The New Sudoku Players' Forum

[Myth Jellies]

Myth Jellies's Sashimi/Filet of Anything Rule:

Considering only the candidate locations for a single digit, if there exists a pattern, rule, or process that results in the removal of that candidate from a given cell, then that candidate digit can still be removed regardless of the existance of that digit as a candidate in any cell which shares a group with the given cell.

In other words, the deletion of a candidate from a given cell is dependent only on the part of a pattern that does not share a group with the given cell.

The proof of this concept is fairly simple. For any setup of candidates for digit X that you have, you will have a number of solution patterns, N, that run through cell A. N may or may not equal zero. If you alter the setup slightly so that a previously blocked out cell, B, now has the candidate digit X, then some new solution patterns may be created that all run through B. But if B shares a group with A, then none of those new patterns can run through A, and so N is unchanged. Likewise, if cell C already has candidate digit X, and we alter the setup by removing it as a possibility, then we remove all of the solution patterns that ran through C. But, once again, if C shares a group with A, then none of those removed patterns could have run through A, so N is still unchanged. Thus, if N is zero before the alteration, then N is zero after the alteration.

So, how can you use this principle?

You can apply it to an X-Wing, or any NxN Swordfish, and you get the Filet-O-Fish

You can apply it to Simple Coloring Rule 4, and you get Simple Coloring Rule 5.

You can apply it to Simple Coloring Rule 1, and get a limited form of coloring with groups. For example:

Code: Select all

 .   .   2   | 2*  2   2   | .   2   .
 .   .   2   | 2*  2   .   | .   2   2
 .   .   .   | .   2B  .   | 2A  .   .
-------------+-------------+-----------
 .   2   .   | .   2*  2   | .   .   2
 .   .   .   | 2A  .   .   | 2B   .   .
 .   2   .   | 2   2*  2   | .   2   2
-------------+-------------+-----------
 .   .   .   | 2   2   .   | .   2   2
 .   .   .   | 2   2   2   | .   2   2
 .   .   .   | .   .   .   | .   .   .


Simple Colors Rule 1 lets you remove the candidate 2's from the starred cells above. If you alter the grid a bit...

Code: Select all

 .   .   2   | 2*  2   .   | .   2   .
 .   .   2   | 2*  2   .   | .   2   2
 .   .   .   | 2   2(B)2   | 2A  .   .
-------------+-------------+-----------
 .   2   .   | .   2   2   | .   .   2
 .   .   .   | 2A  .   .   | 2B   .   .
 .   2   .   | 2   2   2   | .   2   2
-------------+-------------+-----------
 .   .   .   | 2   2   .   | .   2   2
 .   .   .   | 2   2   2   | .   2   2
 .   .   .   | .   .   .   | .   .   .


You can use the Filet of Colors rule to ignore the existance of r3c4 and r3c6 to eliminate candidates in r1c3 and r2c3. You no longer can eliminate the candidates in box 5 however, because they do not share a group with your ignored candidates.

You can probably find ways to apply this principle to many of our single digit methods. Turbot Fish, X-Cycles, X-Cycles with groups...give it a shot.

[Jeff]

You can probably find ways to apply this principle to many of our single digit methods. Turbot Fish, X-Cycles, X-Cycles with groups...give it a shot.

Interesting MJ, This anything concept, in nice loop terms, is the use of a node of single cell or a node containing a few grouped cells. In other words, the additional cells in the altered grid requires the x-cycle nice loop to be promoted to grouped x-cycle to produce the same eliminations.

[Myth Jellies]

It works in reverse, too. For example, when you pick a likely cell for your discontinuous X-cycle loop, you can "question mark" out all cells sharing a group with that cell. Then you can include or exclude candidates from those question mark cells as needed to perhaps create a simpler loop that requires no groups.

[Jeff]

It works in reverse, too. For example, when you pick a likely cell for your discontinuous X-cycle loop, you can "question mark" out all cells sharing a group with that cell. Then you can include or exclude candidates from those question mark cells as needed to perhaps create a simpler loop that requires no groups.

That would definitely simplify the identification process for the nice loop.