127.0.0.1: Created page with "{{develop}} The '''Almost Locked Candidates''', or '''ALC''', solving technique refers to a line-box intersection and a set of digits '''S''' such that: * An..."

2021-10-25T11:51:35Z

Created page with "{{develop}} The '''Almost Locked Candidates''', or '''ALC''', solving technique refers to a line-box intersection and a set of digits '''S''' such that: * An..."

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The '''Almost Locked Candidates''', or '''ALC''', [[solving technique]] refers to a [[line]]-[[box]] intersection and a set of [[digit]]s '''S''' such that:
* An [[Almost Locked Set]] (ALS) for the set of digits '''S''' exists in the line outside the intersection; and
* An ALS for the set of digits '''S''' exists in the box outside the intersection.

Then the following [[eliminate|elimination]]s can be made:
* If all the [[cell]]s in the line that are not in the intersection or the line-ALS contains no digits from '''S''', then the digits from '''S''' can be eliminated from the cells in the box that are not in the intersection or the box-ALS.
* If all the [[cell]]s in the box that are not in the intersection or the box-ALS contains no digits from '''S''', then the digits from '''S''' can be eliminated from the cells in the line that are not in the intersection or the line-ALS.

== Illustration ==
The ALC technique is best illustrated by using a example.

{{grid|4=XY|5=/|6=/|7=/|8=/|9=/|10=XY|11=*|12=*|19=*|20=*|21=*}}

In the above grid, each cell marked '''XY''' means that it has the [[candidate]]s '''X''' and '''Y''', and each cell marked '''/''' means that it does not have '''X''' or '''Y''' as candidates. Now, if '''r1c4=X''', then all the candidates for '''Y''' in row 1 are being confined in box 1. This triggers a [[Locked Candidates]] move, resulting in '''Y''' being eliminated from all cells in box 1 that are outside the intersection. But this also means that '''r2c1=X''', so all the cells marked '''*''' cannot contain the digits '''X''' or '''Y'''. A similar deduction can be made if '''r1c4=Y'''. Therefore, in both cases, we can safely eliminate '''X''' and '''Y''' from all cells marked '''*'''.

== More examples ==
{{grid|cellwidth=30px|4=XYZ|5=XYZ|6=/|7=/|8=/|9=/|10=XYZ|11=XYZ|12=*|19=*|20=*|21=*}}

'''X''', '''Y''' and '''Z''' can be eliminated from all cells marked '''*'''.

== External link ==
* [http://www.sudoku.com/forums/viewtopic.php?t=5186 Variation of Locked Candidates]
* [http://www.sudocue.net/forum/viewtopic.php?t=607 Almost Locked Candidates]

== See also ==
* [[Locked Candidates]]
* [[Almost Locked Set]]

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[[Category:Solving Techniques]]

Almost Locked Candidates - Revision history

127.0.0.1: Created page with "{{develop}} The '''Almost Locked Candidates''', or '''ALC''', solving technique refers to a line-box intersection and a set of digits '''S''' such that: * An..."