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Description
The Locked Candidate technique uses candidates that are locked in place within one region to eliminate candidates within another (intersecting) region.
This technique always only looks at the candidates of one specific digit. (Only 1s or 2s or 3s or...)
Lets start by looking at this example.
See how the 6 in the upper right box prevents a 6 from being in a cell in the third row?
That forces a 6 into one of those two left cells within the row. Since those two cells are also completely inside the top left box and one of them must be a 6, there cannot be another 6 within that box.
What is important with this technique is that those locked candidates are not locked in any arbitrary cells, but that they are completely contained inside the intersection of a box and a line (row or column).
- If the box forces one candidate into the intersection, then the line cannot have this candidate anywhere but the intersection.
- If the line forces one candidate into the intersection, then the box cannot have this candidate anywhere but the intersection.
So this technique can be split into two types:
Line-to-Box Reduction
The previous example was a Line-to-Box Reduction, where the line forced a candidate (6) into the intersection, so we we able to eliminate all 6s from all cells within the box.
Here is another example, where we eliminate 5s.
The candidate 5 is squeezed into one of two cells, so we can eliminate the other 5s from the box.
Box-to-Line reduction
This is the reverse of the previous one.
Here, the 2 at the bottom forces a 2 into two cells within the top box. Since these two cells are also completely inside the sixth column, we can eliminate all other 2s from that column.
(Box-to-Line Reduction is also known as Pointing Pairs or Pointing Triples, but be aware that this has nothing to do with the pairs and triples we encountered in Naked Groups and Hidden Groups. Here, it means that one candidate is locked into one of two or three cells within the intersection.)
What about Line-to-Line Reduction?
Line-to-Line Reductions are redundant. Why?
The intersection of a box with a line is always three cells.
The intersection of a line with a line is always just a single cell.
Applying this technique would mean that there is one candidate locked to one cell, which is simply a Single, and would have already been found by our Singles techniques.
When and how to look for Locked Candidate
You generally start looking for Locked Candidate when there are no Singles or Groups left to find. Of course, you will also find Locked Candidates while looking for Singles and Groups.
The best advice I can give you here is: "look for a region where many cells can be affected at once, so that a number is squeezed into a row/column or box."
This example shows a relatively common pattern that you can look out for.
Here we can see that the bottom middle box is relatively restricted, and we notice that the 5 in the center cell has a great impact on that box, blocking three of five empty cells.
So we investigate further, and have a look at where the 5 is forced to. Luckily it is forced into one of two cells.
This example is notated via Cell&Box Notation, so the 5 is a box candidates, not a cell candidate.
Since the 5 is pinned down to only two cells within the same row, we now know that all other cells in that row cannot hold a 5.
Consequently, this helps us see the Hidden Pair (5, 8) in the bottom left box.