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Captain Pete
Joined: 09 Jun 2007
Posts: 55
Location: Oley, PA
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 Posted: Sun Dec 16, 2007 6:29 pm Post subject: Menneske Super Hard - Help please |
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Where do I go from here?
| Code: |
+---------------+-----------------+------------+
| 3789 139 2 | 149 14 346 | 5 489 367 |
| 3579 6 4 | 59 8 35 | 2 1 37 |
| 3589 1359 39 | 7 1245 23456 | 89 489 36 |
+---------------+-----------------+------------+
| 1 7 69 | 2 459 45 | 46 3 8 |
| 4 8 5 | 3 6 7 | 19 2 19 |
| 2 39 369 | 8 49 1 | 46 7 5 |
+---------------+-----------------+------------+
| 356 235 7 | 1456 1245 9 | 18 58 124 |
| 59 4 8 | 15 3 25 | 7 6 129 |
| 569 259 1 | 456 7 8 | 3 59 249 |
+---------------+-----------------+------------+
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Play this puzzle online at the Daily Sudoku site |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Dec 16, 2007 7:24 pm Post subject: |
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There are two Type 6 UR's on <36> and <37> in B123. You can take out <3> in R1C1 and R1C6.
Not much help, I'm afraid.
Keith |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sun Dec 16, 2007 9:33 pm Post subject: |
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| Code: | *--------------------------------------------------------------------*
| 3789 139 2 | 149 14 346 | 5 489 367 |
| 3579 6 4 | 59 8 35 | 2 1 37 |
| 3589 1359 39 | 7 1245 23456 | 89 489 36 |
|----------------------+----------------------+----------------------|
| 1 7 #69 | 2 #459 45 |#46 3 8 |
| 4 8 5 | 3 6 7 | 19 2 19 |
| 2 39 #369 | 8 #49 1 |#46 7 5 |
|----------------------+----------------------+----------------------|
| 356 235 7 | 1456 1245 9 | 18 58 124 |
| 59 4 8 | 15 3 25 | 7 6 129 |
| 569 259 1 | 456 7 8 | 3 59 249 |
*--------------------------------------------------------------------*
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There is also a deadly pattern 69/49/46 in the marked cells, saying that one of r6c3=3 and r4c5=5 must be true. Both imply r4c5<>4 (r6c3=3 => r6c2=9 => r6c5=4) and r6c3<>9 (r4c5=5 => r6c5=9), but its not a great help either. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sun Dec 16, 2007 9:52 pm Post subject: |
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There is an xy-chain
'35'(26)='54'(46)='46'(47)='69'(43)='93'(33)
that takes out 3 in r2c1 r3c6.
| Code: |
+--------------------------+--------------------------+--------------------------+
| 3789 139 2 | 149 14 346 | 5 489 367 |
| 579 6 4 | 59 8 35 | 2 1 37 |
| 3589 1359 39 | 7 1245 2456 | 89 489 36 |
+--------------------------+--------------------------+--------------------------+
| 1 7 69 | 2 459 45 | 46 3 8 |
| 4 8 5 | 3 6 7 | 19 2 19 |
| 2 39 369 | 8 49 1 | 46 7 5 |
+--------------------------+--------------------------+--------------------------+
| 356 235 7 | 1456 1245 9 | 18 58 124 |
| 59 4 8 | 15 3 25 | 7 6 129 |
| 569 259 1 | 456 7 8 | 3 59 249 |
+--------------------------+--------------------------+--------------------------+
|
After that, with Keith's hint (remove 3 from r1c1 and r1c6) the puzzle is solved
edit: hm. guess it is better to use Keith's hint BEFORE using the xy chain, otherwise the "36" DP is gone ...
Looks like I've finally encountered that dreaded situation where a solving step actually makes the puzzle more difficult. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Dec 16, 2007 10:38 pm Post subject: |
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| nataraj wrote: | | Looks like I've finally encountered that dreaded situation where a solving step actually makes the puzzle more difficult. |
I think this is fairly common, especially where uniqueness techniques are involved.
Take a look at my second post in this thread:
http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2212
If you do the extended XY-wing first, the UR is destroyed and, yes, (I think) the puzzle is harder.
When I first discovered the UR plus strong links pattern, Mike Barker ran tests that showed different success rates in solving very difficult puzzles, depending on the order in which techniques are applied.
Best wishes,
Keith |
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Captain Pete
Joined: 09 Jun 2007
Posts: 55
Location: Oley, PA
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| Posted: Mon Dec 17, 2007 12:07 am Post subject: |
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| Thanks Keith. I thought my understanding of UR was complete at Type 4. I see that isn't so. I've gone back in the forum to read about Type 6 UR, and I get the idea, but can't see the candidates in this puzzle. Can you shed a little more light on the Type 6 UR in B123? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Dec 17, 2007 1:04 am Post subject: |
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In your grid:
R13C69 is a UR on <36> and an X-wing on <6>.
R1C6 cannot be <3>, for it would force <6> on the adjacent corners, and <3> in the opposite corner. A deadly (non-unique) solution.
R12C19 is a UR on <37> and an X-wing on <7>. R1C1 cannot be <3>, etc.
Keith |
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Captain Pete
Joined: 09 Jun 2007
Posts: 55
Location: Oley, PA
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| Posted: Mon Dec 17, 2007 2:43 am Post subject: |
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Keith, In researching Type 6 UR, this is the old forum posting that I used:
"When a rectangle can be found in a single floor or tower, with candidates a and b as the only possibilities in 2 of its corners, and candidates a and b are also present in the other 2 corners along with extra candidates, and the candidates for digit a form an X-Wing pattern, then candidate a can be removed from the 2 corners with extra candidates.
Is that what we have in this puzzle? |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Dec 17, 2007 3:25 am Post subject: |
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Pete,
The old forum posting apparently only describes one of the two possibilities in Type 6 (the coincident X-Wing). Here is a diagram of the two possibilities:
| Code: | "a" forms an X-Wing:
_______________________________
ab abx a bx
becomes
aby ab by a
_______________________________
abz abx az abx
becomes
aby ab aby ab |
It is the second situation that applies in both cases of the puzzle above. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Mon Dec 17, 2007 9:17 am Post subject: |
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| nataraj wrote: | | Looks like I've finally encountered that dreaded situation where a solving step actually makes the puzzle more difficult. |
Of course you can make the UR elimination after the xy-chain also, because a 3 in r1c1 or r1c6 still leads to a deadly pattern
| Code: | 3 . . | . . . | . . 7 | . . 3 | . . 6
7 . . | . . . | . . 3 or | . . . | . . .
. . . | . . . | . . . | . . 6 | . . 3
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This is always deadly for a rectangle in 2 boxes, if none of the 4 numbers is a given.
But normally we dont look for that. |
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