Patterns Game 55.35

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Patterns Game 55.35

Postby ArkieTech » Sun Aug 18, 2013 12:05 am

Code: Select all
 *-----------*
 |...|..1|23.|
 |4..|.5.|...|
 |6..|7..|...|
 |---+---+---|
 |5..|...|7..|
 |.3.|...|.8.|
 |..4|...|..6|
 |---+---+---|
 |...|..3|..9|
 |...|.6.|..4|
 |.19|2..|...|
 *-----------*


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Re: Patterns Game 55.35

Postby pjb » Sun Aug 18, 2013 2:08 am

Code: Select all
 89     5789   578    | 6      4      1      | 2      3      578   
 4      278    13     | 38     5      289    | 169    1679   178   
 6      258    13     | 7      239    289    | 1459   1459   158   
 ---------------------+----------------------+---------------------
 5      6      8-2    | 1348   239    289    | 7      149    123   
 19-2   3     a27     | 14    b279    6      | 1459   8      125   
d1289   789    4      | 138   c27-39  5      | 139    19     6     
 ---------------------+----------------------+---------------------
 27     4      6      | 5      1      3      | 8      27     9     
 238    58     258    | 9      6      7      | 13     12     4     
 37     1      9      | 2      8      4      | 356    567    357   

Continuous nice loop: (2=7) r5c3 - r5c5 = (7-2) r6c5 = r6c1 - r5c3 => r4c3<>2, r5c1<>2, r6c5<>39; stte

Phil
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Re: Patterns Game 55.35

Postby 7b53 » Sun Aug 18, 2013 6:01 am

r6c7<>19, r6c4<>1, r6c5<>9 ... as r5c1 cannot hold two digits.
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Re: Patterns Game 55.35

Postby tlanglet » Sun Aug 18, 2013 2:58 pm

Code: Select all
 *-----------------------------------------------------------*
 | 89    5789  578   | 6     4     1     | 2     3     578   |
 | 4     278   13    | 38    5     289   | 169   1679  178   |
 | 6     258   13    | 7     239   289   | 1459  1459  158   |
 |-------------------+-------------------+-------------------|
 | 5     6    b28    | 1348 b239  b289   | 7     149  *12-3  |
 | 129   3    a27    | 14   a279   6     | 1459  8    *125   |
 | 1289  789   4     | 138   2379  5     | 139   19    6     |
 |-------------------+-------------------+-------------------|
 | 27    4     6     | 5     1     3     | 8     27    9     |
 | 238   58    258   | 9     6     7     | 13    12    4     |
 | 37    1     9     | 2     8     4     | 356   567   357   |
 *-----------------------------------------------------------*

2r4c9=2r5c9-(2=79)r5c35-(9=283)r4c635 => r4c9<>3

Ted
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Re: Patterns Game 55.35

Postby Marty R. » Sun Aug 18, 2013 4:41 pm

Code: Select all
+---------------+---------------+---------------+
| 89   5789 578 | 6    4    1   | 2    3    578 |
| 4    278  13  | 38   5    289 | 169  1679 178 |
| 6    258  13  | 7    239  289 | 1459 1459 158 |
+---------------+---------------+---------------+
| 5    6    28  | 1348 239  289 | 7    149  123 |
| 129  3    27  | 14   279  6   | 1459 8    125 |
| 1289 789  4   | 138  2379 5   | 139  19   6   |
+---------------+---------------+---------------+
| 27   4    6   | 5    1    3   | 8    27   9   |
| 238  58   258 | 9    6    7   | 13   12   4   |
| 37   1    9   | 2    8    4   | 356  567  357 |
+---------------+---------------+---------------+

Play this puzzle online at the Daily Sudoku site

Overlapping M-Wings on 19 in b46

(9=1)r6c8-r6c1=(1-9)r5c1=r6c12=>r6c57<>9
(1=9)r6c8-r6c12=(9-1)r5c1=r6c1=>r6c47<>1=>r6c7<>19
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Re: Patterns Game 55.35

Postby Leren » Mon Aug 19, 2013 7:57 am

In addition to Phil's M Ring Type B there are also:

An M Ring Type C : (2=7) r5c3 - r6c2 = (7-2) r6c5 = r6c1 loop => - 2 r4c3, r5c1, - 39 r6c5; and

An M Ring Type D: (1=9) r6c8 - r6c12 = (9-1) r5c1 = r6c1 loop => - 2 r5c1, - 1 r6c47, - 9 r6c57.

For Types C and D you can swap the role of the two digits for a complementary Type C or D in the same 2 digits
(which looks like it's always the case for Types C and D), so there are 3 (or 5 ? ) M Rings in this puzzle.

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Re: Patterns Game 55.35

Postby daj95376 » Mon Aug 19, 2013 5:20 pm

Leren wrote:In addition to Phil's M Ring Type B there are also:

An M Ring Type C : (2=7) r5c3 - r6c2 = (7-2) r6c5 = r6c1 loop => - 2 r4c3, r5c1, - 39 r6c5; and

An M Ring Type D: (1=9) r6c8 - r6c12 = (9-1) r5c1 = r6c1 loop => - 2 r5c1, - 1 r6c47, - 9 r6c57.

For Types C and D you can swap the role of the two digits for a complementary Type C or D in the same 2 digits
(which looks like it's always the case for Types C and D), so there are 3 (or 5 ? ) M Rings in this puzzle.

My MWSL-Wing/Loop solver blocks equivalent loops and (I've forgotten how) chooses an appropriate starting point and direction as well.

Code: Select all
 +--------------------------------------------------------------+
 |  89    5789  578   |  6     4     1     |  2     3     578   |
 |  4     278   13    |  38    5     289   |  169   1679  178   |
 |  6     258   13    |  7     239   289   |  1459  1459  158   |
 |--------------------+--------------------+--------------------|
 |  5     6     28    |  1348  239   289   |  7     149   123   |
 |  129   3     27    |  14    279   6     |  1459  8     125   |
 |  1289  789   4     |  138   2379  5     |  139   19    6     |
 |--------------------+--------------------+--------------------|
 |  27    4     6     |  5     1     3     |  8     27    9     |
 |  238   58    258   |  9     6     7     |  13    12    4     |
 |  37    1     9     |  2     8     4     |  356   567   357   |
 +--------------------------------------------------------------+
 # 88 eliminations remain

 M-Ring  B (2=7)r5c3 - r5c5  = (7-2)r6c5 = (2)r6c1 - loop  =>  r4c3,r5c1<>2, r6c5<>39
 M-Ring  C (2=7)r5c3 - r6c2  = (7-2)r6c5 = (2)r6c1 - loop  =>  r4c3,r5c1<>2, r6c5<>39
 M-Ring  D (1=9)r6c8 - r6c12 = (9-1)r5c1 = (1)r6c1 - loop  =>  r6c4<>1, r5c1<>2, r6c5<>9, r6c7<>19
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