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Puzzle 11/06/26: ~ XY (extreme!)

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sun Jun 26, 2011 8:18 pm    Post subject: Puzzle 11/06/26: ~ XY (extreme!) Reply with quote

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

Play this puzzle online at the Daily Sudoku site
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PIsaacson



Joined: 13 Jun 2011
Posts: 11
Location: Campbell, CA

PostPosted: Sun Jun 26, 2011 11:31 pm    Post subject: Reply with quote

Basics + coloring until I hit the following position:
Code:
*-----------------------------------------------------------*
 | 1     279   279   | 39    8     2359  | 4     269   2569  |
 | 29    8     6     | 1     4     259   | 3     279   2579  |
 | 4     3     5     | 6     7     29    | 8     1     29    |
 |-------------------+-------------------+-------------------|
 | 8     4     1     |a79    2     6     | 5     79    3     |
 | 7     259   3     | 8     5-1  a19    | 69    4     269   |
 | 6     259   29    | 4     359   379   | 1     2789  2789  |
 |-------------------+-------------------+-------------------|
 | 5     6     8     | 2    b19    4     | 7     3     19    |
 | 39    179   4     |b379   6     378-1 | 2     5     189   |
 | 239   1279  279   | 5    b139   378-1 | 69    689   4     |
 *-----------------------------------------------------------*

 ALS XY  ALS (a) b5x16 -7- (b) b7x248 => r5c5 <> 1, r89c6 <> 1

A few more steps (not really needed) until this position:
 
 *-----------------------------------------------------------*
 | 1     279   279   | 39    8     2359  | 4    a269   56-29 |
 | 29    8     6     | 1     4     259   | 3    a279   57-29 |
 | 4     3     5     | 6     7     29    | 8     1    b29    |
 |-------------------+-------------------+-------------------|
 | 8     4     1     | 79    2     6     | 5    a79    3     |
 | 7     29    3     | 8     5     1     | 69    4     26-9  |
 | 6     5     29    | 4     39    379   | 1     28-79 278-9 |
 |-------------------+-------------------+-------------------|
 | 5     6     8     | 2     19    4     | 7     3    b19    |
 | 39    179   4     | 379   6     378   | 2     5    b189   |
 | 239   1279  27    | 5     139   378   | 69   a689   4     |
 *-----------------------------------------------------------*

  ALS XZ (doubly linked)

  ALS (a) r1249c8 -28- (b) r378c9 => r12c9 <> 29, r56c9 <> 9, r6c8 <> 79

Lots of basic steps + coloring until this position:
 
 *--------------------------------------------------*
 | 1    79   27   | 3    8    29   | 4    6    5    |
 |a29   8    6    | 1    4    5    | 3   *29   7    |
 | 4    3    5    | 6    7    29   | 8    1    29   |
 |----------------+----------------+----------------|
 | 8    4    1    | 9    2    6    | 5    7    3    |
 | 7    2    3    | 8    5    1    | 9    4    6    |
 | 6    5    9    | 4    3    7    | 1    28   28   |
 |----------------+----------------+----------------|
 | 5    6    8    | 2    19   4    | 7    3    19   |
 |a39   19   4    | 7    6    8-3  | 2    5    189  |
 | 29-3 17   27   | 5    19  b38   | 6   b89   4    |
 *--------------------------------------------------*
 
 Death Blossom stem cell r2c8 ALS (a) -2- r28c1 (b) -9- r9c68 => r8c6 <> 3, r9c1 <> 3

 ste

The final DB can also be viewed as an XY-chain or an ALS XY-Wing.

Hope I got the right puzzle this time!!!

Cheers,
Paul

P.S. Just noticed that there is also a quick BUG Type 2 solution with some LBMs that eliminate r8c12 <> 9 and r9c8 <> 9 with ste.

Code:
 *--------------------------------------------------*
 | 1    79   27   | 3    8    29   | 4    6    5    |
 | 29   8    6    | 1    4    5    | 3    29   7    |
 | 4    3    5    | 6    7    29   | 8    1    29   |
 |----------------+----------------+----------------|
 | 8    4    1    | 9    2    6    | 5    7    3    |
 | 7    2    3    | 8    5    1    | 9    4    6    |
 | 6    5    9    | 4    3    7    | 1    28   28   |
 |----------------+----------------+----------------|
 | 5    6    8    | 2    19   4    | 7    3    19   |
 | 3-9  1-9  4    | 7    6    38   | 2    5    18+9 |
 | 23+9 17   27   | 5    19   38   | 6    8-9  4    |
 *--------------------------------------------------*
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Marty R.



Joined: 12 Feb 2006
Posts: 5166
Location: Rochester, NY, USA

PostPosted: Mon Jun 27, 2011 4:35 am    Post subject: Reply with quote

XYZ-Transport; r1c4<>9
Multi-coloring; r4c8<>9
Coloring; r9c2<>9
BUG+2

(Edited June 27.)

The 3rd step just reduced the grid from BUG+3 to BUG+2. However, the step wasn't necessary, as in the BUG+3 all three DP killers are the same and the eliminations are easy.
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Mon Jun 27, 2011 8:29 pm    Post subject: Reply with quote

Paul,

I am still in the "not confident" zone handling ALSs in general. Looking at your first ALS_XZ, I understand the formation and the deletions common to both ALS (a) & (b). However it appears to me that for the second ALS_XZ, you deleted all contributions from both ALS (a) & (b), not just those that were common to both ALSs.

Please clarify......

Ted
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PIsaacson



Joined: 13 Jun 2011
Posts: 11
Location: Campbell, CA

PostPosted: Mon Jun 27, 2011 9:22 pm    Post subject: Reply with quote

Ted,

The 2nd ALS is of the doubly-linked variety - 2 RCCs locking the ALSs together. You can think of it as a closed loop if that helps. Basically, the rules for what can be eliminated are greatly increased and to quote from Hobiwan's HoDoKu web pages:
Hobiwan wrote:
If the two ALS have two RCCs, things get really interesting. Remember that an RCC digit can only be placed in one ALS, thus turning the other ALS into a locked set. If we have two RCCs, one of them has to be placed in ALS A, turning ALS B into a locked set, the other has to be in ALS B, turning ALS A into a locked set (which RCC will be in which ALS, is yet unknown). Both RCCs in one ALS is impossible, because both RCCs would be eliminated from the other ALS leaving only N-1 candidates for N cells, which is of course invalid.

What can be concluded from a Doubly Linked ALS-XZ? Both RCCs are locked into one ALS, so the RCCs can be eliminated from all non ALS cells in the houses providing the RCCs. But more importantly, all non RCC digits get locked within their respective ALS and eliminate all digits outside the ALS that can see all instances of the digit in the ALS (the elimination can even be done in a cell belonging to the other ALS, making the ALS-XZ cannibalistic).

I explored some cannibalistic aspects in the Player's Forum: http://forum.enjoysudoku.com/als-chains-with-overlap-cannibalism-t6580.html

Cheers,
Paul
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Mon Jun 27, 2011 9:42 pm    Post subject: Reply with quote

PIsaacson wrote:
Ted,

The 2nd ALS is of the doubly-linked variety - 2 RCCs locking the ALSs together. You can think of it as a closed loop if that helps. Basically, the rules for what can be eliminated are greatly increased and to quote from Hobiwan's HoDoKu web pages:
Hobiwan wrote:
If the two ALS have two RCCs, things get really interesting. Remember that an RCC digit can only be placed in one ALS, thus turning the other ALS into a locked set. If we have two RCCs, one of them has to be placed in ALS A, turning ALS B into a locked set, the other has to be in ALS B, turning ALS A into a locked set (which RCC will be in which ALS, is yet unknown). Both RCCs in one ALS is impossible, because both RCCs would be eliminated from the other ALS leaving only N-1 candidates for N cells, which is of course invalid.

What can be concluded from a Doubly Linked ALS-XZ? Both RCCs are locked into one ALS, so the RCCs can be eliminated from all non ALS cells in the houses providing the RCCs. But more importantly, all non RCC digits get locked within their respective ALS and eliminate all digits outside the ALS that can see all instances of the digit in the ALS (the elimination can even be done in a cell belonging to the other ALS, making the ALS-XZ cannibalistic).

I explored some cannibalistic aspects in the Player's Forum: http://forum.enjoysudoku.com/als-chains-with-overlap-cannibalism-t6580.html

Cheers,
Paul


Wonderful explanation and a great spot Exclamation

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Jun 29, 2011 9:24 pm    Post subject: Reply with quote

PIsaacson wrote:
A few more steps (not really needed) until this position:

Code:
 *-----------------------------------------------------------*
 | 1     279   279   | 39    8     2359  | 4    a269   56-29 |
 | 29    8     6     | 1     4     259   | 3    a279   57-29 |
 | 4     3     5     | 6     7     29    | 8     1    b29    |
 |-------------------+-------------------+-------------------|
 | 8     4     1     | 79    2     6     | 5    a79    3     |
 | 7     29    3     | 8     5     1     | 69    4     26-9  |
 | 6     5     29    | 4     39    379   | 1     28-79 278-9 |
 |-------------------+-------------------+-------------------|
 | 5     6     8     | 2     19    4     | 7     3    b19    |
 | 39    179   4     | 379   6     378   | 2     5    b189   |
 | 239   1279  27    | 5     139   378   | 69   a689   4     |
 *-----------------------------------------------------------*

  ALS XZ (doubly linked)

  ALS (a) r1249c8 -28- (b) r378c9 => r12c9 <> 29, r56c9 <> 9, r6c8 <> 79

Since my ALS understanding is very limited, I couldn't follow the above.

No problem, I'll simply attack it as a loop starting at r3c9:

Code:
 +-----------------------------------------------------------------------+
 |  1      279    279    |  39     8      2359   |  4      269    56-29  |
 |  29     8      6      |  1      4      259    |  3      279    57-29  |
 |  4      3      5      |  6      7      29     |  8      1      29     |
 |-----------------------+-----------------------+-----------------------|
 |  8      4      1      |  79     2      6      |  5      79     3      |
 |  7      259    3      |  8      159    19     |  69     4      26-9   |
 |  6      259    29     |  4      359    379    |  1      28-79  278-9  |
 |-----------------------+-----------------------+-----------------------|
 |  5      6      8      |  2      19     4      |  7      3      19     |
 |  39     179    4      |  379    6      13789  |  2      5      189    |
 |  239    1279   279    |  5      139    13789  |  69     689    4      |
 +-----------------------------------------------------------------------+
 # 75 eliminations remain

(9=2)r3c9 - (2)r12c8 = (2-8)r6c8 = (8)r9c8 - (8=19)r78c9 - loop

=>  r12c9<>29, r56c9<>9, r6c8<>79

Same results via a cell swap -- r6c8 for r4c8 -- and three fewer values to consider -- <6>, <7>, and <9> -- in [c8].

Regards, Danny
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