Pointing Triple - Revision history

Rooted: Replaced content with "#REDIRECT Locked Candidates"

2022-01-20T03:00:55Z

Replaced content with "#REDIRECT Locked Candidates"

Rooted at 03:00, 20 January 2022

2022-01-20T03:00:20Z

Rooted: Redirected page to Locked Candidates

2022-01-20T02:59:55Z

Redirected page to Locked Candidates

New page

#REDIRECT [[Locked Candidates]]

← Older revision		Revision as of 03:00, 20 January 2022
Line 1:		Line 1:
	#REDIRECT [[Locked Candidates]]		#REDIRECT [[Locked Candidates]]
−
−	~~A [[solving technique]] that uses the [[intersection]]s between [[line]]s and [[box]]es.~~
−
−	~~Aliases include: '''Intersection Removal''', '''Line-Box Interaction'''. The terms '''Pointing''' and '''Claiming'''/'''Box-Line Reduction''' are often used to distinguish the 2 types.~~
−
−	This is a basic solving technique. When all [[candidate]]s for a [[digit]] in a [[house]] are located inside the intersection with another house, we can [[eliminate]] the remaining candidates from the second house outside the intersection.
−
−	~~== Type 1 (Pointing) ==~~
−	~~All the candidates for digit '''X''' in a box are confined to a single line (row or column). The surplus candidates are eliminated from the part of the line that does not intersect with this box.~~
−	~~.-------.-------.-------.~~
−	~~\| * * * \| * * * \| X X X \|~~
−	~~\| \| \| - - - \|~~
−	~~\| \| \| - - - \|~~
−	~~'-------'-------'-------'~~
−	~~Legend:~~
−	~~X : cell which may contain a candidate for digit X~~
−	~~- : cell which does not contain a candidate for digit X~~
−	* : cell from which we may eliminate the candidates for digit X
−	~~Depending on the number of available candidates in the intersection, this technique is also known as a '''Pointing Pair''' or '''Pointing Triple'''.~~
−
−	~~== Type 2 (Claiming or Box-Line Reduction) ==~~
−	~~All the candidates for digit '''X''' in a line are confined to a single box. The surplus candidates are eliminated from the part of the box that does not intersect with this line.~~
−	~~.-------.-------.-------.~~
−	~~\| - - - \| - - - \| X X X \|~~
−	~~\| \| \| * * * \|~~
−	~~\| \| \| * * * \|~~
−	~~'-------'-------'-------'~~
−
−	~~== Example ==~~
−	~~[[Image:PointingPair.png]]~~
−
−	~~There is a Locked Candidates Type 1 (Pointing) for the digit 4 as shown in yellow. The red candidates can be [[eliminate]]d.~~
−
−	~~== Type 3 (Interaction with extra [[house]]s in [[Sudoku Variant]]s) ==~~
−
−	~~There are interactions in the intersections of each extra constraint and a row, column or box. Some of these overlap the regular interactions.~~
−
−	~~In [[Windoku]], the unmarked extra constraints surrounding the 4 windows should also be considered.~~
−
−	In [[Sudoku-X]], but also in varants with disjoint constraints, techniques such as [[Common Peer Elimination]] and [[Crossover]] will provide new methods to use the interactions with extra constraints.
−
−	~~== Killer Sudoku ==~~
−	The [[cage]]s in [[Killer Sudoku]] can offer more modes of the locked candidates technique. We use two examples to illustrate such techniques, both taken from [http://www.sudocue.net/weeklykiller.php?id=1 Ruud's Assassin 1].
−
−	~~For the first example shown below, consider the 17[3] cage in column 8.~~
−
−	~~[[Image:KillerLockedCandidates1.png]]~~
−
−	The possible [[cage combinations]] of the 17[3] cage in column 8 are {2,7,8} or {3,6,8} or {4,5,8} or {4,6,7}. However, in column 8, all cells that has 7 as a candidate are the cells in the 17[3] cage. Therefore, we can strike off the combinations {3,6,8} and {4,5,8}, leaving the combinations {2,7,8} or {4,6,7}. This implies that we can eliminate 3 and 5 from all cells in the cage.
−
−	~~For the second example shown below, consider the 9[3] cage in column 2.~~
−
−	~~[[Image:KillerLockedCandidates2.png]]~~
−
−	The possible [[cage combinations]] of the 9[3] cage in column 2 are {1,3,5} or {2,3,4}. Since both combinations contain the digit 3, this means that one of the cells in the 9[3] cage must contain the digit 3. Hence, 3 can be eliminated from all other cells in column 2.
−
−	~~== See Also ==~~
−	* [[Naked Subset]]
−	* [[Common Peer Elimination]]
−
−	~~[[Category:Solving Techniques]]~~
−	~~[[Category:Single-Digit]]~~
−	~~[[Category:Killer Sudoku]]~~
−	~~[[Category:Sudoku Variants]]~~

← Older revision		Revision as of 03:00, 20 January 2022
Line 1:		Line 1:
	#REDIRECT [[Locked Candidates]]		#REDIRECT [[Locked Candidates]]
		+
		+	A [[solving technique]] that uses the [[intersection]]s between [[line]]s and [[box]]es.
		+
		+	Aliases include: '''Intersection Removal''', '''Line-Box Interaction'''. The terms '''Pointing''' and '''Claiming'''/'''Box-Line Reduction''' are often used to distinguish the 2 types.
		+
		+	This is a basic solving technique. When all [[candidate]]s for a [[digit]] in a [[house]] are located inside the intersection with another house, we can [[eliminate]] the remaining candidates from the second house outside the intersection.
		+
		+	== Type 1 (Pointing) ==
		+	All the candidates for digit '''X''' in a box are confined to a single line (row or column). The surplus candidates are eliminated from the part of the line that does not intersect with this box.
		+	.-------.-------.-------.
		+	\| * * * \| * * * \| X X X \|
		+	\| \| \| - - - \|
		+	\| \| \| - - - \|
		+	'-------'-------'-------'
		+	Legend:
		+	X : cell which may contain a candidate for digit X
		+	- : cell which does not contain a candidate for digit X
		+	* : cell from which we may eliminate the candidates for digit X
		+	Depending on the number of available candidates in the intersection, this technique is also known as a '''Pointing Pair''' or '''Pointing Triple'''.
		+
		+	== Type 2 (Claiming or Box-Line Reduction) ==
		+	All the candidates for digit '''X''' in a line are confined to a single box. The surplus candidates are eliminated from the part of the box that does not intersect with this line.
		+	.-------.-------.-------.
		+	\| - - - \| - - - \| X X X \|
		+	\| \| \| * * * \|
		+	\| \| \| * * * \|
		+	'-------'-------'-------'
		+
		+	== Example ==
		+	[[Image:PointingPair.png]]
		+
		+	There is a Locked Candidates Type 1 (Pointing) for the digit 4 as shown in yellow. The red candidates can be [[eliminate]]d.
		+
		+	== Type 3 (Interaction with extra [[house]]s in [[Sudoku Variant]]s) ==
		+
		+	There are interactions in the intersections of each extra constraint and a row, column or box. Some of these overlap the regular interactions.
		+
		+	In [[Windoku]], the unmarked extra constraints surrounding the 4 windows should also be considered.
		+
		+	In [[Sudoku-X]], but also in varants with disjoint constraints, techniques such as [[Common Peer Elimination]] and [[Crossover]] will provide new methods to use the interactions with extra constraints.
		+
		+	== Killer Sudoku ==
		+	The [[cage]]s in [[Killer Sudoku]] can offer more modes of the locked candidates technique. We use two examples to illustrate such techniques, both taken from [http://www.sudocue.net/weeklykiller.php?id=1 Ruud's Assassin 1].
		+
		+	For the first example shown below, consider the 17[3] cage in column 8.
		+
		+	[[Image:KillerLockedCandidates1.png]]
		+
		+	The possible [[cage combinations]] of the 17[3] cage in column 8 are {2,7,8} or {3,6,8} or {4,5,8} or {4,6,7}. However, in column 8, all cells that has 7 as a candidate are the cells in the 17[3] cage. Therefore, we can strike off the combinations {3,6,8} and {4,5,8}, leaving the combinations {2,7,8} or {4,6,7}. This implies that we can eliminate 3 and 5 from all cells in the cage.
		+
		+	For the second example shown below, consider the 9[3] cage in column 2.
		+
		+	[[Image:KillerLockedCandidates2.png]]
		+
		+	The possible [[cage combinations]] of the 9[3] cage in column 2 are {1,3,5} or {2,3,4}. Since both combinations contain the digit 3, this means that one of the cells in the 9[3] cage must contain the digit 3. Hence, 3 can be eliminated from all other cells in column 2.
		+
		+	== See Also ==
		+	* [[Naked Subset]]
		+	* [[Common Peer Elimination]]
		+
		+	[[Category:Solving Techniques]]
		+	[[Category:Single-Digit]]
		+	[[Category:Killer Sudoku]]
		+	[[Category:Sudoku Variants]]