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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Thu Feb 14, 2008 3:17 pm Post subject: No insects, too |
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I have a theory that any BUG+1 will easily fall to Medusa coloring. (I did this one without Medusa.)
| Code: | Puzzle: M4144279sh(11)
+-------+-------+-------+
| . 3 5 | . . . | . . . |
| . 4 . | . 1 . | 3 9 . |
| 8 . . | . 9 3 | 6 7 . |
+-------+-------+-------+
| . . 8 | 6 . . | . . . |
| . 6 7 | . . . | 8 2 . |
| . . . | . . 7 | 1 . . |
+-------+-------+-------+
| . 7 2 | 3 5 . | . . 8 |
| . 8 9 | . 6 . | . 5 . |
| . . . | . . . | 4 6 . |
+-------+-------+-------+ |
Keith |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Thu Feb 14, 2008 4:32 pm Post subject: |
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| IMHO any BUG+1 can be solved with an xy-chain(at least the one's I've encountered so far), ignoring the BUG+1, there is a 6-cell xy-chain with pincer ends at R9C6 and R6C5, eliminating <8> in R9C5 |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Feb 14, 2008 4:56 pm Post subject: |
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Here is the situation we are discussing:
| Code: | +-------------+-------------+-------------+
| 9 3 5 | 47 47 6 | 2 8 1 |
| 7 4 6 | 28 1 28 | 3 9 5 |
| 8 2 1 | 5 9 3 | 6 7 4 |
+-------------+-------------+-------------+
| 23 19 8 | 6 23 19 | 5 4 7 |
| 13 6 7 | 14 34 5 | 8 2 9 |
| 25 59 4 | 89 28 7 | 1 3 6 |
+-------------+-------------+-------------+
| 6 7 2 | 3 5 4 | 9 1 8 |
| 4 8 9 | 12 6 12 | 7 5 3 |
| 15 15 3 | 789 78 89 | 4 6 2 |
+-------------+-------------+-------------+
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| Johan wrote: | | IMHO any BUG+1 can be solved with an xy-chain(at least the one's I've encountered so far) |
I am sure you are correct. There are probably many XY chains.
(I checked this with Sudoku Susser. It finds a chain to make an elimination in any cell in the situation given above.)
| Johan wrote: | | ... ignoring the BUG+1, there is a 6-cell xy-chain with pincer ends at R9C6 and R6C5, eliminating <8> in R9C5 |
I found the same pincers and elimination with a 4-cell M-wing.
Keith |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Thu Feb 14, 2008 6:15 pm Post subject: |
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| Quote: | I found the same pincers and elimination with a 4-cell M-wing.
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Keith,
I think this M-wing on the <89> pairs also eliminates <8> in R2C4(connected by the strong link on <9> in R9C4, extended with the strong link on <8> in C6 to R2C6, so it may be a double M-wing(can be extended in Row and in Column)? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Feb 14, 2008 6:44 pm Post subject: |
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| Johan wrote: |
Keith,
I think this M-wing on the <89> pairs also eliminates <8> in R2C4 |
Correct! Nice catch!
I think of a basic M-wing as identifying the pair connected by strong links (3 cells) plus a strong link on the other candidate at either end (4 cells).
Here you have a 5-cell chain starting in R2C6 and ending in R6C5:
| Code: |
28=89=789=89=28
@ # @ #
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Any cell that sees both @ cells or both # cells cannot be <8>.
I see this as two overlapping M-wings, because the eliminations are independent. Also, the fact that both ends of the above chain are <28> also has nothing to do with the logic.
Best wishes,
Keith |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Feb 14, 2008 10:12 pm Post subject: |
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| And a reminder... an M-Wing is just a simple case of Medusa. So, we come full circle. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Feb 14, 2008 11:05 pm Post subject: |
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| Asellus wrote: | | And a reminder... an M-Wing is just a simple case of Medusa. So, we come full circle. |
Asellus,
Yes. After I posted my message about not using Medusa, I realized that there was a logical contradiction in that I used an M-wing, which is the simplest chain that Medusa will find (another postulate by Keith).
But, I stand my ground. Compared to other wings (XY, XYZ, W), an M-wing is as easy to describe, and as easy to find. Medusa coloring, on the other hand, is easy to describe and understand, but complex to do.
I made my comment because, if you want to learn Medusa coloring, I think you should practice on BUG+1 patterns. Basic Medusa is guaranteed to work (the first postulate by Keith, see message 1 above).
Keith |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Fri Feb 15, 2008 3:58 am Post subject: |
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| Quote: | Yes. After I posted my message about not using Medusa, I realized that there was a logical contradiction in that I used an M-wing, which is the simplest chain that Medusa will find (another postulate by Keith).
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M-wing
(M)edusa - wing
call it a flying medusa because a flying medusa surely eats more than just bugs for lunch.
images not recommended. |
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