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Unchained?

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Thu Nov 29, 2007 3:29 pm    Post subject: Unchained? Reply with quote

Depending on your definition of chains, this one may not need any.
Code:
Puzzle: M4131746sh(10)
+-------+-------+-------+
| . . . | . . . | 4 . . |
| 8 . . | . . . | . . . |
| 4 . . | 3 . . | 5 6 7 |
+-------+-------+-------+
| . 7 . | 8 . . | . . 4 |
| . . . | . . 6 | 2 7 9 |
| . . 3 | . 4 . | . . . |
+-------+-------+-------+
| . . . | . 2 . | . . . |
| . . 6 | 4 . 8 | 7 3 . |
| . 2 . | . 5 . | 6 9 . |
+-------+-------+-------+

It is much tougher than this site's Very Hards.

Keith
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Nov 29, 2007 4:00 pm    Post subject: Re: Unchained? Reply with quote

keith wrote:
Depending on your definition of chains, this one may not need any.


In my book, coloring (even multi-coloring) is not "chains" (but of course the reasoning uses inference chains, what else). So in that sense removing some "1"s, "2"s and "5"s got me quite far. But here:
Code:

+--------------------------+--------------------------+--------------------------+
| 279     36      1579     | 29      67      159      | 4       8       13       |
| 8       36      157      | 15      67      4        | 9       2       13       |
| 4       19      129      | 3       8       129      | 5       6       7        |
+--------------------------+--------------------------+--------------------------+
| 6       7       129      | 8       19      259      | 3       15      4        |
| 15      4       8        | 15      3       6        | 2       7       9        |
| 259     159     3        | 29      4       7        | 8       15      6        |
+--------------------------+--------------------------+--------------------------+
| 379     8       79       | 6       2       39       | 1       4       5        |
| 59      159     6        | 4       19      8        | 7       3       2        |
| 13      2       4        | 7       5       13       | 6       9       8        |
+--------------------------+--------------------------+--------------------------+


I did need chains. Starting with the useless xy wing pivot r8c1 (19-59-15) I kept looking around. And found these babies:
'51'(51)='13'(91)='31'(96)='19'(85)='95'(81)
'76'(25)='63'(22)='31'(29)='15'(24)='51'(54)='15'(51)='59'(81)='97'(73)
'95'(81)='51'(51)='13'(91)='31'(96)='19'(85)

There are 5 cells that form a loop: -15-15-19-19-59-
How does this help?


(edit. P.S.: another coloroing elimination later on "9"s solved the puzzle for me)
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Thu Nov 29, 2007 4:24 pm    Post subject: Reply with quote

There is a very simple forcing chain solving the puzzle:
Code:
 *------------------------------------------------*
 | 12579  36   1579  | 29  67 B159   | 4  8   13  |
 | 8      36   157   |A15  67  4     | 9  2   13  |
 | 4      19   129   | 3   8  -129   | 5  6   7   |
 |-------------------+---------------+------------|
 | 6      7    1259  | 8   19  1259  | 3  15  4   |
 | 15     4    8     | 15  3   6     | 2  7   9   |
 | 1259   159  3     | 29  4   7     | 8  15  6   |
 |-------------------+---------------+------------|
 | 379    8    79    | 6   2  B39    | 1  4   5   |
 | 159    159  6     | 4   19  8     | 7  3   2   |
 | 13     2    4     | 7   5  B13    | 6  9   8   |
 *------------------------------------------------*
In box 5 the 5 can be in r5c4 (=> r2c4=1) or r4c7 (=> r3c7=2)
In both cases r3c7 cannot be 1.

It can be done with an ALS too (x=5, z=1)
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Nov 29, 2007 4:59 pm    Post subject: Reply with quote

ALSs: chainless in the extreme - by any definition. very elegant.

I tried to use your ALS and avoid (color and other) chains, but this is where it stops:

Code:
 
+--------------------------+--------------------------+--------------------------+
| 2579    36      2579     | 29      67      15       | 4       8       13       |
| 8       36      57       | 15      67      4        | 9       2       13       |
| 4       19      129      | 3       8       29       | 5       6       7        |
+--------------------------+--------------------------+--------------------------+
| 6       7       1259     | 8       19      1259     | 3       15      4        |
| 15      4       8        | 15      3       6        | 2       7       9        |
| 1259    159     3        | 29      4       7        | 8       15      6        |
+--------------------------+--------------------------+--------------------------+
| 379     8       79       | 6       2       39       | 1       4       5        |
| 159     159     6        | 4       19      8        | 7       3       2        |
| 13      2       4        | 7       5       13       | 6       9       8        |
+--------------------------+--------------------------+--------------------------+
 


edit : I see it now. xwing on 2


Last edited by nataraj on Thu Nov 29, 2007 5:12 pm; edited 2 times in total
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Thu Nov 29, 2007 4:59 pm    Post subject: Reply with quote

In the posted position:

Code:
+----------------+----------------+----------------+
| 279  36   1579 | 29   67   159  | 4    8    13   |
| 8    36   157  | 15   67   4    | 9    2    13   |
| 4    19   129  | 3    8    129  | 5    6    7    |
+----------------+----------------+----------------+
| 6    7    -129 | 8    19   259# | 3    15@  4    |
| 15@  4    8    | 15#   3    6    | 2    7    9    |
| 259  159  3    | 29   4    7    | 8    15   6    |
+----------------+----------------+----------------+
| 379  8    79   | 6    2    39   | 1    4    5    |
| 59   159  6    | 4    19   8    | 7    3    2    |
| 13   2    4    | 7    5    13   | 6    9    8    |
+----------------+----------------+----------------+

@@ is a W-wing connected by the link ## on <5>. It takes out <1> in r4c3.

After some cleaning up, coloring on <9> solves R8C1 as <5>, and the puzzle is done.

Keith
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Thu Nov 29, 2007 6:50 pm    Post subject: Chains Reply with quote

I thought I had a simple solution, but it was just dumb luck.

Earl


Last edited by Earl on Thu Nov 29, 2007 7:51 pm; edited 2 times in total
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Thu Nov 29, 2007 7:48 pm    Post subject: Re: chains Reply with quote

SORRY - my error - Senior moment !

Earl
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