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Another toughie

 
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Wed Jun 20, 2007 11:06 am    Post subject: Another toughie Reply with quote

This is Andrew Stuart's latest Extreme which caused me much thought but can I think be done without too much reliance on Alternate inference Chains or ALS's.

If you are finding VH a little too easy this will be fun !

Code:
+---+---+---+
|..6|4.2|1..|
|.4.|...|.9.|
|7..|...|...|
+---+---+---+
|86.|5.4|.2.|
|9..|.7.|..3|
|.3.|2.1|.78|
+---+---+---+
|...|...|..2|
|.7.|...|.5.|
|..8|6.3|7..|
+---+---+---+
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Wed Jun 20, 2007 11:08 am    Post subject: Reply with quote

The shape is cool too don't you think ?
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Ruud



Joined: 18 Jan 2006
Posts: 31

PostPosted: Wed Jun 20, 2007 6:32 pm    Post subject: Reply with quote

After the basic steps, including an XY-Wing, there are 4 XY-chains with some cleanup inbetween.


(5=8)r1c5 - (8=3)r1c8 - (3=6)r3c8 - (6=5)r2c9
(this grid also allows a Sue-de-Coq move, but that doesn't add any value)
Code:
.-------------------.------------------.------------------.
| 35    9     6     | 4    #58    2    | 1    *38    7    |
| 1235  4     1235  | 137   168-5 7-5  | 238   9    #56   |
| 7     8     1235  | 139   156   59   | 234  *36    456  |
:-------------------+------------------+------------------:
| 8     6     7     | 5     3     4    | 9     2     1    |
| 9     12    12    | 8     7     6    | 5     4     3    |
| 45    3     45    | 2     9     1    | 6     7     8    |
:-------------------+------------------+------------------:
| 1346  15    1349  | 179   145   5789 | 348   368   2    |
| 12346 7     12349 | 19    124   89   | 348   5     46   |
| 24    25    8     | 6     245   3    | 7     1     9    |
'-------------------'------------------'------------------'


(5=8)r1c5 - (8=3)r1c8 - (3=5)r1c1 - (5=4)r6c1 - (4=2)r9c1 - (2=5)r9c2
Code:
.-------------------.------------------.------------------.
|*35    9     6     | 4    #58    2    | 1    *38    7    |
|*12    4     1235  | 13    168   7    | 238   9     56   |
| 7     8     1235  | 139   156   59   | 234   36    456  |
:-------------------+------------------+------------------:
| 8     6     7     | 5     3     4    | 9     2     1    |
| 9     12    12    | 8     7     6    | 5     4     3    |
|*45    3     45    | 2     9     1    | 6     7     8    |
:-------------------+------------------+------------------:
| 1346  15    349   | 7     145   589  | 348   368   2    |
| 12346 7     349   | 19    124   89   | 348   5     46   |
|*24   #25    8     | 6     24-5  3    | 7     1     9    |
'-------------------'------------------'------------------'


(3=8)r1c8 - (8=2)r2c7 - (2=5)r2c3 - (5=6)r2c9 - (6=3)r3c8
Code:
.---------------.---------------.----------------.
| 35   9    6   | 4    58   2   | 1    #38   7   |
| 1    4   *25  | 3    68   7   |*28    9   *56  |
| 7    8    235 | 19   156  59  | 24-3 #36   456 |
:---------------+---------------+----------------:
| 8    6    7   | 5    3    4   | 9     2    1   |
| 9    2    1   | 8    7    6   | 5     4    3   |
| 45   3    45  | 2    9    1   | 6     7    8   |
:---------------+---------------+----------------:
| 346  1    349 | 7    45   589 | 348   68-3 2   |
| 2346 7    349 | 19   124  89  | 348   5    46  |
| 24   5    8   | 6    24   3   | 7     1    9   |
'---------------'---------------'----------------'

(4=5)r6c1 - (5=3)r1c1 - (3=8)r1c8 - (8=5)r1c5 - (5=4)r7c5
Code:
.----------------.---------------.---------------.
|*35    9    6   | 4   *58   2   | 1   *38   7   |
| 1     4    25  | 3    68   7   | 28   9    56  |
| 7     8    235 | 19   156  59  | 24   36   456 |
:----------------+---------------+---------------:
| 8     6    7   | 5    3    4   | 9    2    1   |
| 9     2    1   | 8    7    6   | 5    4    3   |
|#45    3    45  | 2    9    1   | 6    7    8   |
:----------------+---------------+---------------:
| 36-4  1    349 | 7   #45   589 | 348  68   2   |
| 2346  7    349 | 19   124  89  | 348  5    46  |
| 24    5    8   | 6    24   3   | 7    1    9   |
'----------------'---------------'---------------'

This enables the XY-Wing that breaks the puzzle.
A nice exercise in XY-chains. Cool

Ruud
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Wed Jun 20, 2007 8:49 pm    Post subject: Reply with quote

A good puzzle.

I reached this stage and the same conclusions...

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Ruud



Joined: 18 Jan 2006
Posts: 31

PostPosted: Wed Jun 20, 2007 10:22 pm    Post subject: Reply with quote

The last xy-chain can also be shortened to this AIC:

(4=5)r6c1 - (5)r1c1 = (5)r1c5 - (5=4)r7c5

The strong link for digit 5 in row 1 replaces the longer route via r1c8.

This no longer qualifies as xy-chain, though, but it has skyscraper-like qualities that makes it easy to spot. It was your coloring that did the trick for me.
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Wed Jun 20, 2007 10:24 pm    Post subject: Reply with quote

Many Thanks Ruud !
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