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Free Press Sep 17, 2010

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Sep 18, 2010 3:17 pm    Post subject: Free Press Sep 17, 2010 Reply with quote
Not yet started.
Code:

Puzzle: FP091710
+-------+-------+-------+
| . . . | . 1 . | . . 9 |
| . 3 9 | . 4 . | . 6 . |
| . . . | 9 . 6 | . . 8 |
+-------+-------+-------+
| . . . | 3 . 4 | . 2 6 |
| . 6 . | . . . | . 7 . |
| 3 7 . | 6 . 8 | . . . |
+-------+-------+-------+
| 1 . . | 7 . . | . . . |
| . 2 . | . 3 . | 4 9 . |
| 5 . . | . 8 . | . . . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

Keith
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Sep 18, 2010 4:10 pm    Post subject: Reply with quote
Quote:
UR1 15; XY -135.

Keith
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Mon Sep 20, 2010 2:53 pm    Post subject: Reply with quote
keith wrote:
Quote:
UR1 15; XY -135.

Keith


Keith, I got the same solution as you posted.

As an aside, I initially found an interesting Type 2 UR.

The code after basics:
Code:
*--------------------------------------------------------------------*
 | 24678  58     24568  | 258    1      3      | 257    45     9      |
 | 28     3      9      | 258    4      7      |*125    6     *125    |
 | 247    15     1245   | 9      25     6      | 2357   345    8      |
 |----------------------+----------------------+----------------------|
 | 89     158    158    | 3      7      4      | 1589   2      6      |
 | 2489   6      2458   | 125    259    15     | 3589   7      345    |
 | 3      7      1245   | 6      259    8      | 159    15     145    |
 |----------------------+----------------------+----------------------|
 | 1      4      3      | 7      6      9      |*25     8     *25     |
 | 68     2      68     | 15     3      15     | 4      9      7      |
 | 5      9      7      | 4      8      2      | 6      13     13     |
 *--------------------------------------------------------------------*

Note the Type 2 UR(25)r27c79 marked *. As a Type 2 UR, this pattern does not make any deletions since no other "1"s exist in row 2 or box3. However, if we look at the Type 2 UR as another AUR and perfrom an external analysis we find the following.

Digit 2 For AUR cells r2c79, we have two house choices: row2 which consists of r2c14=2 or col7/box3 which consists of r13c7. For AUR cells r7c79, we can select the box9 house which is empty.
DIgit 5 Many external cells containing digit 5 share a house with the four AUR cells. However, if we select row2 as the house to cover AUR cells r2c79 and box9 as the house to cover AUR cells r7c79, then the only external cell containing a 5 is r2c4=5.

At his point we a choice of houses, row2 or col7/box3, for digit 2 plus r2c4=5 for digit 5. We only require one house to cover digit 2, but in this case the result in the same for either house. For house row2 we get the following:
If r2c14=2, then r2c79<>2, then r13c7=2, then r7c7=5, then r2c7<>5
If r2c4=5, then r2c7<>5 thus r2c7<>5

Or if we use the col7/box3 house for digit 2, then:
If r13c7=2, then r7c7=5, then r2c7<>5
If r2c4=5, then r2c7<>5 thus r2c7<>5

In summary we obtained a deletion from a Type 2 UR that did not directly provide a deletion. (And yes, in this case the deletion was not obviously useful but maybe next time it will be a one step solution. That is Sudoku!)

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Mon Sep 20, 2010 3:45 pm    Post subject: Reply with quote
Ted, an alternate way to derive your elimination.

Code:
*) <25> Naked Pair in [r7]

*) strong link in [c9] on <2>

*) r2c7=5, r7c7=2, r7c9=5, r2c9=2 ; DP

*) r2c7<>5   q.e.d.
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Mon Sep 20, 2010 9:21 pm    Post subject: Reply with quote
daj95376 wrote:
Ted, an alternate way to derive your elimination.

Code:
*) <25> Naked Pair in [r7]

*) strong link in [c9] on <2>

*) r2c7=5, r7c7=2, r7c9=5, r2c9=2 ; DP

*) r2c7<>5   q.e.d.


I believe that the pattern can also be called a Type 4 UR given the presence of the strong link, and maybe even a "Hidden" UR (or does a Hidden UR only have one cell without extra digits).

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Mon Sep 20, 2010 10:20 pm    Post subject: Reply with quote
tlanglet wrote:
I believe that the pattern can also be called a Type 4 UR given the presence of the strong link, and maybe even a "Hidden" UR (or does a Hidden UR only have one cell without extra digits).

It's not a UR Type 4 because neither UR value is in an X-Wing pattern. As for a Hidden UR, my notes indicate a single bivalue cell and the elimination occurs in the cell common to both strong links.

What I do have is a "template" UR pattern that can be applied multiple times with respect to a UR Type 1 and Type 4. The "template" accounts for a single elimination, and that's what we have here.

Code:
===== ===== ===== ===== template for Unique Rectangle Type 1/4
                        (*) bivalues w/ 2x strong links in an "L" pattern

+--------------+
|  .   .   .   |
| 1x-2 .  12y  |
|  .   .   .   |
+--------------+
|*12   . *12   |<  strong link on <1>
|  .   .   .   |
|  .   .   .   |
+--------------+
           ^       strong link on <1>
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ronk



Joined: 07 May 2006
Posts: 398
PostPosted: Mon Sep 20, 2010 11:34 pm    Post subject: Reply with quote
daj95376 wrote:
What I do have is a "template" UR pattern that can be applied multiple times with respect to a UR Type 1 and Type 4. The "template" accounts for a single elimination, and that's what we have here.

Code:
===== ===== ===== ===== template for Unique Rectangle Type 1/4
                        (*) bivalues w/ 2x strong links in an "L" pattern

+--------------+
|  .   .   .   |
| 1x-2 .  12y  |
|  .   .   .   |
+--------------+
|*12   . *12   |<  strong link on <1>
|  .   .   .   |
|  .   .   .   |
+--------------+
           ^       strong link on <1>

That elimination doesn't require a strong link in row 4.

(x)r2c1 = (y-1)r2c3 = (1)r4c3 - (1=2)r4c1 ==> r2c1<>2
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Tue Sep 21, 2010 2:00 am    Post subject: Reply with quote
ronk wrote:
That elimination doesn't require a strong link in row 4.

I created my "template" quite awhile back and now agree that the strong link in [r4] is extraneous. It works with the bivalue cells and one strong link on <1>:

Code:
 *           *           *
(2)r2c1 - (2=1)r4c1 - (1=2)r4c3 ; DP contradiction  =>  r2c1<>2
                      ( =1)r2c3
                         *

Thanks!
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