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| The '''Franken Swordfish''' is a [[fish]] pattern of the [[Franken Fish]] type. This type allows either the [[defining set]] or the [[secondary set]] to contain [[box]]es, as well as [[line]]s. | | The '''Franken Swordfish''' is a [[fish]] pattern of the [[Franken Fish]] type. This type allows either the [[defining set]] or the [[secondary set]] to contain [[box]]es, as well as [[line]]s. |
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| === Maximal Franken Swordfish ===
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| This is a [[project:fish diagram|fish diagram]] of a Franken Swordfish with all 12 possible [[candidate]]s present. Note that this rarely happens:
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| {{grid|5=/|7='''n'''|8='''n'''|9=e|14=/|16='''n'''|17='''n'''||18=e|23=/|25='''n'''|26='''n'''|27=e|32=/|34=/|35=/|36=a|37=e|38=e|39=e|40=e|41='''n'''|42=e|43='''n'''|44='''n'''|45=e|50=/|52=/|53=/|54=a|59=/|61=/|62=/|63=b|64=e|65=e|66=e|67=e|68='''n'''|69=e|70='''n'''|71='''n'''|72=e|77=/|79=/|80=/|81=b}}
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| ;Legend: | | ;Legend: |
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| * b: one or both of these must have candidate n, or the pattern collapses to a [[Pointing Pair]], [[Hidden Single]] and [[Locked Candidates]] | | * b: one or both of these must have candidate n, or the pattern collapses to a [[Pointing Pair]], [[Hidden Single]] and [[Locked Candidates]] |
| * e: candidate n can be eliminated from each of these cells | | * e: candidate n can be eliminated from each of these cells |
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| | === Maximal Franken Swordfish cccrrb === |
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| | This is a [[project:fish diagram|fish diagram]] of a Franken Swordfish with all 12 possible [[candidate]]s present. Note that this rarely happens. |
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| | {{grid|5=/|7='''n'''|8='''n'''|9=e|14=/|16='''n'''|17='''n'''||18=e|23=/|25='''n'''|26='''n'''|27=e|32=/|34=/|35=/|36=a|37=e|38=e|39=e|40=e|41='''n'''|42=e|43='''n'''|44='''n'''|45=e|50=/|52=/|53=/|54=a|59=/|61=/|62=/|63=b|64=e|65=e|66=e|67=e|68='''n'''|69=e|70='''n'''|71='''n'''|72=e|77=/|79=/|80=/|81=b}} |
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| The [[defining set]] contains columns 5, 7 & 8. The secondary set contains rows 5 & 8 and box 3. All the [[candidate]]s in the defining set (marked with '''n''') are located inside the [[secondary set]]. The remaining candidates from these 3 [[constraint]]s can be eliminated. | | The [[defining set]] contains columns 5, 7 & 8. The secondary set contains rows 5 & 8 and box 3. All the [[candidate]]s in the defining set (marked with '''n''') are located inside the [[secondary set]]. The remaining candidates from these 3 [[constraint]]s can be eliminated. |
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| | Rotate the diagram 90 degrees for a '''rrrccb''' pattern. |
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| | === Same with both rows in 1 band === |
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| | {{grid|5=/|7='''n'''|8='''n'''|9=e|14=/|16='''n'''|17='''n'''||18=e|23=/|25='''n'''|26='''n'''|27=e|32=/|34=/|35=/|36=e|37=e|38=e|39=e|40=e|41='''n'''|42=e|43='''n'''|44='''n'''|45=e|46=e|47=e|48=e|49=e|50='''n'''|51=e|52='''n'''|53='''n'''|54=e|59=/|61=/|62=/|63=a|68=/|70=/|71=/|72=a|77=/|79=/|80=/|81=a}} |
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| | This pattern will be processed in 2 separate steps: |
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| | # [[Locked Candidates]] (labeled '''a''') in box 9 and column 9. This eliminates the candidates in r1-6c9. |
| | # '''Franken Swordfish''', which eliminates the remaining candidates for '''n''' in rows 5 and 6. |
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| | === Maximal Franken Swordfish ccbrrr === |
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| | {{grid|2=/|5=/|7=/|8=/|9=/|10=e|11='''n'''|12=e|13=e|14='''n'''|15=e|16='''n'''|17='''n'''|18='''n'''|19=e|20='''n'''|21=e|22=e|23='''n'''|24=e|25='''n'''|26='''n'''|27='''n'''|29=/|32=/|37=e|38='''n'''|39=e|40=e|41='''n'''|42=e|43=e|44=e|45=e|47=/|50=/|56=/|59=/|65=/|68=/|74=/|77=/}} |
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| | The defining set consists of columns 2 and 5 with box 3. The secondary set are rows 2, 3 and 5. |
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| | Rotate the diagram 90 degrees for a '''rrcccb''' pattern. |
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| | === Same with both columns in 1 band === |
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| | {{grid|1=e|2=/|3=/|7=/|8=/|9=/|10=e|11='''n'''|12='''n'''|13=e|14=e|15=e|16='''n'''|17='''n'''|18='''n'''|19=e|20='''n'''|21='''n'''|22=e|23=e|24=e|25='''n'''|26='''n'''|27='''n'''|28=e|29=/|30=/|37=e|38='''n'''|39='''n'''|40=e|41=e|42=e|43=e|44=e|45=e|46=e|47=/|48=/|55=a|56=/|57=/|64=a|65=/|66=/|73=a|74=/|75=/}} |
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| | This pattern will be processed in 3 separate steps: |
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| | # '''Locked Candidates 1''' (labeled '''a''') in box 7 and column 1. This eliminates the candidates for '''n''' in the intersection of column 1 with boxes 1 and 4. |
| | # '''Locked Candidates 1''' (labeled '''n''') in box 4 and row 5. This eliminates the candidates for '''n''' in the intersection of row 5 with boxes 5 and 6. |
| | # '''Locked Candidates 2''' (labeled '''n''') in box 1 and 3. This eliminates the remaining candidates for '''n''' in the intersection of box 2 with rows 2 and 3. |
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| === Reduced Patterns for the Franken Swordfish === | | === Reduced Patterns for the Franken Swordfish === |
The Franken Swordfish is a fish pattern of the Franken Fish type. This type allows either the defining set or the secondary set to contain boxes, as well as lines.
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Maximal Franken Swordfish cccrrb
This is a fish diagram of a Franken Swordfish with all 12 possible candidates present. Note that this rarely happens.
The defining set contains columns 5, 7 & 8. The secondary set contains rows 5 & 8 and box 3. All the candidates in the defining set (marked with n) are located inside the secondary set. The remaining candidates from these 3 constraints can be eliminated.
Rotate the diagram 90 degrees for a rrrccb pattern.
Same with both rows in 1 band
This pattern will be processed in 2 separate steps:
- Locked Candidates (labeled a) in box 9 and column 9. This eliminates the candidates in r1-6c9.
- Franken Swordfish, which eliminates the remaining candidates for n in rows 5 and 6.
Maximal Franken Swordfish ccbrrr
The defining set consists of columns 2 and 5 with box 3. The secondary set are rows 2, 3 and 5.
Rotate the diagram 90 degrees for a rrcccb pattern.
Same with both columns in 1 band
This pattern will be processed in 3 separate steps:
- Locked Candidates 1 (labeled a) in box 7 and column 1. This eliminates the candidates for n in the intersection of column 1 with boxes 1 and 4.
- Locked Candidates 1 (labeled n) in box 4 and row 5. This eliminates the candidates for n in the intersection of row 5 with boxes 5 and 6.
- Locked Candidates 2 (labeled n) in box 1 and 3. This eliminates the remaining candidates for n in the intersection of box 2 with rows 2 and 3.
Reduced Patterns for the Franken Swordfish
The previous example is the maximum pattern for the franken swordfish. It contains 12 cells and because of this its occurence is much rarer than the any of the other 4 patterns.
Logical analysis of the minimum pattern shows that 4 of the cells in box 3 of the example are redundant. Reduced patterns occur when 1, 2, 3, 4 of these redundant cells are removed. The only restriction on this: there must be at least 1 cell in each of the box 3 columns in the pattern.
Further reduction is possible by removing one of the pattern candidates in box 6 and one from box 9. The removed candidates from box 6 and 9 cannot both be taken from the same column. Like a regular Swordfish each of the defining constaints must have 2 candidates.
There is nothing finnish or sashimish about any of the reduced patterns. In a finned or sashimi row or column swordfish cell eliminations occur only in the box with the fin. In contrast the franken swordfish patterns with 6 through 12 cells all give exactly the same cell eliminations.
Combined Franken/Column Swordfish
It is possible to have a 6 to 8 cell pattern which is both a franken swordfish and a column(row) swordfish. In this case additional cell eliminations can be made.
This pattern can eliminate up to 20 candidates for digit n.
Minimal Franken Swordfish
Similar to a regular Swordfish pattern, it is possible to have empty spots in the pattern, but these are limited to the rows or columns running through the box of the pattern. This is the smallest possible (6 cell) pattern.
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- n: Franken Swordfish pattern for digit n
- /: May not contain candidate for digit n
- .: part of the pattern without a candidate n
- a: one or both of these must have candidate n, or the pattern collapses to a Pointing Pair
- b: one or both of these must have candidate n, or the pattern collapses to a Pointing Pair
- e: candidate n can be eliminated from each of these cells
Finned Franken Swordfish (ineffective)
It is also possible to have a 9 cell pattern which is both a franken swordfish and a finned column(row) swordfish. In this case the finned swordfish pattern does not have any effect on eliminations.
The fin is a regular part of the fish pattern, not an addition.
Finned Franken Swordfish (effective)
Here is example of a finned franken swordfish. The fin in this example occurs in box 5 and the only cell eliminations for this pattern are also in box 5.
See Also
