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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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 Posted: Wed Dec 09, 2009 4:49 pm Post subject: Stuck on a Menneske |
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This is #4696888, SH (31). After three Hidden URs, an ER and Finned X-Wing I came to a halt.
| Code: |
+----------------+--------------+------------+
| 27 3 1 | 5 27 8 | 9 4 6 |
| 2589 459 45 | 29 6 3 | 1 7 58 |
| 578 5679 67 | 1 479 47 | 2 58 3 |
+----------------+--------------+------------+
| 3 56 2567 | 4 8 1 | 57 25 9 |
| 1 8 9 | 27 257 257 | 6 3 4 |
| 4 57 27 | 6 3 9 | 578 258 1 |
+----------------+--------------+------------+
| 6 1 3 | 28 245 245 | 458 9 7 |
| 59 2 457 | 789 1 457 | 3 6 58 |
| 579 4579 8 | 3 4579 6 | 45 1 2 |
+----------------+--------------+------------+
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Play this puzzle online at the Daily Sudoku site |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Wed Dec 09, 2009 6:07 pm Post subject: |
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Here is a long chain solution:
(7=2)r1c1-(2)r1c5=(2-9)r2c4=(9-8)r8c4=(8-5)r8c9=(5)r2c9-(5=4)r2c3-(4)r8c3=(4)r8c6 -(4=7)r3c6 => r1c5,r3c123<>7 |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Dec 09, 2009 10:06 pm Post subject: |
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| Thanks. Is that an XY-Chain or other type of chain? |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Wed Dec 09, 2009 10:51 pm Post subject: |
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| An xy-chain has only cells with 2 values. This chain is called an AIC (some of the cells have more than two. I think it stands for "Alternate Inference Chain". I find them by locating two pinchers where where one end or the other will be true by connecting with a chain. Candidates of the same value that see both can be eliminated. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Dec 09, 2009 11:00 pm Post subject: |
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| Marty R. wrote: | | Is that an XY-Chain or other type of chain? |
| Code: | (SI-based) XY-Chains have Eureka notation:
(a=b)cell_1 - (b=c)cell_2 - ... - (n=a)cell_m => list_of_cells <> a
(WI-based) XY-Chains have Eureka notation:
(a)list_of_cells - (a=b)cell_1 - (b=c)cell_2 - ... - (n=a)cell_m - (a)list_of_cells
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Wed Dec 09, 2009 11:12 pm Post subject: |
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Its the same idea with pincers at r1c1 and r3c6 but some steps involve cells which are not bivalue namely r7c346. It doesn't matter though because when landing on a multivalue cell eg going from r2c4 (If not 9 then r8c4 must be 9 and it can't be 8 and if it is not 8 then r8c9 is 8 etc)
(2-9)r2c4=(9-8)r8c4=(8-5)r8c9
the effect is the same - all decisions are binary just like an xy chain.
An xy chain is really just another AIC |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Dec 09, 2009 11:43 pm Post subject: |
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There is another chain present that I find interesting. It's a single-digit chain until it ends like an M-Wing.
| Code: | (4)r2c2 = r2c3 - r8c3 = r8c6 - r3c6 = (4-9)r3c5 = (9)r2c4 => r2c2<>9
+---------------------------------------------------------------+
| 27 3 1 | 5 27 8 | 9 4 6 |
| 2589 a45-9 b45 | g29 6 3 | 1 7 58 |
| 578 5679 67 | 1 f479 e47 | 2 58 3 |
|---------------------+--------------------+--------------------|
| 3 56 2567 | 4 8 1 | 57 25 9 |
| 1 8 9 | 27 257 257 | 6 3 4 |
| 4 57 27 | 6 3 9 | 578 258 1 |
|---------------------+--------------------+--------------------|
| 6 1 3 | 28 245 245 | 458 9 7 |
| 59 2 c457 | 789 1 d457 | 3 6 58 |
| 579 4579 8 | 3 4579 6 | 45 1 2 |
+---------------------------------------------------------------+
# 61 eliminations remain
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