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keith
Joined: 19 Sep 2005 Posts: 3355 Location: near Detroit, Michigan, USA
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Posted: Sun Nov 30, 2008 3:19 am Post subject: Another not difficult (? ) Menneske |
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This one is rated Very Hard (0). After an XYZ-wing, I am at a loss. Still working on it.
Code: | Puzzle: M543856vh
+-------+-------+-------+
| . . 6 | . . . | 2 . . |
| . 3 . | . 4 . | . 9 . |
| 2 8 . | . 7 . | . 3 1 |
+-------+-------+-------+
| . . . | . 2 4 | . . . |
| . 2 4 | 9 . 5 | 6 1 . |
| . . . | 6 1 . | . . . |
+-------+-------+-------+
| 1 9 . | . 6 . | . 4 5 |
| . 7 . | . 8 . | . 6 . |
| . . 2 | . . . | 1 . . |
+-------+-------+-------+ |
Keith |
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keith
Joined: 19 Sep 2005 Posts: 3355 Location: near Detroit, Michigan, USA
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Posted: Sun Nov 30, 2008 3:33 am Post subject: |
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After basics and the XYZ-wing:
Code: | +-------------------+-------------------+-------------------+
| 457 14 6 | 138 9 138 | 2 578 78 |
| 57 3 157 | 128 4 128 | 578 9 6 |
| 2 8 9 | 5 7 6 | 4 3 1 |
+-------------------+-------------------+-------------------+
| 36789 16 137 | 78 2 4 | 35789 578 39 |
| 78 2 4 | 9 3 5 | 6 1 78 |
| 3789 5 378 | 6 1 78 | 3789 2 4 |
+-------------------+-------------------+-------------------+
| 1 9 38 | 237 6 237 | 78 4 5 |
| 345 7 35 | 134 8 139 | 39 6 2 |
| 3468 46 2 | 347 5 379 | 1 78 39 |
+-------------------+-------------------+-------------------+ |
Quote: | Aha! A W-wing <78> taking out <7> in R6C7 R7C6. |
Still working ...
Keith |
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keith
Joined: 19 Sep 2005 Posts: 3355 Location: near Detroit, Michigan, USA
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Posted: Sun Nov 30, 2008 3:42 am Post subject: |
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...
Quote: | A W-wing <78> taking out <8> in R4C8.
A W-wing <57> that takes out <7> in R4C1.
A W-wing <57> that (with coloring) takes out <5> in R2C3.
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... working ... |
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storm_norm
Joined: 18 Oct 2007 Posts: 1741
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Posted: Sun Nov 30, 2008 9:46 am Post subject: |
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keith if you aren't done then close your eyes.
Code: | .---------------------.---------------------.---------------------.
|*457 14 6 | 138 9 138 | 2 578 78 |
|*57 3 #157 | 128 4 128 |5-78 9 6 |
| 2 8 9 | 5 7 6 | 4 3 1 |
:---------------------+---------------------+---------------------:
| 36789 16 1378 | 78 2 4 | 35789 578 39 |
|#78 2 4 | 9 3 5 | 6 1 78 |
| 3789 5 378 | 6 1 78 | 3789 2 4 |
:---------------------+---------------------+---------------------:
| 1 9 38 | 237 6 237 |#78 4 5 |
| 345 7 35 | 134 8 139 | 39 6 2 |
|#3468 46 2 | 347 5 379 | 1 #78 39 |
'---------------------'---------------------'---------------------' |
1.extended w-wing (7)r2c3 = (7)r12c1 - (7=8)r5c1 - (8)r9c1 = (8)r9c8 - (8=7)r7c7; r2c7 <> 7
2. (8=5)r2c7 - (5=7)r2c1 - (7)r5c1 = (7)r5c9 - (7=8)r1c9; r1c8 <> 8
the same cells form a xy-chain
3. xy-wing {5,7,8}...(7=8)r7c7 - (8=5)r2c7 - (5=7)r1c8; r9c8 <> 7
gets it to here
Code: | .---------------------.---------------------.---------------------.
| 45 14 6 | 138 9 138 | 2 #57 78 |
|#57 3 1-57 | 128 4 128 |#58 9 6 |
| 2 8 9 | 5 7 6 | 4 3 1 |
:---------------------+---------------------+---------------------:
|36-789 16 137 | 78 2 4 | 3589 #57 39 |
|#78 2 4 | 9 3 5 | 6 1 #78 |
|3-789 5 37 | 6 1 78 | 389 2 4 |
:---------------------+---------------------+---------------------:
| 1 9 8 | 23 6 23 | 7 4 5 |
| 345 7 35 | 14 8 19 | 39 6 2 |
| 346 46 2 | 47 5 79 | 1 8 39 |
'---------------------'---------------------'---------------------' |
extended w-wing loop since the ends end in the same row.
4. (5)r2c7 = (5)r1c8 - (5=7)r4c8 - (7)r5c9 = (7)r5c1 - (7=5)r2c1; r2c3 <> 5 and r46c1 <> 7
then
Code: | .------------------.------------------.------------------.
| 45 14 6 | 138 9 138 | 2 57 78 |
| 57 3 17 | 128 4 128 | 58 9 6 |
| 2 8 9 | 5 7 6 | 4 3 1 |
:------------------+------------------+------------------:
| 689 16 #137 | 78 2 4 | 3589 57 #39 |
| 78 2 4 | 9 3 5 | 6 1 78 |
| 89 5 #37 | 6 1 #78 | 389 2 4 |
:------------------+------------------+------------------:
| 1 9 8 | 23 6 23 | 7 4 5 |
| 34 7 5 | 14 8 1-9 |#39 6 2 |
| 346 46 2 | 47 5 #79 | 1 8 #39 |
'------------------'------------------'------------------' |
5. (9=3)r8c7 - (3)r9c9 = (3)r4c9 - (3)r4c3 = (3-7)r6c3 = (7)r6c6 - (7=9)r9c6; r8c6 <> 9
this basically follows the useless m-wing on {3,9} around, but doesn't jump back to 9. instead follows 3 to 7 |
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daj95376
Joined: 23 Aug 2008 Posts: 3854
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Posted: Sun Nov 30, 2008 6:34 pm Post subject: |
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Nothing brilliant or even interesting.
Code: | XYZ-Wing, Skyscraper, short chain, long XY-Chain, short XY-Chain.
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It sure would be nice to see a solution from the puzzle source. There appears to be plenty of potential for a UR or DP. Unfortunately, too much potential for me. |
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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA
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Posted: Tue Dec 02, 2008 12:47 am Post subject: |
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daj95376 wrote: | There appears to be plenty of potential for a UR or DP. |
You picqued my interest. After basics without the XYZ Wing:
Code: | +--------------------+-----------------+----------------+
| 457 14 6 | 138 9 138 | 2 578 78 |
| 57 3 $157 | 1[28] 4 1[28] | 578 9 6 |
| 2 8 9 | 5 7 6 | 4 3 1 |
+--------------------+-----------------+----------------+
| 36789 16 13[78] |[78] 2 4 | 35789 578 39 |
| 78 2 4 | 9 3 5 | 6 1 78 |
| 3789 5 3[78] | 6 1 [78] | 3789 2 4 |
+--------------------+-----------------+----------------+
| 1 9 $38 | 3[27] 6 3[27] | 78 4 5 |
| 345 7 35 | 134 8 139 | 39 6 2 |
| 3468 46 2 | 347 5 379 | 1 78 39 |
+--------------------+-----------------+----------------+ |
There is an 8-cell DP as marked. The <1> and <3> in the cells marked $ are weakly linked as a result since if they are both true, the DP results. (One might note that the potential 78 NP in r46c3 is invalid due to r5c1 so why not just use that? To do so, I would have to group the <3>s in r78c3, which isn't as useful.) This can be denoted as: DP[(1)r2c3-(3)r7c3]. A simple bit of Medusa multi-coloring using this weak link bridge reveals:
(8-6)r9c1=(6)r9c2 - (6=1)r4c2 - (1)r4c3=DP[(1)r2c3 - (3)r7c3]=(8)r7c3 - (8)r9c1; r9c1<>8
Most often it is an induced strong inference that is exploited in a DP. But this shows that the weak inference created between exterior candidates that force the DP can also be useful.
The grid becomes:
Code: | +----------------+-------------+--------------+
| 45 14 6 | 138 9 138 | 2 57 78 |
| 57 3 157 | 128 4 128 | 58 9 6 |
| 2 8 9 | 5 7 6 | 4 3 1 |
+----------------+-------------+--------------+
| 36789 16 137 | 78 2 4 | 3589 57 39 |
| 78 2 4 | 9 3 5 | 6 1 78 |
| 3789 5 37 | 6 1 78 | 389 2 4 |
+----------------+-------------+--------------+
| 1 9 8 | 23 6 23 | 7 4 5 |
| 345 7 35 | 14 8 19 | 39 6 2 |
| 346 46 2 | 47 5 79 | 1 8 39 |
+----------------+-------------+--------------+ |
At this point, those two 57 W-Wings with transport can be applied. They can also be viewed as a Remote Naked Pair with transport, since a "double W-Wing" is a RNP. Alternately, the same eliminations occur via a continuous AIC loop:
(7)r2c1=(7-1)r2c3=(1-4)r1c2=(4-5)r1c1=(5-7)r1c8=(7)r4c8 - (7)r5c9=(7)r5c1 - (7)r2c1:Loop; r46c1<>7, r2c3<>5
This gets us here where we can use a UR:
Code: | +---------------+-------------+----------------+
| 45 14 6 | 138 9 138 | 2 57 78 |
| 57 3 17 | 128 4 128 | 58 9 6 |
| 2 8 9 | 5 7 6 | 4 3 1 |
+---------------+-------------+----------------+
| 6[89] 16 137 |$78 2 4 | 35[89] 57 $39 |
| 78 2 4 | 9 3 5 | 6 1 78 |
| [89] 5 37 | 6 1 78 | 3[89] 2 4 |
+---------------+-------------+----------------+
| 1 9 8 | 23 6 23 | 7 4 5 |
| 34 7 5 | 14 8 19 | 39 6 2 |
| 346 46 2 | 47 5 79 | 1 8 39 |
+---------------+-------------+----------------+ |
In this case, we use an "almost Type 4" 89UR. If r4c9 is <3> the resulting Type 4 UR requires r4c4=8. If r4c9 is not <3>, then:
r9c9=3 => r9c12=46 => r9c4=7 => r4c4=8.
Thus, r4c4=8. |
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keith
Joined: 19 Sep 2005 Posts: 3355 Location: near Detroit, Michigan, USA
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Posted: Tue Dec 02, 2008 1:09 am Post subject: |
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Thank you, all!
I think I got more than I thought I was signing up for!
Keith |
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