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2025-07-20T15:28:28Z

Created page with "A solving technique that uses the intersections between lines and boxes. Aliases include: '''Intersection Removal''', '''Line-Box Interaction'''. The terms ''..."

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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.

== 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]]

Claiming - Revision history

Rooted: Created page with "A solving technique that uses the intersections between lines and boxes. Aliases include: '''Intersection Removal''', '''Line-Box Interaction'''. The terms ''..."