Claim

Two definitions:

• Bandit — a horizontal sequence of three Cells which lies entirely within one Row and one Block (a Bandit is the intersection of a Row and a Block).

• Twit — a vertical sequence of three Cells which lies entirely within one Column and one Block (a Twit is the intersection of a Column and a Block).

What if all of a Block's 9-candies fall in one Bandit?  Then a 9 has to lie in those three Cells, so there can't be any 9s elsewhere in the Row containing that Bandit — therefore you can kill any 9-candies in the Row that aren't inside that Bandit. The Block has laid a Claim on the Row. (Same for 8s, 7s, 6s, . . .)

Instead, what if all of the Row's 9-candies fell in that Bandit?  Then a 9 would have to be there in those three Cells, so there couldn't be any 9s elsewhere in the Block, and you could kill any 9-candies in the Block that aren't inside that Bandit. The Row has laid a Claim on the Block. (Same for 8s, . . .)

The same kind of situation applies to an intersecting Column and Block.

This is all too abstract. We need to look at examples.

 

B-on-R Claim (Block-on-Row Claim);
B-on-C Claim (Block-on-Column Claim)

External synonyms:  intersection removal, pointing candidates.

Example:

Block-on-Column Claim; Block-on-Row Claim. In the Middle Left Block, all the Block's 7-candies happen to fall in the Twit that's part of Column 2. There's going to be a 7 in that Twit, so you can kill any 7-candies elsewhere in the Column. And all the Block's 2-candies happen to fall in the Bandit that's part of Row 4. There's going to be a 2 in that Bandit, so you can kill any 2-candies elsewhere in the Row.

Apply this Tactic to all nine Blocks. For each Block, go through all the digits 1 to 9.

One of the most important things about this is that while you're looking at the arrangement of the candies for each digit, you will occasionally notice that there's only one Cell in the Block that contains a specific candie:  crown that candie! (That's the Hidden Locked Single Tactic.)

Looking at a Block, mumble to yourself things like, "The 1s are oblique. The 3s are all aligned in a Column, so I can kill the other 3s in that Column. There's only one Cell with a 6-candie, so I can put a BigNum 6 in that Cell."

For legibility reasons, on this site I can't distribute the candies in a Cell in a nice orderly fashion. But on your own Grid, you have the candies laid out in a 3 x 3 matrix, which speeds things up a lot when you're looking for Claims. You'll see that when you're checking a Block for possible Claims on a Row or Column.

 

R-on-B Claim (Row-on-Block Claim)

External synonyms:  intersection removal, block-row reduction.

Example:

Row-on-Block Claim. In Row 1, all the Row's 1-candies happen to fall in the Bandit that's part of the Upper Left Block. There's going to be a 1 in that Bandit, so you can kill any 1-candies elsewhere in the Block.

Apply this Tactic to all nine Rows. For each Row, go through the digits 1 to 9. (In the process, as usual, watch for Hidden Locked Singles.)

Looking at a Row, mutter to yourself things like, "The 1s are scattered (in different Blocks). The 5s are trapped in one Block, so I can kill the other 5s in that Block. There's only one Cell with a 7-candie, so I can enter a BigNum 7 in that Cell."

Again, your having the candies laid out in a 3 x 3 matrix is a big help.  When you're checking a Row, you can learn to check the 1s, 2s, 3s all together (to check whether each is scattered or not). And you can check the 4s, 5s, 6s all together, and the 7s, 8s, 9s all together. You really can do that — and it will make the search go much faster.

 

C-on-B Claim (Column-on-Block Claim)

External synonyms:  intersection removal, block-column reduction.

Example:

Column-on-Block Claim. In Column 2, all the Column's 3-candies happen to fall in the Twit that's part of the indicated Block. There's going to be a 3 in that Twit, so you can kill any 3-candies elsewhere in the Block.

Apply this Tactic to all nine Columns. For each Column, go through the digits 1 to 9. (And keep your eye out for Hidden Locked Singles.)

Looking at a Column, think things like, "The 1s are scattered (in different Blocks). The 4s are trapped in one Block, so I can kill the other 4s in that Block. There's only one Cell with an 8-candie, so I can enter a BigNum 8 in that Cell."

The layout of the candies in a 3 x 3 matrix is a very helpful here too.  When you're checking a Column, you can learn to check the 1s, 4s, 7s all together, then the 2s, 5s, 8s all together, and then the 3s, 6s, 9s all together. That greatly increases the speed of the search.

 

OK, So What Do We Do with All This?

When you start, the first thing you want to do is exhaust the Local Tactics before going on to the other Tactics. So do you do Claims first, or do you do Locked Sets first?

Rule of thumb:  when the candies in the empty Cells are dense (meaning there are not very many Pair Cells and a lot of Cells containing four or more candies), do Claims first. This will clean up the Grid and make the search for Locked Sets much easier.

(However, before doing Claims, most people will start off by just eyeing the Grid and picking off the really easy-to-spot Locked Sets — Hidden Locked Singles, Locked Pairs, & Locked Trios.)

When you check the Grid methodically to find all existing Claims, you'll do this:

• In every Block, check every digit for a possible B-on-R/C Claim.

• In every Row, check every digit for a possible R-on-B Claim.

• In every Column, check every digit for a possible C-on-B Claim.

As pointed out in the two immediately preceding sections, when you're doing R/C-on-B Claims, you can eventually learn to check the digits in groups rather than one at a time.

You would like to have all the possibilities for Locked Sets and Claims carried out before you go on to other Tactics, because when you're applying Fish Tactics, Unique Rectangles, or Chains, things are much easier if the Grid has already been cleaned out as much as possible.

But there's a problem:  as you apply Locked Sets or Claims, you sometimes create other Claims or Locked Sets. So in principle you might have to reapply Locked Sets and Claims to the Grid until you're convinced that there aren't any more. Getting too hung up on that could drive you nuts, of course. But after you've done a lot of Sudokus, you will have developed a sense of whether a Grid is free of Locked-Set or Claim opportunities. And there is absolutely no reason for you to avoid applying any Tactic at any time if you see the opportunity to do so.  So the problem isn't all that bad.