I have decided to compile a complete minimal set of these pattern of chains which i call "split wings"{s-wing for short}; mostly impart because the links of a and b diverge from the initial cell.
SPECIFIC DEFINITION :
S-Wing: (X)a = (X)b - (X=Y)c - (Y)d = (Y)e "a" and "e" in same unit; a<>Y, e<>X
but not in the same cell -- else M-Ring
It is neither my expectation nor my intent that solvers use the "Type" numbers below. They are included merely to facilitate unambiguous discussion in this thread.
A general note about the exemplars: All cells required to be void (empty) of candidates 'a' and 'b' are not explicitly marked with '/'. However, there are only two grouped conjugate links and the unit (row, column, box) containing each should be clear. If not, I'm willing to consider changing the presentation.
these patterns are only discontinuous;
the continuous variations are explicitly covered underM-Rings
MINIMAL EXEMPLAR SET:
SPLIT - WINGS
- Code: Select all
Type: 1
+------------+---------+-----------------+
| . . . | . . . | . . . |
| . A . | . . . | -B A . . |
| . . . | . . . | . -A B . |
+------------+---------+-----------------+
| . . . | . . . | . . . |
| . AB . | . . . | . B . |
| . . . | . . . | . . . |
+------------+---------+-----------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+------------+---------+-----------------+
Type: 1a
+------------+---------+---------------+
| . . . | . . . | . A . |
| . B . | . . . | -A B A . |
| . . . | . . . | . A . |
+------------+---------+---------------+
| . . . | . . . | . . . |
| . AB . | . . . | . A . |
| . . . | . . . | . . . |
+------------+---------+---------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+------------+---------+---------------+
Type: 1b
+------------+-------------+-----------+
| . . . | . . . | . . . |
| . A . | . -B A . | . B . |
| . . . | . . . | . . . |
+------------+-------------+-----------+
| . . . | . . . | . . . |
| . AB . | . . . | . B . |
| . . . | . . . | . . . |
+------------+-------------+-----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+------------+-------------+-----------+
Type: 1c {row then box}
+------------+-------------+-----------+
| . . . | . . . | . . . |
| . A . | . -B A . | . . . |
| . . . | . . . | . . . |
+------------+-------------+-----------+
| . . . | . . . | . . . |
| . AB . | B B B | . . . |
| . . . | . B-A . | . . . |
+------------+-------------+-----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+------------+-------------+-----------+
Type: 1d {row then col}
+------------+-------------+-----------+
| . . . | . . . | . . . |
| . A . | . A . | . . . |
| . . . | . . . | . . . |
+------------+-------------+-----------+
| . . . | . . . | . . . |
| . AB . | . B . | . . . |
| . . . | . B-A . | . . . |
+------------+-------------+-----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+------------+-------------+-----------+
Type: 2
+------------+---------+-----------------+
| . . . | . . . | . . . |
| . A . | . . . | -B A . . |
| . B . | . . . | . -A B . |
+------------+---------+-----------------+
| . . . | . . . | . . . |
| . AB . | . . . | . . . |
| . . . | . . . | . . . |
+------------+---------+-----------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+------------+---------+-----------------+
Type: 2a
+------------+---------+-----------------+
| . . . | . . . | . . . |
| . A . | . . . | -B A . . |
| . B . | . . . | B B B |
+------------+---------+-----------------+
| . . . | . . . | . . . |
| . AB . | . . . | . . . |
| . . . | . . . | . . . |
+------------+---------+-----------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+------------+---------+-----------------+
Type: 2b
+------------+-------------+---------+
| . . . | . . . | . . . |
| . A . | . -B A . | . . . |
| . . . | . . . | . . . |
+------------+-------------+---------+
| . . . | . . . | . . . |
| . AB . | . . . | . . . |
| . . . | . . . | . . . |
+------------+-------------+---------+
| . B . | . -A B . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+------------+-------------+---------+
Type: 3
+----------------+---------+---------+
| . A . | . . . | . . . |
| -B A A . | . . . | . . . |
| . A . | . . . | . . . |
+----------------+---------+---------+
| . . . | . . . | . . . |
| . AB . | . . . | . . . |
| . . . | . . . | . . . |
+----------------+---------+---------+
| . B . | . . . | . . . |
| -A B B . | . . . | . . . |
| . B . | . . . | . . . |
+----------------+---------+---------+
Type: 3a
+----------------+---------+---------+
| A A . | . . . | . . . |
| A A . | . . . | . . . |
| A A . | . . . | . . . |
+----------------+---------+---------+
| . . . | . . . | . . . |
| . AB . | . . . | . . . |
| . . . | . . . | . . . |
+----------------+---------+---------+
| . B . | . . . | . . . |
| -A B B . | . . . | . . . |
| . B . | . . . | . . . |
+----------------+---------+---------+
Type: 4
+--------------+---------+-------------+
| . . . | . . . | . . . |
| B A . | . . . | . -B A . |
| . . . | . . . | . . . |
+--------------+---------+-------------+
| B . . | . . . | . . . |
| B AB . | . . . | . . . |
| B . . | . . . | . . . |
+--------------+---------+-------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+--------------+---------+-------------+
Type: 4a
+----------------+-------------+---------+
| . . . | . . . | . . . |
| -B A . . | . -A B . | . . . |
| . . . | . . . | . . . |
+----------------+-------------+---------+
| A . . | . . . | . . . |
| A AB . | . B . | . . . |
| A . . | . . . | . . . |
+----------------+-------------+---------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------------+-------------+---------+
Type: 4b
+--------------------+---------+---------+
| . . . | . . . | . . . |
| -A B . -B A | . . . | . . . |
| . . . | . . . | . . . |
+--------------------+---------+---------+
| B . A | . . . | . . . |
| B AB A | . . . | . . . |
| B . A | . . . | . . . |
+--------------------+---------+---------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+--------------------+---------+---------+
Type: 4c
+------------------+---------+---------+
| . . A | . . . | . . . |
| -A B . A | . . . | . . . |
| . . A | . . . | . . . |
+------------------+---------+---------+
| B . A | . . . | . . . |
| B AB A | . . . | . . . |
| B . A | . . . | . . . |
+------------------+---------+---------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+------------------+---------+---------+
Type: 4D {uses rows instead of box}
+----------------+-------------+---------+
| . . . | . . . | . . . |
| A B B-A | . . . | . . . |
| . . . | . . . | . . . |
+----------------+-------------+---------+
| A . . | . . . | . . . |
| A AB . | . . . | . . . |
| A . . | . . . | . . . |
+----------------+-------------+---------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------------+-------------+---------+
Type: 5
+----------------+---------+-------------+
| . A . | . . . | . . . |
| A A A | . . . | . -A B . |
| . A . | . . . | . . . |
+----------------+---------+-------------+
| . . . | . . . | . . . |
| . AB . | . . . | . B . |
| . . . | . . . | . . . |
+----------------+---------+-------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------------+---------+-------------+
Type: 5a
+----------------+---------+-------------+
| . A . | . . . | . . . |
| A AB+ A | . . . | . -A B . |
| . A . | . . . | . . . |
+----------------+---------+-------------+
| . . . | . . . | . . . |
| . AB . | . . . | . . . |
| . . . | . . . | . . . |
+----------------+---------+-------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------------+---------+-------------+
Type: 6
+------------------+---------+---------+
| . A B | . . . | . . . |
| -B A A B | . . . | . . . |
| . A B | . . . | . . . |
+------------------+---------+---------+
| . . B | . . . | . . . |
| . AB B | . . . | . . . |
| . . B | . . . | . . . |
+------------------+---------+---------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+------------------+---------+---------+
Type: 6a
+----------------+---------+---------+
| . B B | . . . | . . . |
| . B B | . . . | . . . |
| . B B | . . . | . . . |
+----------------+---------+---------+
| . . A | . . . | . . . |
| . AB A | . . . | . . . |
| . . A | . . . | . . . |
+----------------+---------+---------+
| . . . | . . . | . . . |
| . . -B A | . . . | . . . |
| . . . | . . . | . . . |
+----------------+---------+---------+
Type: 6b
+----------------+---------+-------------+
| . B . | . . . | . . . |
| -A B B . | . . . | . -B A . |
| . B . | . . . | . . . |
+----------------+---------+-------------+
| . . . | . . . | . . . |
| . AB . | . . . | . A . |
| . . . | . . . | . . . |
+----------------+---------+-------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------------+---------+-------------+
ab' means a bivalued cell with candidates 'a' and 'b'
'ab+' means the cell must contain both 'a' and 'b' candidates, and possibly others
