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Vanhegan fiendish 4/27/12

 
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
PostPosted: Fri Apr 27, 2012 8:27 am    Post subject: Vanhegan fiendish 4/27/12 Reply with quote
Code:

 *-----------*
 |...|..2|7..|
 |.3.|.1.|.9.|
 |2.8|.3.|4..|
 |---+---+---|
 |7..|148|...|
 |.46|7.5|38.|
 |...|963|..4|
 |---+---+---|
 |..4|.7.|1.3|
 |.6.|.8.|.5.|
 |..2|3..|...|
 *-----------*
 

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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Fri Apr 27, 2012 6:04 pm    Post subject: Reply with quote
M-Wing. R6c3=5-->r1c2=5. R1c2<>1-->r1c3=1; r8c3<>1.


Code:

+--------------+-------------+--------------+
| 46  159  159 | 468  59 2   | 7    3  68   |
| 46  3    57  | 4568 1  467 | 2568 9  2568 |
| 2   79   8   | 56   3  79  | 4    1  56   |
+--------------+-------------+--------------+
| 7   25   3   | 1    4  8   | 2569 26 2569 |
| 9   4    6   | 7    2  5   | 3    8  1    |
| 158 1258 15  | 9    6  3   | 25   7  4    |
+--------------+-------------+--------------+
| 58  589  4   | 256  7  69  | 1    26 3    |
| 3   6    179 | 24   8  149 | 29   5  279  |
| 15  1579 2   | 3    59 169 | 689  4  6789 |
+--------------+-------------+--------------+

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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
PostPosted: Fri Apr 27, 2012 6:59 pm    Post subject: Reply with quote
I finally found one with an e digit Very Happy
Code:

 *-----------------------------------------------------------*
 | 46    15-9  159   | 468   59    2     | 7     3     68    |
 | 46    3     57    | 4568  1     467   | 2568  9     2568  |
 | 2    *79    8     | 56    3     79    | 4     1     56    |
 |-------------------+-------------------+-------------------|
 | 7     25    3     | 1     4     8     | 2569  26    2569  |
 | 9     4     6     | 7     2     5     | 3     8     1     |
 | 158   1258  15    | 9     6     3     | 25    7     4     |
 |-------------------+-------------------+-------------------|
 |*58   x589   4     | 256   7     69    | 1     26    3     |
 | 3     6     79-1  | 24    8     149   | 29    5     279   |
 |x15   x1579  2     | 3     59    169   | 689   4     6789  |
 *-----------------------------------------------------------*
Sue de Cog ab=79 cd=58 e=1 => r1c2<>9, r8c3<>1; stte

Applying keith's definition

An SdC exists in one box(b7) and one line(c2).

(x) sets up two intersecting sets of exactly five distinct candidates a,b,c,d, and e. One in the box and one in the line.

A cell in the line but not in the box (r2c2) contains only candidates a, b.

A cell in the box but not in the line (r7c1) contains only candidates c, d.

We can eliminate a, b, and e from all other cells in the line, and we can eliminate c, d, and e from all other cells in the box.

I hope I got it right this time.


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DonM



Joined: 15 Sep 2009
Posts: 51
PostPosted: Sat Apr 28, 2012 12:34 am    Post subject: Reply with quote
arkietech wrote:
I finally found one with an e digit Very Happy
Code:

 *-----------------------------------------------------------*
 | 46    15-9  159   | 468   59    2     | 7     3     68    |
 | 46    3     57    | 4568  1     467   | 2568  9     2568  |
 | 2    *79    8     | 56    3     79    | 4     1     56    |
 |-------------------+-------------------+-------------------|
 | 7     25    3     | 1     4     8     | 2569  26    2569  |
 | 9     4     6     | 7     2     5     | 3     8     1     |
 | 158   1258  15    | 9     6     3     | 25    7     4     |
 |-------------------+-------------------+-------------------|
 |*58   x589   4     | 256   7     69    | 1     26    3     |
 | 3     6     79-1  | 24    8     149   | 29    5     279   |
 |x15   x1579  2     | 3     59    169   | 689   4     6789  |
 *-----------------------------------------------------------*
Sue de Cog ab=79 cd=58 e=1 => r1c2<>9, r8c3<>1; stte

Applying keith's definition

An SdC exists in one box(b7) and one line(c2).

(x) sets up two intersecting sets of exactly five distinct candidates a,b,c,d, and e. One in the box and one in the line.

A cell in the line but not in the box (r2c2) contains only candidates a, b.

A cell in the box but not in the line (r7c1) contains only candidates c, d.

We can eliminate a, b, and e from all other cells in the line, and we can eliminate c, d, and e from all other cells in the box.

I hope I got it right this time.


Good find on a SDC with 5 candidates in 2 cells. The candidates used and the eliminations shown are accurate. However, the definition given above applies to only one form of SDC wherein there are 5 candidates (abcde) in 3 cells on the line in a box, a cell with candidates ab on the line outside the box and a cell cd in the box outside the line. In that case: 'We can eliminate a, b, and e from all other cells in the line, and we can eliminate c, d, and e from all other cells in the box.'

In the present case, there are 5 candidates (15789) in 2 cells on the line in the box, a cell on the line outside the box with (79) and 2 cells in the box that collectively and accurately contain (158) to satisfy this form of SDC, but in this case, we can eliminate a and b (not e) from all other cells in the line, and we can eliminate c, d, and e from all other cells in the box.

Of course, there can be other variations of SDC wherein there are 4 or 6 candidates in 2 cells or 7 candidates in 3 cells on the line in the box and so on.

Last edited by DonM on Sat Apr 28, 2012 1:15 am; edited 1 time in total
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DonM



Joined: 15 Sep 2009
Posts: 51
PostPosted: Sat Apr 28, 2012 12:38 am    Post subject: Reply with quote
DonM wrote:
arkietech wrote:
I finally found one with an e digit Very Happy
Code:

 *-----------------------------------------------------------*
 | 46    15-9  159   | 468   59    2     | 7     3     68    |
 | 46    3     57    | 4568  1     467   | 2568  9     2568  |
 | 2    *79    8     | 56    3     79    | 4     1     56    |
 |-------------------+-------------------+-------------------|
 | 7     25    3     | 1     4     8     | 2569  26    2569  |
 | 9     4     6     | 7     2     5     | 3     8     1     |
 | 158   1258  15    | 9     6     3     | 25    7     4     |
 |-------------------+-------------------+-------------------|
 |*58   x589   4     | 256   7     69    | 1     26    3     |
 | 3     6     79-1  | 24    8     149   | 29    5     279   |
 |x15   x1579  2     | 3     59    169   | 689   4     6789  |
 *-----------------------------------------------------------*
Sue de Cog ab=79 cd=58 e=1 => r1c2<>9, r8c3<>1; stte

Applying keith's definition

An SdC exists in one box(b7) and one line(c2).

(x) sets up two intersecting sets of exactly five distinct candidates a,b,c,d, and e. One in the box and one in the line.

A cell in the line but not in the box (r2c2) contains only candidates a, b.

A cell in the box but not in the line (r7c1) contains only candidates c, d.

We can eliminate a, b, and e from all other cells in the line, and we can eliminate c, d, and e from all other cells in the box.

I hope I got it right this time.


Good find on a SDC with 5 candidates in 2 cells. The candidates used and the eliminations shown are accurate. However, the definition given above applies to only one form of SDC wherein there are 5 candidates (abcde) in 3 cells on the line in a box, a cell with candidates ab on the line outside the box and a cell cd in the box outside the line. In that case: 'We can eliminate a, b, and e from all other cells in the line, and we can eliminate c, d, and e from all other cells in the box.'

In the present case, there are 5 candidates (15789) in 2 cells on the line in the box, a cell on the line outside the box with (79) and 2 cells in the box that collectively and accurately contain (158) to satisfy this form of SDC, but in this case, we can eliminate a and b (not e) from all other cells in the line, and we can eliminate c, d, and e from all other cells in the box.

Of course, there can be other variations of SDC wherein there are 4 or 6 candidates in 2 cells or 7 candidates in 3 cells on the line in the box and so on.
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
PostPosted: Sat Apr 28, 2012 1:01 am    Post subject: Reply with quote
DonM wrote:
In the present case, there are 5 candidates (15789) in 2 cells on the line in the box, a cell on the line outside the box with (79) and 2 cells in the box that collectively and accurately contain (158) to satisfy this form of SDC, but in this case, we can eliminate a and b (not e) from all other cells in the line, and we can eliminate c, d, and e from all other cells in the box.

Thanks, you are right. This(getting a good definition) is quite complex. Back to the drawing board. Confused

The e's being removed have to "see" all the e's in the set in the block...?? going to take some thought.
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SudoQ



Joined: 02 Aug 2011
Posts: 127
PostPosted: Sat Apr 28, 2012 7:51 am    Post subject: Reply with quote
You can also show that r8c3<>1 like this:
r3c2=x -> r8c3=x (x=7/9)

/SudoQ
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