000000300040030068000205090000008027080060030120700000050804000960020050002000000
or
Code: Select all
. . .|. . .|3 . .
. 4 .|. 3 .|. 6 8
. . .|2 . 5|. 9 .
-----+-----+-----
. . .|. . 8|. 2 7
. 8 .|. 6 .|. 3 .
1 2 .|7 . .|. . .
-----+-----+-----
. 5 .|8 . 4|. . .
9 6 .|. 2 .|. 5 .
. . 2|. . .|. . .
Code: Select all
·-------------·-------------·-------------·
| 7 *7 7 | · *7 7 | · 7 · |
| *7 · *7 | · · *7 | · · · |
| 7 *7 7 | · *7 · | #7 · · |
·-------------+-------------+-------------·
| · · · | · · · | · · 7 |
| 7 · 7 | · · · | · · · |
| · · · | 7 · · | · · · |
·-------------+-------------+-------------·
| 7 · 7 | · · · | · 7 · |
| · · · | · · 7 | 7 · · |
| · *7 · | · *7 7 | 7 7 · |
·-------------·-------------·-------------·
- (7): r2c13 = r2c6 - r13c5 = r9c5 - r9c2 = r13c2 - r2c13
A previous thread (here) which I introduced some time ago discussed general fish patterns. To recap: For a general fish of size N for some particular digit X, we look for some set of N houses, called the "base set," such that each digit X candidate in the base set is "covered by" (i.e., lies within the union of) some other set of N houses, called the "cover set". If such sets can be identified, then each digit X candidate in the cover set, but not the base set, can be eliminated. (In some cases we can say a bit more, as discussed in the referenced thread, but this will suffice for the present discussion.)
A conclusion of the referenced thread was that for any single-digit AIC loop, there naturally corresponds a fish pattern. If the loop has 2*N nodes, the fish will be of size N. The base set will be those N houses in which the links of strong inference occur, and the cover set will be those N houses in which the links of weak inference occur. The AIC loop conclusion, that the (initially identified) links of weak inference are links of strong inference as well, translates directly into the general fish conclusion, that candidates in the cover set but not the base set can be eliminated.
I find it much easier to see single digit AIC loops than general fish patterns. In this case, though, it was well worth the effort to consider the above loop in its equivalent fish formulation, because it's then fairly easy to see how to augment the associated base and cover sets to produce a fish one size larger.
Diagram and AIC loop repeated for convenience:
Code: Select all
·-------------·-------------·-------------·
| 7 *7 7 | · *7 7 | · 7 · |
| *7 · *7 | · · *7 | · · · |
| 7 *7 7 | · *7 · | #7 · · |
·-------------+-------------+-------------·
| · · · | · · · | · · 7 |
| 7 · 7 | · · · | · · · |
| · · · | 7 · · | · · · |
·-------------+-------------+-------------·
| 7 · 7 | · · · | · 7 · |
| · · · | · · 7 | 7 · · |
| · *7 · | · *7 7 | 7 7 · |
·-------------·-------------·-------------·
- (7): r2c13 = r2c6 - r13c5 = r9c5 - r9c2 = r13c2 - r2c13
- Base set: row 2, column 2, column 5 (all candidates marked with "*" in the diagram)
Cover set: box 1, box 2, row 9 (all candidates marked with "*" lie in these houses)
- Base set: row 2, row 3, column 2, column 5
Cover set: boxes 1, 2, and 3; and row 9
(Observant readers may have noticed that the originally claimed eliminations of (7)r3c13 from the smaller fish do not directly follow from the larger fish, since those cells become part of the larger fish's base set. However, the larger fish produces a hidden single in box 3, at r3c7, and this of course eliminates (7)r3c13, among others.)