The New Sudoku Players' Forum

[elisatems]

Hodoku finds a Sue De Coq in an Enjoy Sudoku Fiendish puzzle that seems to fall outside the usual definition of a Sue De Coq, so I was wondering what the most general definition of this pattern is. Here is the puzzle at the point where the SDC becomes apparent:

Code: Select all

.--------------.--------------.--------------.
| 8   2    136 | 17  79   367 | 5   369  4   |
| 4   7    36  | 5   29   236 | 8   1    69  |
| 9   156  356 | 8   13   4   | 2   36   7   |
:--------------+--------------+--------------:
| 67  16   8   | 2   4    37  | 19  5    139 |
| 5   9    4   | 6   13   8   | 7   2    13  |
| 2   3    17  | 17  5    9   | 6   4    8   |
:--------------+--------------+--------------:
| 67  456  9   | 3   278  257 | 14  68   126 |
| 3   8    2   | 49  6    1   | 49  7    5   |
| 1   456  567 | 49  278  25  | 3   689  269 |
'--------------'--------------'--------------'

The pattern is: r7c56 (2578); r7c18 (678); r9c6 (25). (Hodoku adds the naked pair 49 in r89c4 to the 25 in r9c6, but this seems unnecessary.)

This seems to work because:

(1) r7c1568 form an N+1 ALS (25678 over 4 cells); if any of {6,7,8} is the solution in any other cell in r7, then they become a locked set. Since 2 and 5 only occur in r7c5 and r7c6, r9c6 is forced to be empty.

(2) r7c56 and r9c6 form an N+1 ALS (2578 over 3 cells); if either of {2,5} is the solution in any other cell in block 8, then they become a locked set. Since 7 and 8 only occur in r7c5 and r7c6, both r7c1 and r7c8 are forced to be 6.

SDC seems to work by taking an N+2 ALS at the intersection of a line and a block, and two N+1 ALSes (I'll call them component ALSes), one in the line and the other in the block, to form two larger intersecting N+1 ALSes. The component ALSes must be disjoint. Any candidate in the larger line ALS in a cell in the line outside the pattern, and any candidate in the larger block ALS in a cell in the block outside the pattern, can then be eliminated.

But... even this doesn't seem general enough, since the 2- or 3-cell pattern at the line-block intersection (the "intersection component") might be an N+3 or greater ALS as well. It seems the strategy will work as long as the disjoint component ALSes, whatever their order, combine with the intersection component to form two intersecting N+1 ALSes. That way any candidate in a cell outside the pattern that can see all instances of that candidate inside the pattern would, if it were true, reduce either the larger block or line ALS to a locked set, preventing a solution in one or more cells in one or the other component ALSes.

Is this correct? Is there a more general description of SDC? References would be appreciated - the most general one I could find is on Andrew Stuart's site (which also gives the more general definition of WXYZ-Wing, thanks @jco)... and that definition doesn't seem to allow for the addition of candidates into the pattern not contained in the intersection component.

[StrmCkr]

Sue de coq are DDS

The generalized deffintion is a*ls where * is any number of degree of freedom

Then that first set is connected to any number of other als so that it has * dof links as rcc for a mutual elimination between the sets

Or with *+1 links so that all sets are locked.

Specifically coqs all rcc occupy 2 sectors.
Deathblossoms all rcc occupy 3 sectors

http://forum.enjoysudoku.com/collection-of-solving-techniques-t3315.html DDs and coqs are in here
as well as generalized als rules

[eleven]

There are several ways to define or look at Sue-de-Coqs. As StrmCkr pointed out, DDS (look here) is one of them.

My general approach is:
If you have n cells with n digits, and none can be twice in these cells (i.e. all occurances of the digit are in one unit), then all of them must be in these cells. Therefore you can eliminate each digit from the rest of the unit, in which it is in these cells.
In your example you have the 5 digits 25678 in 5 cells, and 25 is restricted to the box (eliminate 25 from the rest of the box), 678 to the row (eliminate 678) from the rest of the row.

This argument is of course not restricted to a box&line.
It eg. also solves ..VWXYZ-wings, but then you might have to take into account, that a digit can also be twice in the pattern cells, to find the eliminations.