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XY-Loop--yet again

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5158
Location: Rochester, NY, USA

PostPosted: Fri Nov 19, 2010 5:42 pm    Post subject: XY-Loop--yet again Reply with quote

Here I am after a UR and a couple of X-Wings:

Code:

+-------------+-----------+------------+
| 6  247  8   | 5  24  1  | 249 79  3  |
| 34 127  27  | 9  238 6  | 5   178 24 |
| 5  1234 9   | 23 7   48 | 248 18  6  |
+-------------+-----------+------------+
| 2  5    4   | 8  1   7  | 6   3   9  |
| 1  9    3   | 6  5   2  | 7   4   8  |
| 8  67   67  | 4  9   3  | 1   2   5  |
+-------------+-----------+------------+
| 7  2348 25  | 23 6   9  | 248 58  1  |
| 34 268  1   | 7  238 5  | 289 689 24 |
| 9  2468 256 | 1  248 48 | 3   568 7  |
+-------------+-----------+------------+

Play this puzzle online at the Daily Sudoku site

I've done this a couple of times and ended with an invalidity and wonder if I'm messing up a loop. Consider this loop:

R7c3=5-->r7c8=8-->r3c8=1-->r2c8=7-->r2c3=2

First, is it still considered an XY-Loop if there's a non-bivalue cell, i.e., r2c8?

As to eliminations, I feel confident about eliminating the 2 from r9c3. What about the 8s from c8? Can I eliminate 8 from c8r289? I think I've got the eliminations down pretty well when all cells are bivalue, but I'm confused where there are polyvalue cells.
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Fri Nov 19, 2010 10:09 pm    Post subject: Reply with quote

Marty,

This is some kind of loop, but not an XY-loop. I don't know what to call it.

First, you are not done with basics. If you were, the puzzle reveals an XYZ-wing and then an XY-wing to solve it.

But, to return to your question. In the cells you quote, we have the following:

If R7C3 = 5: (Counterclockwise)
Code:
+-------------+-----------+------------+
| 6  247  8   | 5  24  1  | 249 79  3  |
| 34 127  @2  | 9  238 6  | 5   @7  24 |
| 5  1234 9   | 23 7   48 | 248 @1  6  |
+-------------+-----------+------------+
| 2  5    4   | 8  1   7  | 6   3   9  |
| 1  9    3   | 6  5   2  | 7   4   8  |
| 8  67   67  | 4  9   3  | 1   2   5  |
+-------------+-----------+------------+
| 7  2348 *5  | 23 6   9  | 248 @8  1  |
| 34 268  1   | 7  238 5  | 289 689 24 |
| 9  2468 256 | 1  248 48 | 3   568 7  |
+-------------+-----------+------------+


If R7C3 = 2: (Clockwise)
Code:
+-------------+-----------+------------+
| 6  247  8   | 5  24  1  | 249 79  3  |
| 34 127  @7  | 9  238 6  | 5   @18 24 |
| 5  1234 9   | 23 7   48 | 248 18  6  |
+-------------+-----------+------------+
| 2  5    4   | 8  1   7  | 6   3   9  |
| 1  9    3   | 6  5   2  | 7   4   8  |
| 8  67   67  | 4  9   3  | 1   2   5  |
+-------------+-----------+------------+
| 7  2348 *2  | 23 6   9  | 248 @5  1  |
| 34 268  1   | 7  238 5  | 289 689 24 |
| 9  2468 256 | 1  248 48 | 3   568 7  |
+-------------+-----------+------------+

Pincers on:
1: R23C8
2: R27C3
5: R7C38
7: R2C38
8: R237C8

and there are a number of eliminations. Unfortunately, they do not seem to progress the puzzle.

If you made an error, look closely at what you have for pincers on 8.

> Can I eliminate 8 from c8r289?

Not from c8r2.

I hope this helps.

Keith

PS: By the way, your grid after all basics:
Code:

+----------------+----------------+----------------+
| 6    247  8    | 5    24   1    | 249  79   3    |
| 34   127  27   | 9    238  6    | 5    178  24   |
| 5    1234 9    | 23   7    48   | 248  18   6    |
+----------------+----------------+----------------+
| 2    5    4    | 8    1    7    | 6    3    9    |
| 1    9    3    | 6    5    2    | 7    4    8    |
| 8    67   67   | 4    9    3    | 1    2    5    |
+----------------+----------------+----------------+
| 7    34   25   | 23   6    9    | 248  58   1    |
| 34   268  1    | 7    238  5    | 29   69   24   |
| 9    268  256  | 1    248  48   | 3    56   7    |
+----------------+----------------+----------------+
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Nov 19, 2010 10:52 pm    Post subject: Reply with quote

Code:
 Marty's Grid
 +-------------+-----------+------------+
 | 6  247  8   | 5  24  1  | 249 79  3  |
 | 34 127  27  | 9  238 6  | 5   178 24 |
 | 5  1234 9   | 23 7   48 | 248 18  6  |
 +-------------+-----------+------------+
 | 2  5    4   | 8  1   7  | 6   3   9  |
 | 1  9    3   | 6  5   2  | 7   4   8  |
 | 8  67   67  | 4  9   3  | 1   2   5  |
 +-------------+-----------+------------+
 | 7  2348 25  | 23 6   9  | 248 58  1  |
 | 34 268  1   | 7  238 5  | 289 689 24 |
 | 9  2468 256 | 1  248 48 | 3   568 7  |
 +-------------+-----------+------------+

This is not an XY-Loop. Depending on how you write the logic ...

Code:
 (2=5)r7c3 - (5=8)r7c8 - (18=7)r32c8 - (7=2)r2c3 - loop

... you have a loop where the formation of the <18> pair in r23c8 must be taken into account in the clockwise direction.

Code:
 Counter-clockwise: r7c3=5
 *-----------------------------------------------------------*
 | 6     47    8     | 5     24    1     | 249   9     3     |
 | 34    1    d2     | 9     38    6     | 5    c7     4     |
 | 5     34    9     | 23    7     48    | 248  c1     6     |
 |-------------------+-------------------+-------------------|
 | 2     5     4     | 8     1     7     | 6     3     9     |
 | 1     9     3     | 6     5     2     | 7     4     8     |
 | 8     67    67    | 4     9     3     | 1     2     5     |
 |-------------------+-------------------+-------------------|
 | 7     234  a5     | 23    6     9     | 24   b8     1     |
 | 34    268   1     | 7     238   5     | 29    69    24    |
 | 9     2468  6     | 1     248   48    | 3     56    7     |
 *-----------------------------------------------------------*

Code:
 Clockwise: r7c3=2
 *-----------------------------------------------------------*
 | 6     24    8     | 5     24    1     | 249   79    3     |
 | 34    12   b7     | 9     238   6     | 5    c18    24    |
 | 5     1234  9     | 23    7     48    | 24   c18    6     |
 |-------------------+-------------------+-------------------|
 | 2     5     4     | 8     1     7     | 6     3     9     |
 | 1     9     3     | 6     5     2     | 7     4     8     |
 | 8     67    6     | 4     9     3     | 1     2     5     |
 |-------------------+-------------------+-------------------|
 | 7     348  a2     | 3     6     9     | 48   d5     1     |
 | 34    68    1     | 7     238   5     | 289   69    24    |
 | 9     468   56    | 1     248   48    | 3     6     7     |
 *-----------------------------------------------------------*

Code:
 Eliminations: r9c3<>2, r89c8<>8   &   r2c2<>7 thanks to Keith


Last edited by daj95376 on Fri Nov 19, 2010 11:10 pm; edited 2 times in total
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Fri Nov 19, 2010 11:06 pm    Post subject: Reply with quote

daj95376 wrote:

Code:
 Eliminations: r9c3<>2, r89c8<>8


How about r2c2<>7?

Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Nov 19, 2010 11:11 pm    Post subject: Reply with quote

keith wrote:
daj95376 wrote:

Code:
 Eliminations: r9c3<>2, r89c8<>8

How about r2c2<>7?

You caught me sleeping. _ Embarassed _

I updated my post.
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Marty R.



Joined: 12 Feb 2006
Posts: 5158
Location: Rochester, NY, USA

PostPosted: Fri Nov 19, 2010 11:57 pm    Post subject: Reply with quote

Thanks Keith and Danny. My invalid elimination of 8 from r2c8 was based on what Danny told me in another thread:

"Instead of getting technical, I'm going to provide a "do this" answer.

* Look at each assignment and its corresponding elimination(s) in the loop.

* Delete that value from any cells that see the assignment and elimination cells."

I considered the 8 to be an assignment and elimination. Danny did go on to say additional instructions would be needed in loops more complicated than XY-Loops, which this obviously is.

Quote:
First, you are not done with basics.

I'm sure I'll kick myself, but even knowing I'm not done, I'm still not seeing it. Embarassed
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sat Nov 20, 2010 12:25 am    Post subject: Reply with quote

Marty R. wrote:
My invalid elimination of 8 from r2c8 was based on what Danny told me in another thread:

"Instead of getting technical, I'm going to provide a "do this" answer.

* Look at each assignment and its corresponding elimination(s) in the loop.

* Delete that value from any cells that see the assignment and elimination cells."

I considered the 8 to be an assignment and elimination.

In defense of my instructions in the other thread, it was based on the assumption of a chain. You stepped outside that assumption when you used r7c8=8 and r3c8=1 to perform r2c8<>18=7. You were then incorporating network logic because r2c8=7 does not follow from r3c8=1 alone. The easiest way for me to get around your network was to alter the representation. I did this through an ALS in the chain that I wrote above.

Regards, Danny

FWIW: When I wrote my first Sudoku solver, I spent what seemed like countless hours on the chain() routine... only to discover that it was useless because I had implemented network logic by mistake.


Last edited by daj95376 on Sat Nov 20, 2010 12:47 am; edited 1 time in total
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Sat Nov 20, 2010 12:47 am    Post subject: Reply with quote

Marty R. wrote:

Quote:
First, you are not done with basics.

I'm sure I'll kick myself, but even knowing I'm not done, I'm still not seeing it. Embarassed

Marty, your grid:
Code:
+----------------+----------------+----------------+
| 6    247  8    | 5    24   1    | 249  79   3    |
| 34   127  27   | 9    238  6    | 5    178  24   |
| 5    1234 9    | 23   7    48   | 248  18   6    |
+----------------+----------------+----------------+
| 2    5    4    | 8    1    7    | 6    3    9    |
| 1    9    3    | 6    5    2    | 7    4    8    |
| 8    67   67   | 4    9    3    | 1    2    5    |
+----------------+----------------+----------------+
| 7    2348 25   | 23   6    9    | 248  58   1    |
| 34   268  1    | 7    238  5    | 289  689  24   |
| 9    2468 256  | 1    248  48   | 3    568  7    |
+----------------+----------------+----------------+

R9C2 is not 4.
R7C2 r8C1 are a hidden pair 34.
R89B8 are not 8.
That completes the basics. There is an XYZ-wing -249 in R3C7, leading to an XY-wing -234 in R2C3.

None of this changes the discussion above.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5158
Location: Rochester, NY, USA

PostPosted: Sat Nov 20, 2010 1:56 am    Post subject: Reply with quote

Quote:
R9C2 is not 4.
R7C2 r8C1 are a hidden pair 34.
R89B8 are not 8.
That completes the basics.

I hate to be a pest, but I'm not seeing it. Of course, if r9c2<>4, then I see the hidden pair or, more appropriate for me, a 2568 quad. But I don't know why r9c2<>4 nor why r89b8<>8. I've looked and looked and see nothing in subsets or locked candidates. Question Question
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Sat Nov 20, 2010 2:07 am    Post subject: Reply with quote

Marty,

The 4 in R9 is in B8 ...

Then, after the 34 pair, the 8 in R7 is in B9.

(Or, the 4 in B8 is in R9, and the 8 in B9 is in R7.)

I am going from the grid you posted, quoted above.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5158
Location: Rochester, NY, USA

PostPosted: Sat Nov 20, 2010 2:21 am    Post subject: Reply with quote

How could I miss those 4s in box 8? Thanks again. Embarassed Embarassed
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