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Puzzle 11/04/19: A Moderate

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Apr 19, 2011 2:58 pm    Post subject: Puzzle 11/04/19: A Moderate Reply with quote

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

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Marty R.



Joined: 12 Feb 2006
Posts: 5121
Location: Rochester, NY, USA

PostPosted: Thu Apr 21, 2011 12:44 am    Post subject: Reply with quote

I think I read something by Keith that said you have the equivalent of Remote Pairs if you have a chain that starts and ends with the same pair even if some of the intermediate cells are not that pair.

Remote Pairs (36), as above; r1c3<>36
Remote Pairs (36), conventional; r2c3<>36
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peterj



Joined: 26 Mar 2010
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Location: London, UK

PostPosted: Fri Apr 22, 2011 8:07 am    Post subject: Reply with quote

Marty, nice spot on the first "remote pair"!
If I am interpreting you correctly the key feature is the 3 and 6 ERI in block 2; or thinking more like an xy-chain, the two ALS(3=679) and ALS(6=379) in r123c4.

I dont think it is sufficient to be a "remote pair" just if the last two cells are the same pair - that won't give you both eliminations usually. Each strong link in the chain has to be both A=B and B=A (in the same direction over the same cells). So directly as a bivalue or as an ALS(ABcdef)[A=B] or as an ERI .... or something.. not sure I am describing that entirely right!
[Edit. See link to Keith's post. My understanding of remote-pair is probably too restrictive!]


Last edited by peterj on Fri Apr 22, 2011 5:15 pm; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
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PostPosted: Fri Apr 22, 2011 3:37 pm    Post subject: Reply with quote

Peter, I don't have any intermediate grids to know anything about particular cells. Also, sorry, but I'm not understanding your post with the talk about ALS and ERIs.
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peterj



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PostPosted: Fri Apr 22, 2011 3:58 pm    Post subject: Reply with quote

Marty R. wrote:
Also, sorry, but I'm not understanding your post

Fair enough. I was assuming your chains for the first "remote pair" were..
Code:
(3): (3=6)r6c3 - (6=3)r4c1 - (3=6)r4c5 - (6=3)r5c4 - (3)r123c4=r1c6 ; r1c3<>3
(6): (6=3)r6c3 - (3=6)r4c1 - (6=3)r4c5 - (3=6)r5c4 - (6)r123c4=r1c6 ; r1c3<>6

with the second conventional remotepair instead ending with (36)r5c8, (36)r2c8.

It's not important, I just sometimes take the time to understand your less conventional moves and as you don't write them down explicitly it's not always straightforward Smile
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Marty R.



Joined: 12 Feb 2006
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PostPosted: Fri Apr 22, 2011 4:43 pm    Post subject: Reply with quote

Peter, I can't follow the notation. I did this again. I started with a 3 in r1c6, went through box 8, then r7c1, r4c1 and r6c3. Even though that seemed to prove that r1c3<>3. I assumed, based on what I thought I knew, that it qualified as Remote Pairs and eliminated both the 36 from r1c3.

I subsequently tested that if r1c6=6, then r6c3<>6, so the elimination of both 36 from r1c3 was valid.

Whether that was a coincidence or not, I don't know now. I may have misinterpreted Keith's 2nd post here:

http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2143

Code:

+-----------------+-------------+----------+
| 4   5     369   | 369  2  36  | 8 1  7   |
| 8   13679 13679 | 3679 5  4   | 2 36 369 |
| 367 3679  2     | 3679 8  1   | 5 4  369 |
+-----------------+-------------+----------+
| 36  14    14    | 8    36 5   | 9 7  2   |
| 5   79    79    | 36   4  2   | 1 36 8   |
| 2   8     36    | 1    9  7   | 4 5  36  |
+-----------------+-------------+----------+
| 37  2     5     | 4    37 9   | 6 8  1   |
| 1   467   4678  | 2    67 68  | 3 9  5   |
| 9   36    368   | 5    1  368 | 7 2  4   |
+-----------------+-------------+----------+

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peterj



Joined: 26 Mar 2010
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PostPosted: Fri Apr 22, 2011 5:00 pm    Post subject: Reply with quote

Marty, thanks for taking the time to explain.
I guess I have always thought of remote-pairs as a chain of bivalues/als rather than two remote pairs connected by bilocation strong links. Name's eh?
Thanks for the link to Keiths post - very informative.
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keith



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

PostPosted: Fri Apr 22, 2011 9:02 pm    Post subject: Reply with quote

Marty asked my opinion. After basics, with coloring on 3:
Code:
+-------------------+-------------------+-------------------+
| 4     5     369   | 369   2     36A   | 8     1     7     |
| 8     13679 13679 | 3679  5     4     | 2     36A   369   |
| 367   3679  2     | 3679  8     1     | 5     4     369   |
+-------------------+-------------------+-------------------+
| 36A   14    14    | 8     36a   5     | 9     7     2     |
| 5     79    79    | 36A   4     2     | 1     36a   8     |
| 2     8     36a   | 1     9     7     | 4     5     36A   |
+-------------------+-------------------+-------------------+
| 37a   2     5     | 4     37A   9     | 6     8     1     |
| 1     467   4678  | 2     67    68    | 3     9     5     |
| 9     36    368   | 5     1     368a  | 7     2     4     |
+-------------------+-------------------+-------------------+

Any two cells A and a are pincers on 3. If they both happen to be <36> they are a remote pair. In particular, R6C3 makes a (classic) remote pair with R2C8 and another (general) remote pair with R1C6.

(You can reach the same conclusion by coloring on 6, but you only need one variable to establish the remote pairs.)

Keith


Last edited by keith on Fri Apr 22, 2011 9:39 pm; edited 1 time in total
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ronk



Joined: 07 May 2006
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PostPosted: Fri Apr 22, 2011 9:18 pm    Post subject: Reply with quote

Will the real remote pair please stand up?
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keith



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

PostPosted: Fri Apr 22, 2011 9:53 pm    Post subject: Reply with quote

"When I use a word," Humpty Dumpty said, in a rather scornful tone, "it means just what I choose it to mean--neither more nor less."

- Lewis Carroll Laughing
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daj95376



Joined: 23 Aug 2008
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PostPosted: Fri Apr 22, 2011 10:35 pm    Post subject: Reply with quote

Consider the following chains (that I created from Keith's grid):

Code:
(    3)r1c6 = r9c6 - r7c5 = r4c5 - r4c1 = (3    )r6c3  =>  r1c3<>3
(6=  3)r1c6 - r9c6 = r7c5 - r4c5 = r4c1 - (3  =6)r6c3  =>  r1c3<>6

+-------------------+-------------------+-------------------+
| 4     5     369   | 369   2     36A   | 8     1     7     |
| 8     13679 13679 | 3679  5     4     | 2     36A   369   |
| 367   3679  2     | 3679  8     1     | 5     4     369   |
+-------------------+-------------------+-------------------+
| 36A   14    14    | 8     36a   5     | 9     7     2     |
| 5     79    79    | 36A   4     2     | 1     36a   8     |
| 2     8     36a   | 1     9     7     | 4     5     36A   |
+-------------------+-------------------+-------------------+
| 37a   2     5     | 4     37A   9     | 6     8     1     |
| 1     467   4678  | 2     67    68    | 3     9     5     |
| 9     36    368   | 5     1     368a  | 7     2     4     |
+-------------------+-------------------+-------------------+

When all of the links (used) on <3> are strong links (conjugate pairs), then the general Remote Pair works.

Coloring is a convenient way to create a chain of strong links for a value. Checking for identical bivalue cells with different colors is all that remains.


Last edited by daj95376 on Sat Apr 23, 2011 2:38 am; edited 1 time in total
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keith



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PostPosted: Sat Apr 23, 2011 1:50 am    Post subject: Reply with quote

Danny,

Thank you for that. Your chains clearly show how both eliminations can be made with essentially identical logic.

Except: r4c6 in your chains should be r4c5.

Humpty
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