Setti's Rule First posited on this website by 'Setti' in the Weekly Extreme no 25, on 15th of December 2010. I've been helped by SlowThinker's original posts and by several other posters, many thanks.
The rule makes use of the observation that, regardless of compartments, every digit appears in exactly the same number of rows and columns. This is due to the Str8ts rule that says numbers must be unique to each row and column. For example, if 8 appears in four columns, then it must appear in exactly four rows as well.
To see how this rule is useful, lets look at one of the first examples ever discussed, on Extreme number 31.
At this stage of play we'about half way and I'm interested in number 6. Firstly, I've satisfied myself that there will be a 6 in every column - nine 6s all together. Some are clues (columns 2 and 3), some are solved cells, and the rest are necessary candidates in the remaining columns.
If every column needs a 6 then every row needs a 6 as well. In row C we have a lone 6 in C9. Unlike Sudoku, where a lone digit screams 'me me', the black cell in C6 means not all 1 to 9 will be used. The 3-cell compartment could contain 7-8-9 (or 9-8-7) just as well as 7-8-6.
However, 6 must appear in row C by Setti's Rule, so in the case of C9 we can fix the solution of that cell.
The trick, when 'counting the numbers' is to only include necessary numbers. These are candidates that MUST appear somewhere in the row or column. Optional candidates will occur at the head and tail of a str8ts. For example, a four cell compartment might have the possible numbers 1-2-3-4-5. It will certainly contain 2-3-4 so these are 'necessary', while 1 and 5 are optional - one will be chosen but it's too early to know which. Setti is only safe to use if all the candidiates are known to be necessary.
However, say you have two str8ts in the same row with [1-2-3-4-5] and [5-6-7], and 5 is optional in either Str8t but it could be necessary in the whole row - so 5 counts as necessary. You judge the X under consideration by whether must appear in the row or column, not just the compartment. For a row or column with just one compartment it's the same thing.
- If you have a particularly good example, please send it to me, I'd be delighted to include them soon
More work to be done here, but in the meantime...
An excellent write up of Str8ts strategies by SlowThinker - including Setti can be found here