... by: Banjo
In your example of Finned Exwings, why is it that neither row D or H complete the Exwing with row B, instead of relying upon row F? In fact, the combination of rows B, D, and H would seem to give a 2 x 3 situation would seem cannot exist.
... by: sean t
In the example, the 7 in J7 and J8 cannot be eliminated because it is possible that G6 contains a 7. If that's the case, then C9 does as well, but none of G7, G8, G9 or H9 do. That leaves only J7 and J8 as candidates for the 7 in box 9. Therefore, the 7 in J7 and J8 cannot be eliminated.
In general, for a finned x-wing, only those cells that can see all the fin cells AND are cells that would be eligible for elimination if it were just a regular x-wing can be eliminated. In this example, without the fin cells present, J7 and J8 would not be eligible for elimination via the regular x-wing.
... by: Anton Delprado
I agree with Roland that Finned X-Wings are just a specific form of Grouped X-Cycles. Also they are underneath Grouped X-Cycles in the solver. So why does the solver find them at all? Shouldn't it find them as Grouped X-Cycles first? or does the solver deliberately avoid classing them as Grouped X-Cycles?
Andrew Stuart writes:
There are no restrictions on Grouped X-Cycles or any other strategy, especially in terms of 'letting through' to any other strategy. However, what I am searching for may be limited to how I search and the generalization I've made. I'll look again at the correspondance to X-Cycles and see if there is something the solver is missing.
... by: David
In the "real example" given following the Finned X-Wing explanation, the rule that is stated is: "If you can form an X-Wing by ignoring the fin cells, then you can keep your elimination of any cell that shares the same unit as all the cells in the fin." Why, then is only the red-circled 7 eliminated as sharing the same unit, but not the 7s at cells J7 and J8, which appear also to share the same unit (i.e. the box being the unit in which the two yelleo fin cells are located). I thought I understood the fin strategy, but if the 7s at J7 and J8 cannot be eliminated, the theory is completely lost on me! Someone please explain why only the red-circled 7 is elinated but not that other two at J7 and J8. Thx.
... by: SueinOz
I think in this example that the fin is green not yellow, and also the E5/F6 reference at the end should be E6/F6.
This site is so amazing! I'm learning so much. A few typos should be expected when your mind is full of all these incredible strategies. My head hurts just reading them!
Andrew Stuart writes:
Typos fixed - many thanks for spotting them and letting me know :)
... by: John Wilcox
Above, under Sashimi Finned X-Wings, 5th paragraph, 2nd line, I think the reference to E5/F6 should be E6/F6. Same correction at the very end of the sentence.
... by: suneet
Despite removing tick mark solver does use this strategy. which normally it should not use in that case. I request you to remove this anomaly
thanks, love your site
... by: Roland Zito-Wolf
It's worth mentioning that the finned x-wings can be explained as grouped x-cycles of the rule-3 nice loop variety, the kind with 2 weak links in a row.
For example 1, we have C6=C9-H9-[G7,G8,G9]=G6-C6, allowing 7 at H9 to be removed. This clarifies why the 7 at H9 can be removed but not the ones at J7 and J8: only H9 has a link to C9.
The sashimi variation works because it uses exactly the same kind of grouped x-cycle: H9=H6-E4-[D4,D5]=D9-H9 and likewise for F5.
That raises the question of whether the Swordfish and Jellyfish can be related to more general strategies as well...
love your site!