [[Nishio]]<br />
: Trial & Error limited to single digit.<br />
<br />
; [[Templating]] | [[Pattern Overlay Method]] | POM<br />
: All possible ways to place a digit in the remaining candidate space are investigated.<br />
<br />
; [[Guess]]ing<br />
: Random moves are made, without any logic behind them.<br />
<br />
== Brute Force ==<br />
These are primarily designed for computer solver programs.<br />
* [[Backtracking Algorithms]]<br />
<br />
== External Links ==<br />
* [http://www.sudoku.com/boards/viewtopic.php?p=21790 Collection of solving techniques]<br />
<br />
[[Category:Solving Techniques]]</div>Rooted