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Another good Menneske

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Nov 22, 2008 11:30 pm    Post subject: Another good Menneske Reply with quote
Try this one on:
Code:
Puzzle: M2534023vh
+-------+-------+-------+
| . . . | . 1 . | . . . |
| 6 5 . | . . . | . 3 8 |
| . 4 3 | . 6 . | 1 5 . |
+-------+-------+-------+
| . . . | 5 9 . | . . . |
| 5 . 9 | 1 . 3 | 8 . 2 |
| . . . | . 8 2 | . . . |
+-------+-------+-------+
| . 9 5 | . 3 . | 6 1 . |
| 1 7 . | . . . | . 2 3 |
| . . . | . 7 . | . . . |
+-------+-------+-------+

Go to http://www.menneske.no/sudoku/eng/

and ask for a Super Hard. Often, it returns with a Very Hard. I really enjoy these!

Keith
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Sun Nov 23, 2008 12:56 am    Post subject: Reply with quote
A couple of URs were hard to overlook, then a w-wing made a deletion plus two more deletions by transporting the pincers, and finally an xy-wing finished it off for me.

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sun Nov 23, 2008 1:24 am    Post subject: Reply with quote
One-Stepper wrote:
M-Wing: [r3c6] ... [r7c1] => [r7c6]<>8


Last edited by daj95376 on Sun Nov 23, 2008 5:07 am; edited 3 times in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sun Nov 23, 2008 2:47 am    Post subject: Reply with quote
daj95376 wrote:
One-Stepper wrote:
M-Wing: [r3c6] ... [r7c1] => [r7c6]<>8

Danny,

Help me out here. I either missed something in my basics and/or I don't see the technique you used, at least based on what I think that technique is.

Code:

+------------+-------------+------------+
| 9   8   7  | 3    1 5    | 2   46 46  |
| 6   5   1  | 49   2 49   | 7   3  8   |
| 2   4   3  | 78   6 78   | 1   5  9   |
+------------+-------------+------------+
| 378 123 28 | 5    9 67   | 34  46 146 |
| 5   6   9  | 1    4 3    | 8   7  2   |
| 37  13  4  | 67   8 2    | 35  9  156 |
+------------+-------------+------------+
| 48  9   5  | 2    3 48   | 6   1  7   |
| 1   7   68 | 4689 5 4689 | 49  2  3   |
| 34  23  26 | 469  7 1    | 459 8  45  |
+------------+-------------+------------+

Play this puzzle online at the Daily Sudoku site
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sun Nov 23, 2008 5:28 am    Post subject: Reply with quote
Marty R. wrote:
Help me out here. I either missed something in my basics and/or I don't see the technique you used, at least based on what I think that technique is.

Keith wrote:
Nataraj and / or Asellus pointed out that the chain can be

XY ... (X) ... bXY = aY

where b is anything. The logic is a little different, but the conclusion still is: One, or both, of the pincers is Y.

Code:
      a         b           c         d
 (8=7)r3c6 - (7)r4c6 = (7-8)r4c1 = (8)r8c1  =>  [r8c6]<>8
 +--------------------------------------------------------------+
 |  9     8     7     |  3     1     5     |  2     46    46    |
 |  6     5     1     |  49    2     49    |  7     3     8     |
 |  2     4     3     |  78    6    a78    |  1     5     9     |
 |--------------------+--------------------+--------------------|
 | c378   123   28    |  5     9    b67    |  34    46    146   |
 |  5     6     9     |  1     4     3     |  8     7     2     |
 |  37    13    4     |  67    8     2     |  35    9     156   |
 |--------------------+--------------------+--------------------|
 | d48    9     5     |  2     3     4-8   |  6     1     7     |
 |  1     7     68    |  4689  5     4689  |  49    2     3     |
 |  34    23    26    |  469   7     1     |  459   8     45    |
 +--------------------------------------------------------------+


Last edited by daj95376 on Sun Nov 23, 2008 5:54 am; edited 2 times in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sun Nov 23, 2008 5:43 am    Post subject: Reply with quote
Quote:
Nataraj and / or Asellus pointed out that the chain can be

XY ... (X) ... bXY = aY

where b is anything. The logic is a little different, but the conclusion still is: One, or both, of the pincers is Y.

Yes, thank you, I had read that and forgot it, but it's easy to see when someone else points it out!!

P.S. Consider this fragment:

Code:

+--------------+-------+-------+
| .   .    .   | . . . | . . . |
| .   .    .   | . . . | . . . |
| .   .    .   | . . . | . . . |
+--------------+-------+-------+
| 4   1    7   | . . . | . . . |
| 28  28   3   | . . . | . . . |
| 6   9    5   | . . . | . . . |
+--------------+-------+-------+
| 3   267  126 | . . . | . . . |
| 9   2567 126 | . . . | . . . |
| 258 4    268 | . . . | . . . |
+--------------+-------+-------+

Play this puzzle online at the Daily Sudoku site

The 8s are all strong links. So do I have an M-Wing involving the 28 in r5c1 and the 268 in r9c3, connected by the two strong links on 8? And extending the 2 from r5c1 to r5c2 I can now eliminate the 2s in r78c2?
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sun Nov 23, 2008 6:27 am    Post subject: Reply with quote
Marty R. wrote:
Consider this fragment:

Code:
+--------------+-------+-------+
| .   .    .   | . . . | . . . |
| .   .    .   | . . . | . . . |
| .   .    .   | . . . | . . . |
+--------------+-------+-------+
| 4   1    7   | . . . | . . . |
| 28  28   3   | . . . | . . . |
| 6   9    5   | . . . | . . . |
+--------------+-------+-------+
| 3   267  126 | . . . | . . . |
| 9   2567 126 | . . . | . . . |
| 258 4    268 | . . . | . . . |
+--------------+-------+-------+

The 8s are all strong links. So do I have an M-Wing involving the 28 in r5c1 and the 268 in r9c3, connected by the two strong links on 8? And extending the 2 from r5c1 to r5c2 I can now eliminate the 2s in r78c2?

Okay, here's what I see:

To have a generalized M-Wing from r5c1 through r9c3 using (8), you would need:

Code:
(2=8)r5c1 - (8)r9c1 = (8-2)r9c3 = (2)???

Unfortunately, you lack a (specified) strong link for (2) from cell r9c3.

Last edited by daj95376 on Sun Nov 23, 2008 6:35 am; edited 2 times in total
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sun Nov 23, 2008 6:29 am    Post subject: Reply with quote
Quote:
the chain can be

XY ... (X) ... bXY = aY

I missed that in this puzzle (and, no doubt, many others)! Embarassed Embarassed
Keith
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Sun Nov 23, 2008 6:46 am    Post subject: Reply with quote
Quote:
Nataraj and / or Asellus pointed out that the chain can be

XY ... (X) ... bXY = aY

where b is anything. The logic is a little different, but the conclusion still is: One, or both, of the pincers is Y.


I actually think this is a little confusing because the pincer y is not on the end.

should look like this:

YX = bX = bXY = bY; and b can be any number of candidates.

now you can see the Y's are true on either end.

in Marty's chain, one link from the beginning of the M-wing would mean that the 2 in r5c2 is "false"

Y - (Y=X) - X = (X-bY) or

(2)r5c2 - (2=8)r5c1 - (8)r9c1 = (8-2)r9c3 = ???

this proves that either the Y at the beginning is false or the Y (or any other candidates in that cell) at the end is false. which does not qualify as a pincer.
and the 2 at the end is not strongly linked to any 2's in that box.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Sun Nov 23, 2008 7:05 am    Post subject: Reply with quote
danny,
what about this one?

(2)r78c2 = (2)r5c2 - (2=8)r5c1 - (8)r9c1 = (8)r9c3; r9c3 <> 2
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
PostPosted: Sun Nov 23, 2008 8:43 am    Post subject: Reply with quote
Marty R. wrote:
So do I have an M-Wing involving the 28 in r5c1 and the 268 in r9c3, connected by the two strong links on 8?

Dannny said it already: no, you don't (and he gave the reason, as well: no strong link on "2")

For (generalized) m-wings we're not looking for two strong links in the same candidate, but:
________________________________
Nataraj's gm-wing recipe:


· two strong links (in different candidates a,b), sharing one common cell
· a bi-value cell with those same candidates {a,b}, which sees either free end of the strong links.
________________________________

Danny's one-step winner had it all (I'm taking it directly from his post):

two strong links in 7 and 8, connected in r4c1 (cell c):
(7)r4c6=r4c1 (b=c)
(8)r4c1=r8c1 (c=d)
and a bi-value {7,8} (cell a), which sees a free end (cell b)

poor unfortunate 8 in r8c6: it sees both the bi-value (cell a) and the other free end (cell d) and gets eliminated.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sun Nov 23, 2008 5:15 pm    Post subject: Reply with quote
OK, thanks for saving me from myself and the many puzzles which would have resulted in contradictions.

By the way, I might be the only one here who doesn't understand notation, even something as simple-looking as:

XY ... (X) ... bXY = aY Embarassed Embarassed
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
PostPosted: Sun Nov 23, 2008 5:23 pm    Post subject: Reply with quote
Marty R. wrote:
By the way, I might be the only one here who doesn't understand notation, ...


You are NOT ... (and I'm sure we're not talking ONE but many notations Very Happy )

For a totally notation-free cooking recipe for gm-wings, see here
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sun Nov 23, 2008 5:47 pm    Post subject: Reply with quote
storm_norm wrote:
danny, what about this one?

(2)r78c2 = (2)r5c2 - (2=8)r5c1 - (8)r9c1 = (8)r9c3; r9c3 <> 2

I was only assured of strong links in (8). Your chain, which is not an M-Wing, starts off with the assumption of a strong link in (2). Otherwise, your chain seems correct to me.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sun Nov 23, 2008 10:10 pm    Post subject: Reply with quote
nataraj wrote:
Marty R. wrote:
By the way, I might be the only one here who doesn't understand notation, ...


You are NOT ... (and I'm sure we're not talking ONE but many notations Very Happy )

For a totally notation-free cooking recipe for gm-wings, see here

Your explanation two posts before the quoted post was pretty clear.
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