New Simple Rule

Advanced methods and approaches for solving Sudoku puzzles

New Simple Rule

I've only recently started looking at Sudoku. Many of the methods in list are rather complex and very difficult to apply. But unless I missed it, there is a relatively simple method that isn't listed. First, consider the Row/Column Subsets rule.

Row/Column Subsets

If for a certain digit, there are N distinct rows each with 2 to N candidate cells and these cells fall on exactly N common columns, then remove all candidates for this digit in these N columns except for those that lie within the defining rows.

Am I really the only one who has noticed that you can replace either row or column with block and you still have a valid rule? Sudoku has some equivalent formulations in which there is no distinction between constraints. So generally speaking, any rule that involves rows or columns is going to have an equivalent one with blocks. (note that this rule with blocks is useful only for N=2, and it is undefined for N=4 or higher because at most three rows can intersect one block.)

Posts: 3
Joined: 23 August 2006

Re: New Simple Rule

When i understood you right, your "Row/Column Subsets" are the ordinary fishes x-wing, swordfish, jellyfish (N=2,3,4) and the box variation with N=2 is known as Locked Candidates 2 or Block/Block Interaction.
ravel

Posts: 998
Joined: 21 February 2006

Re: New Simple Rule

"Row/Column Subsets" are indeed just another name for "fishes." The new rule is the box variation with N=2 and it is not covered by "Locked Candidates 2" nor "Block/Block Interaction." I don't seem to have the ability to post html stuff so I'll try an ascii diagram.

Code: Select all
`+---+---+---+---+---+---+---+---+---+|   |   |   | * |   |   |   |   | * |+---+---+---+---+---+---+---+---+---+|   |   |   |   |   |   |   |   |   |+---+---+---+---+---+---+---+---+---+|   |   |   |   | * |   | * |   |   |+---+---+---+---+---+---+---+---+---+`

Suppose the only occurrences of some digit in rows 1 and 3 are at the indicated cells. The new rule (obtained by replacing both occurrences of "columns" with "blocks" in the "Row/Column Subsets" rule) applies. For the digit, there are two rows each with two candidate cells that fall in exactly two common blocks, namely blocks 2 and 3. So we can remove all candidates for this digit in blocks 2 and 3 except for those that lie on rows 1 and 3 (i.e. remove all candidates in blocks 2 and 3 that lie on row 2). This isn't exactly the most useful rule in the world but it is simple and unless I missed it, doesn't fall under any other reasonably simple rule.

Posts: 3
Joined: 23 August 2006

This is just a simple case of "locked candidates type 2"...

The candidate on r2 must be locked in r2c123, so eliminate it from r2c456789...

Nothing special I'm afraid...
udosuk

Posts: 2698
Joined: 17 July 2005

Ah, now I see. But it looks like "locked candidates type 1" (not type 2) to me.
The candidate in block 1 is locked in row 2, so eliminate all other occurrences
in row 2. I couldn't understand how everybody could have missed such a
simple rule but I failed to notice that it was subsumed by another simple rule.

Posts: 3
Joined: 23 August 2006

Okay, I must confess I didn't check the type 1/2 when I posted last time, just took a 50/50 punt... Wrong bet...

So, in type 1 we eliminate the candidate along the row/column while in type 2 we eliminate it within the box... Will remember next time...
udosuk

Posts: 2698
Joined: 17 July 2005