There Was a Time: 04/02/13

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There Was a Time: 04/02/13

Postby daj95376 » Tue Apr 02, 2013 5:06 am

A 2-SIS single-stepper.

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

Play this puzzle online at the Daily Sudoku site
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Re: There Was a Time: 04/02/13

Postby Leren » Tue Apr 02, 2013 6:05 am

Code: Select all
*-----------------------------------------------------*
| 4    9    7     | 3    68   68    | 2    5    1     |
| 8    1    56    |c49   59   2     |b469  7    3     |
| 3    56   2     | 7    159  149   | 469 a46   8     |
|-----------------+-----------------+-----------------|
| 5    2    4     | 689  1689 1689  | 16   3    7     |
| 79   78   189   |d456  3    146   | 1456 48-6 2     |
| 6    3    18    |d45   2    7     | 145  48   9     |
|-----------------+-----------------+-----------------|
| 1    4    689   | 689  689  3     | 7    2    5     |
| 2    568  568   | 1    7    568   | 3    9    4     |
| 79   57   3     | 2    4    59    | 8    1    6     |
*-----------------------------------------------------*

(6=4) r3c8 - r2c7 = r2c4 - (4=6) r56c4 => -6 r5c8; stte

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Re: There Was a Time: 04/02/13

Postby ArkieTech » Tue Apr 02, 2013 8:41 am

Leren wrote:(6=4) r3c8 - r2c7 = r2c4 - (4=6) r56c4 => -6 r5c8; stte


Is this an als w-wing? 8-)
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Re: There Was a Time: 04/02/13

Postby Leren » Tue Apr 02, 2013 8:58 am

ArkieTech wrote:
Leren wrote:(6=4) r3c8 - r2c7 = r2c4 - (4=6) r56c4 => -6 r5c8; stte


Is this an als w-wing? 8-)


Either an ALS w-wing or Conjugate Linked ALSs. Unfortunately I'm 1 SIS over budget :(

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Re: There Was a Time: 04/02/13

Postby Leren » Tue Apr 02, 2013 11:41 am

I'll take a punt at this before I'm off to bed.

Considering the potential 45 DP r56c47 can we write (6=45) r56c4 - DP - (45=16) r456c7 => -6 r5c8; stte

Is that a 2-SIS move or a forcing net ?

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Re: There Was a Time: 04/02/13

Postby ArkieTech » Tue Apr 02, 2013 12:45 pm

Leren wrote: 45 DP r56c47 can we write (6=45) r56c4 - DP - (45=16) r456c7 => -6 r5c8; stte


I like.. :D .. How about:

(6=1)45r56c47-(1=6)r4c7 => -6r5c8
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Re: There Was a Time: 04/02/13

Postby JC Van Hay » Tue Apr 02, 2013 2:23 pm

ArkieTech wrote:
Leren wrote: 45 DP r56c47 can we write (6=45) r56c4 - DP - (45=16) r456c7 => -6 r5c8; stte


I like.. :D .. How about:

(6=1)45r56c47-(1=6)r4c7 => -6r5c8
Nice catch !
Code: Select all
+--------------+-------------------+-----------------+
| 4   9    7   | 3      68    68   | 2       5     1 |
| 8   1    56  | 49     59    2    | 469     7     3 |
| 3   56   2   | 7      159   149  | 469     46    8 |
+--------------+-------------------+-----------------+
| 5   2    4   | 689    1689  1689 | (16)    3     7 |
| 79  78   189 | (456)  3     146  | (1456)  48-6  2 |
| 6   3    18  | (45)   2     7    | (145)   48    9 |
+--------------+-------------------+-----------------+
| 1   4    689 | 689    689   3    | 7       2     5 |
| 2   568  568 | 1      7     568  | 3       9     4 |
| 79  57   3   | 2      4     59   | 8       1     6 |
+--------------+-------------------+-----------------+
Chain[5] :

Either, as in a Kraken, ...
UR(45)r56c47 ... [False if the puzzle has a unique solution]
||
6r5c47
||
1r56c7-(1=6)r4c7
or, as in an AAIC, ...
UR(45)r56c47=*[6r5c47=*1r56c7-(1=6)r4c7]

-> UR(45)r56c47=6r5c47=6r4c7 :=> -6r5c8; ste

I don't like hair-splitting, but, this is a 5-SIS whatever you want to call it as the ("native") SIS are the 5 cells R56C47+R4C7.
The so called referred to "2-SIS" are in fact 1 derived SIS + 1 native SIS.
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Re: There Was a Time: 04/02/13

Postby daj95376 » Tue Apr 02, 2013 4:44 pm

)___

My use of "2-SIS" could easily be incorrect. I should have said "2-SI" to match what I was thinking.

However, I refuse to identify the full UR in the solution when I've already marked it in the grid. What I did was separate the candidate cells on the left side of the second SI from the candidate cells on the right side. Thus, r5c7 is repeated.

BTW: the UR candidates are always the candidates not mentioned in the cells identified as part of the UR.

Congratulations on finding this unusual solution.

Code: Select all
 +--------------------------------------------------------------+
 |  4     9     7     |  3     68    68    |  2     5     1     |
 |  8     1     56    |  49    59    2     |  469   7     3     |
 |  3     56    2     |  7     159   149   |  469   46    8     |
 |--------------------+--------------------+--------------------|
 |  5     2     4     |  689   1689  1689  |  16    3     7     |
 |  79    78    189   | *45+6  3     146   | *45+16 48-6  2     |
 |  6     3     18    | *45    2     7     | *45+1  48    9     |
 |--------------------+--------------------+--------------------|
 |  1     4     689   |  689   689   3     |  7     2     5     |
 |  2     568   568   |  1     7     568   |  3     9     4     |
 |  79    57    3     |  2     4     59    |  8     1     6     |
 +--------------------------------------------------------------+
 # 57 eliminations remain

 (6=1)r4c7 - (1=UR=6)r56c7,r5c47  =>  r5c8<>6
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Re: There Was a Time: 04/02/13

Postby Leren » Wed Apr 03, 2013 12:53 am

- :D
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Re: There Was a Time: 04/02/13

Postby Marty R. » Wed Apr 03, 2013 1:16 am

Code: Select all
+------------+---------------+------------+
| 4  9   7   | 3   68   68   | 2    5   1 |
| 8  1   56  | 49  59   2    | 469  7   3 |
| 3  56  2   | 7   159  149  | 469  46  8 |
+------------+---------------+------------+
| 5  2   4   | 689 1689 1689 | 16   3   7 |
| 79 78  189 | 456 3    146  | 1456 468 2 |
| 6  3   18  | 45  2    7    | 145  48  9 |
+------------+---------------+------------+
| 1  4   689 | 689 689  3    | 7    2   5 |
| 2  568 568 | 1   7    568  | 3    9   4 |
| 79 57  3   | 2   4    59   | 8    1   6 |
+------------+---------------+------------+

Play this puzzle online at the Daily Sudoku site

I threw in the towel on a one-stepper.

XY-Chain (8=4)r6c8-(4=6)r3c8-(6=5)r3c2-(5=7)r9c2-(7=8)r5c2=>r5c8,r6c3<>8
XYZ-Wing (456), pivot r5c4=>r5c6<>4
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Re: There Was a Time: 04/02/13

Postby eleven » Wed Apr 03, 2013 1:24 pm

Because no one mentioned the DP45 version with external candidates 4r2c4, 4r23c7:
Code: Select all
    *-----------------------------------------------------*
    | 4    9    7     | 3    68   68    | 2    5    1     |
    | 8    1    56    |*49   59   2     |*469  7    3     |
    | 3    56   2     | 7    159  149   |*469  46   8     |
    |-----------------+-----------------+-----------------|
    | 5    2    4     | 689  1689 1689  | 16   3    7     |
    | 79   78   189   |#456  3    146   |#1456 48-6 2     |
    | 6    3    18    |#45   2    7     |#145  48   9     |
    |-----------------+-----------------+-----------------|
    | 1    4    689   | 689  689  3     | 7    2    5     |
    | 2    568  568   | 1    7    568   | 3    9    4     |
    | 79   57   3     | 2    4    59    | 8    1    6     |
    *-----------------------------------------------------*

r2c4=4->r56c4=56
r23c7=4->r3c8=6
=> r5c8<>6

(6=45)r56c4-4r2c4=(DP)=4r23c7-(4=6)r3c8 => r5c8<>6
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