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.
For the Franken Swordfish, 1 of the defining (or secondary) rows (or columns) is replaced by a box, but 2 of the 3 secondary (or defining) columns (or rows) must intersect with this box.
This gives us 4 varieties:
- rrr-ccb
- rrb-ccc
- ccc-rrb
- ccb-rrr
If only 1 row or column would intersect with the box, the other rows or columns are anX-Wing pattern.
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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.
When a computer solver tries the Finned Swordfish before the Franken Swordfish, it will find it 3 times, with the base Swordfish in rows 1, 2, 3 respectively, eliminating just a single candidate in box 3 each time. For this reason the Franken Swordfish should be tried before the Finned Swordfish.
Rotate the diagram 90 degrees for a rrrccb pattern.
Same with both rows in 1 band
This pattern, although it has the appearance of a Franken Swordfish, degenerates into a series of locked candidates.
Before being recognized as a Franken Swordfish, this pattern will be processed in 3 easy steps:
- Locked Candidates (labeled a) in the intersection of box 9 and column 9. This eliminates the candidates in the intersection of boxes 3 and 6 with column 9.
- Locked Candidates in the intersection of box 5 and column 5. This eliminates the candidates in the intersection of box 5 with columns 4 and 6.
- Locked Candidates in the intersection of box 4 and row 4. This eliminates the candidates in the intersection of box 4 with rows 5 + 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 rrbccc pattern.
Same with both columns in 1 band
This pattern, although it has the appearance of a Franken Swordfish, degenerates into a series of locked candidates.
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 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 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 examples above are the maximum patterns for the Franken Swordfish. They contain 12 cells, and as such will not be spotted a lot in the wild.
Logical analysis of the minimum pattern shows that 4 of the candidates in the defining box are redundant. Reduced patterns occur when 1, 2, 3 or 4 of these redundant cells are removed. There must be at least 1 candidate in each of the intersections between the defining rows or columns and the box in the pattern.
Further reduction is possible by removing one of the pattern candidates in the rows or columns which run through the box which belongs to the pattern. The candidates cannot both be removed from the same row or column. Like a regular Swordfish each of the defining constaints must have 2 candidates.
Below are some effects for reduced patterns.
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.
Franken Swordfish with a Fake Fin
It is also possible to have a 9 cell pattern which is both a Franken Swordfish and a Finned Swordfish.
In this case the finned swordfish pattern does not have any effect on eliminations, because the fin is not real. The fin is a regular part of the Franken Swordfish pattern, not an addition.
Finned Franken Swordfish
Here is example of a genuine Finned Franken Swordfish. The fin here does not occur in the defining box 3.
The fin in this example occurs in box 5 (marked f) and the only cell eliminations for this pattern are also in box 5.
See Also
