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strmckr
Joined: 18 Aug 2009
Posts: 64
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 Posted: Tue Jan 26, 2010 6:51 am Post subject: Split - Wing: exemplars and examples |
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Thanks to 999_Spring's posting of "anything" wings type 5 displayed here
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 PENDING:
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 under M-Rings
MINIMAL EXEMPLAR SET:
SPLIT - WINGS
| Code: |
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: 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: 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
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edits: (1-3) minor graphical modifications, typos, fixed & added chains. (4) added type 5a,(5,6,7) added types 3b noted that type 3b is equivalent of 3a.
Last edited by strmckr on Sun May 23, 2010 7:51 am; edited 3 times in total |
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strmckr
Joined: 18 Aug 2009
Posts: 64
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| Posted: Tue Jan 26, 2010 6:51 am Post subject: |
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