Hidden Locked Pair, Trio, . . .

For this page to make any sense, you have to be familiar with the material discussed on the Locked Sets page.

Hidden Locked Pair

External synonyms:  hidden locked pair, hidden pair.

A "Hidden Locked Pair" is not a Pair(!).  It's two Cells — the only two Cells in a House which happen to contain two specific candies a, b (but there are also other candies in these two Cells!).

If only two Cells in a House contain 2- and 5-candies (despite the presence of other candies in these two Cells), then the BigNums 2 and 5 will have to wind up in those two Cells — so you can kill all the other candies in those two Cells.

I imagine you find that clear as mud. We have to look at an example:

Hidden Locked Pair. In Row 2, only the two yellow cells contain the two candies 5 and 7. So the Row's 5 and 7 must (eventually) go in those two Cells. Therefore you can kill all the other candies in the yellow Cells.

Notice that after you've killed the "other" candies in the two yellow Cells, those two Cells become an explicit Locked Pair (a Naked Locked Pair, as it's sometimes called).

It turns out that Hidden Locked Sets and Locked Sets are not independent concepts — they're complementary:

Locked Quartet analysis of the preceding Grid. In Row 2, the green Cells form a Locked Quartet in 1,2,4,6. So any 1,2,4,6 in the two white Cells can be killed. The result is the same as the one gotten by the Hidden Locked Pair analysis in the preceding Grid.

Well, if the result's the same, then what good is the Hidden Locked Pair Tactic anyway?

To see that it's not useless, look at this:

Hidden Locked Pair. Look at the Upper Center Block. There's a Locked Septet in this Block; good luck on finding it. There's also a Hidden Locked Pair . . . The 6,7 look hopeful, but there's a 7 in a third Cell. The 3,5?  No, they're all over the place. The 2,4?  Bingo! The 2,4 are a Locked Pair in two Cells, and you can kill the extraneous candies (8,3,5) in those two Cells.

So this is the point:  you look for a Hidden Locked Pair when you've had no luck with a Locked-Set analysis of a House that has a lot of empty Cells.

 

Hidden Locked Trio

A "Hidden Locked Trio" is not a Trio. It's three Cells — the only three Cells in a House each of which happens to contain some or all of three specific candies a, b, c (but there are also other candies in those three Cells).

If only three Cells in a House contain 1-, 4-, and 7-candies (despite the presence of other candies in these three Cells), then the BigNums 1, 4, 7 will have to wind up in those three Cells — so you can kill all the other candies in those three Cells.

However, trying to find a Hidden Locked Trio is too hard; I don't think anybody ever looks for one of these.

An example will convince you of that:

Hidden Locked Trio. Look at Column 5. There's a Hidden Locked Trio in here. There's a Locked Quintet too. Neither is easy to find. Bummer.

So you won't be likely to decompose that Column (or at least I won't). What saves us? Some other Tactic, probably Claims, will clean up this Column to the extent that some simpler Locked Sets emerge. Fortunately, the different Sudoku Tactics help each other.

In case you're curious, the Hidden Locked Trio is the only three Cells that contain the candies 3,6,9.

 

Connection to Hidden Locked Single

On the page where a Hidden Locked Single is defined, I mentioned that the name of that Tactic would make more sense once Hidden Locked Sets had been explained.

A Hidden Locked Single is the simplest Hidden Locked Set:  it's one Cell that happens to be the only Cell in a House which contains a certain specific candie. So clearly you can crown that candie in that Cell.

 

How Does This Tactic Fit In?

See the last section of the Locked Sets page for a full description of how to apply Locked Sets, including Hidden Locked Singles and Hidden Locked Pairs.