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competition #1027

 
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Sun May 04, 2008 6:08 am    Post subject: competition #1027 Reply with quote
competition #1027

Code:
. 4 .|. . .|. . .
. . .|8 . 9|. 4 .
. . 1|5 . .|8 . .
-----+-----+-----
4 . .|. 9 .|. 7 3
. . 8|. 1 .|9 . .
3 6 .|. 2 .|. . 5
-----+-----+-----
. . .|. 8 6|7 . .
. 7 .|9 . 4|. . .
. . .|. . .|. 1 .


Code:
.------------------.------------------.------------------.
| 8     4     37   | 27    367   1    | 356   2359  269  |
| 25    35    237  | 8     367   9    | 36    4     1    |
| 6     9     1    | 5     4     23   | 8     23    7    |
:------------------+------------------+------------------:
| 4     1     5    | 6     9     8    | 2     7     3    |
| 7     2     8    | 3     1     5    | 9     6     4    |
| 3     6     9    | 4     2     7    | 1     8     5    |
:------------------+------------------+------------------:
| 259   35    4    | 1     8     6    | 7     2359  29   |
| 1     7     236  | 9     35    4    | 356   235   8    |
| 59    8     36   | 27    357   23   | 4     1     69   |
'------------------'------------------'------------------'


the xy-chain that finishes this off has two ends in the same box. Very Happy
------

extreme # 84

Code:
6 2 9|. . .|. 1 .
3 . .|. . .|8 9 6
. . .|7 . .|. . .
-----+-----+-----
. . 5|. 3 9|. 7 .
. . .|. . .|. . .
. 7 .|4 5 .|3 . .
-----+-----+-----
. . .|. . 1|. . .
4 9 3|. . .|. . 1
. 1 .|. . .|5 4 8


Code:
.---------------------.---------------------.---------------------.
| 6      2      9     | 3      8      45    | 47     1      457   |
| 3      45     7     | 125    12     245   | 8      9      6     |
| 158    458    148   | 7      9      6     | 24     235    2345  |
:---------------------+---------------------+---------------------:
| 28     468    5     | 1268   3      9     | 1246   7      24    |
| 289    3      2468  | 1268   126    7     | 12469  2568   2459  |
| 1289   7      1268  | 4      5      28    | 3      268    29    |
:---------------------+---------------------+---------------------:
| 2578   568    268   | 26     4      1     | 2679   236    2379  |
| 4      9      3     | 58     267    58    | 267    26     1     |
| 27     1      26    | 9      267    3     | 5      4      8     |
'---------------------'---------------------'---------------------'
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Sun May 04, 2008 8:14 am    Post subject: Reply with quote
here is a beginning volley on the extreme monster.

this image should show a w-wing that has been extended.
the pair is {2,6} in r7c4 and r8c8, and the strong link is on 6 in row 6.
sorry i am not yet fluent in the correct notation to express this.

if you follow around from r7c4 is not 2
then r7c4 is 6, r7c23 is not 6, r9c3 is 6, r6c3 is not 6, r6c8 is 6, r8c8 is 2
other way...
r8c8 is not 2, r8c8 is 6, r6c8 is not 6, r6c3 is 6, r79c3 is not 6, r7c1 is 6, r7c4 is 2

since either r7c4 and r8c8 is a 2 then we can eliminate any 2's they see.

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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI
PostPosted: Sun May 04, 2008 10:50 am    Post subject: Reply with quote
At a quick look, this is indeed a serious puzzle. Your starter is very attractive - I like pairs like this that can be linked in some useful way. There's one easy move as well: there's a kite in 6s in c2 & r6 that removes 6 from r7c8.

And here's one of my XY-chain-extended AICs that may or may not be much help. Say r5c3 is 8. Then r4c2 must be 4, r4c9 must be 2, and r4c1 must be 8. That's a contradiction (two 8s in the same box) and so we can remove the 8 from r5c3.

Last edited by Victor on Sun May 04, 2008 11:33 am; edited 1 time in total
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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI
PostPosted: Sun May 04, 2008 11:31 am    Post subject: Reply with quote
That takes us to here.
Code:

+---------------+---------------+----------------+
| 6    2   9    | 3    8    45  | 47   1    457  |
| 3    45  7    | 125  12   245 | 8    9    6    |
| 158  458 148  | 7    9    6   | 24   25   3    |
+---------------+---------------+----------------+
| 128  468 5    | 1268 3    9   | 124  7    24   |
| 289  3   246  | 1268 126  7   | 1249 2568 2459 |
| 1289 7   1268 | 4    5    28  | 3    268  29   |
+---------------+---------------+----------------+
| 2578 568 268  | 26   4    1   | 679  3    79   |
| 4    9   3    | 58   67   58  | 267  26   1    |
| 27   1   26   | 9    267  3   | 5    4    8    |
+---------------+---------------+----------------+


I can offer one more mini-AIC. If r5c3 is 2, then r4c2 is 4, r7c2 is 6, and r9c3 is 2. This contradiction means that we can remove 2 from r5c3. Doesn't seem to help much.

PS. I suppose you can see your sort-of-W-wing as W-wing + ER.The right-hand 6 in r6 sees the 26 under it directly, while the left-hand 6 'sees' the other 26 via the ER in box 7.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Sun May 04, 2008 11:42 pm    Post subject: Reply with quote
Victor,

Your last posted grid is messed up somehow. It should be:
Code:
+---------------+---------------+-----------------+
| 6    2   9    | 3    8    45  | 47    1    457  |
| 3    45  7    | 125  12   245 | 8     9    6    |
| 158  458 148  | 7    9    6   | 24    25   3    |
+---------------+---------------+-----------------+
| 28   468 5    | 1268 3    9   | 1246  7    24   |
| 289  3   246  | 1268 126  7   | 12469 2568 2459 |
| 1289 7   1268 | 4    5    28  | 3     268  29   |
+---------------+---------------+-----------------+
| 2578 568 268  | 26   4    1   | 679   3    79   |
| 4    9   3    | 58   67   58  | 267   26   1    |
| 27   1   26   | 9    267  3   | 5     4    8    |
+---------------+---------------+-----------------+
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Sun May 04, 2008 11:49 pm    Post subject: Reply with quote
Since that W-Wing step, there has been an X-Wing on <2> in r38.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Mon May 05, 2008 12:27 am    Post subject: Reply with quote
After applying the X-Wing (that removes <2>s from c78 of b6), some Medusa multi-coloring reveals the following AIC that solves the puzzle:

(5)r8c6-(5=5)r1c69-(5=5)r5c89-(5=2)r3c8-(2=6)r8c8-(6=8)r6c8-(8=8)r68c6-(8=5)r8c4-(5)r8c6; r8c6<>5

For those who don't follow Eureka notation: If r1c6 is <5>, then r8c6 is not <5>. If r1c6 is not <5>, then r1c9 is <5> and r5c8 is <5>, r3c8 is <2>, r8c8 is <6>, r6c8 is <8> (remember that the <2> is gone from this cell... though the AIC would work in any case), so r8c6 is <8>, r8c4 is <5> and r8c6 is not <5>. Either way, r8c6 is not <5>.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Mon May 05, 2008 3:33 am    Post subject: Reply with quote
yay, we got that one done
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