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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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 Posted: Sun Sep 16, 2007 2:01 am Post subject: |
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| Tracy wrote: | | Are you saying that in all cases the end cells of an XY-wing are conjugate pairs? |
My bad!! 
The <2>s on the end of an XY Wing have a "strong inferential" link (at least one is true). So, the coloring logic IS the same as discussed elsewhere for the W-Wing.
So, I was, in part, lucky. But not entirely... there is still a sort of "wrap" in this case. Let me revise my grid:
| Code: | *--------------------------------------------------*
| 2R3 -26 8 | 4 236 5 | 1 9 7 |
| 257 67 9 | 1 26 8 | 2r5 4 3 |
| 1 4 35 | 27 237 9 | 6 2g5 8 |
|----------------+----------------+----------------|
|-2r5 1 7 | 9 8 4 | 2g5 3 6 |
| 9 2g5 6 | 3 1 7 | 8 2r5 4 |
| 8 3 4 | 6 5 2 | 7 1 9 |
|----------------+----------------+----------------|
| 37 79 2 | 5 49 6 | 34 8 1 |
| 6 59 35 | 8 49 1 | 34 7 2 |
| 4 8 1 | 27 27 3 | 9 6 5 |
*--------------------------------------------------* |
I have used "R" and "g" for the strong inferential link of the XY Wing. Eliminations occur between "R" and "g". (Because there is no R-G color chain in this case, we don't have to worry about the fact that "G" and "r" do not produce eliminations.)
The R-g pair in R1C1 and R5C2 causes two eliminations, R1C2 and R4C1, as shown. However, the <2> in R4C1 is colored "r", so all "r" <2>s are eliminated as the chain collapses. It is still a sort of color "wrap." It's just that one can't say that "R" <2>s are eliminated as well ... as I mistakenly did earlier.
I hasten to add that it's not necessary to consider this as some new sort of "wrap" technique. The color chain will collapse naturally if such an elimination occurs. |
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