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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Sat May 29, 2010 2:31 pm Post subject: Puzzle 10/05/29: (C) Advanced |
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| Code: | +-----------------------+
| 5 . . | 9 . . | . . . |
| . . . | . 7 . | . . 6 |
| . . . | 5 . . | 1 9 . |
|-------+-------+-------|
| 7 . 1 | 2 9 . | . 8 4 |
| . 8 . | 1 4 . | . . 5 |
| . . . | . . . | . 1 . |
|-------+-------+-------|
| . . 5 | . . . | 7 2 . |
| . . 7 | 4 . 2 | 9 . 1 |
| . 1 . | 7 5 . | . 6 8 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sat May 29, 2010 3:58 pm Post subject: |
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I had not the remotest idea......
| Quote: | | Remote pair 36 @ r3c1 and r5c6 removes 36 from r3c6 (!!!) solving the puzzle. |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Sat May 29, 2010 11:10 pm Post subject: |
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| Mogulmeister wrote: | I had not the remotest idea......
| Quote: | | Remote pair 36 @ r3c1 and r5c6 removes 36 from r3c6 (!!!) solving the puzzle. |
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I'd extend my admiration had you w-winged it instead  |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun May 30, 2010 1:23 am Post subject: |
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Thanks Mogulmeister for catching the general Remote Pair and giving me a chance to verify some tests in my chains() routine.
To me, a general Remote Pair is two concurrent chains -- or a single chain with additional constraints.
The first chain (below) is a generic AIC with strong and weak inferences. However, force all weak inferences in this chain to be strong links and you have a general Remote Pair. The second chain (below) shows how the additional strong links constraint results in a companion chain.
| Code: | (3=6)r3c1 - r6c1 = r5c3 - (6=3)r5c6 => r3c6<>3
( 6)r3c1 = r6c1 - r5c3 = (6 )r5c6 => r3c6<>6
+--------------------------------------------------------------+
| 5 47 36 | 9 126 1346 | 8 34 27 |
| 1 2 9 | 38 7 348 | 5 34 6 |
| a36 47 8 | 5 26 346 | 1 9 27 |
|--------------------+--------------------+--------------------|
| 7 3 1 | 2 9 5 | 6 8 4 |
| 9 8 c26 | 1 4 d36 | 23 7 5 |
| b26 5 4 | 368 68 7 | 23 1 9 |
|--------------------+--------------------+--------------------|
| 4 9 5 | 68 168 168 | 7 2 3 |
| 8 6 7 | 4 3 2 | 9 5 1 |
| 23 1 23 | 7 5 9 | 4 6 8 |
+--------------------------------------------------------------+
# 34 eliminations remain
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As wapati indicated, the first chain is a W-Wing that's sufficient to crack the puzzle.
[Edit: demoted "General" to "general" thanks to ronk keeping my feet planted on the ground.  ]
Last edited by daj95376 on Sun May 30, 2010 5:26 am; edited 1 time in total |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Sun May 30, 2010 2:10 am Post subject: |
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Thanks daj,
I learn sudoku stuff every day, thanks to your posts and the replies to them. |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Sun May 30, 2010 2:17 am Post subject: |
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| daj95376 wrote: | Thanks Mogulmeister for catching the General Remote Pair and giving me a chance to verify some tests in my chains() routine.
To me, a General Remote Pair is two concurrent chains -- or a single chain with additional constraints.
The first chain (below) is a generic AIC with strong and weak inferences. However, force all weak inferences in this chain to be strong links and you have a General Remote Pair. The second chain (below) shows how the additional strong links constraint results in a companion chain.
| Code: | (3=6)r3c1 - r6c1 = r5c3 - (6=3)r5c6 => r3c6<3> r3c6<>6
+--------------------------------------------------------------+
| 5 47 36 | 9 126 1346 | 8 34 27 |
| 1 2 9 | 38 7 348 | 5 34 6 |
| a36 47 8 | 5 26 346 | 1 9 27 |
|--------------------+--------------------+--------------------|
| 7 3 1 | 2 9 5 | 6 8 4 |
| 9 8 c26 | 1 4 d36 | 23 7 5 |
| b26 5 4 | 368 68 7 | 23 1 9 |
|--------------------+--------------------+--------------------|
| 4 9 5 | 68 168 168 | 7 2 3 |
| 8 6 7 | 4 3 2 | 9 5 1 |
| 23 1 23 | 7 5 9 | 4 6 8 |
+--------------------------------------------------------------+
# 34 eliminations remain
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As wapati indicated, the first chain is a W-Wing that's sufficient to crack the puzzle. |
Well, I was told it was there and looked for how.
I would not find this using pen/paper. Above my level, this method. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sun May 30, 2010 3:11 am Post subject: |
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I used a flightless xy-wing 2-36 with vertex r6c1 plus transport: (3)r6c7 - r5c7 = (3)r5c6; r3c6<>3 to complete the puzzle.
This obviously uses many of the same cells as posted by MM, but a different pattern.
Ted |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sun May 30, 2010 3:16 am Post subject: |
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An alternate one step solution is the AUR34 in r12c68. The outside row implications to prevent the deadly pattern are (4)r1c2 = (3)r2c4 - (3=4)r2c8; r1c8<>4.
Ted |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sun May 30, 2010 3:40 am Post subject: |
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| daj95376 wrote: | | To me, a General Remote Pair is two concurrent chains -- or a single chain with additional constraints. |
When the overlapping patterns are a kite and a w-wing, is it a Brigadier General Remote Pair ... or a Lieutenant General Remote Pair? I've forgotten.  |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun May 30, 2010 5:30 am Post subject: |
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After all of the above discussion, this solution is probably anti-climactic.
| Code: | r5c1 2-String Kite <> 6 r3c6
<68> UR r67c45 [(1)r7c5 = (3)r6c4] - (3=6)r5c6 - (6=1)r1c6 - r1c5 = (1)r7c5
+-----------------------------------------------------+
| 5 47 36 | 9 126 16 | 8 34 27 |
| 1 2 9 | 38 7 348 | 5 34 6 |
| 36 47 8 | 5 26 34 | 1 9 27 |
|-----------------+-----------------+-----------------|
| 7 3 1 | 2 9 5 | 6 8 4 |
| 9 8 26 | 1 4 36 | 23 7 5 |
| 26 5 4 | 368 68 7 | 23 1 9 |
|-----------------+-----------------+-----------------|
| 4 9 5 | 68 168 168 | 7 2 3 |
| 8 6 7 | 4 3 2 | 9 5 1 |
| 23 1 23 | 7 5 9 | 4 6 8 |
+-----------------------------------------------------+
# 31 eliminations remain
BUG+1 = 3 r2c6
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sun May 30, 2010 8:40 am Post subject: |
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| daj95376 wrote: |
As wapati indicated, the first chain is a W-Wing that's sufficient to crack the puzzle. |
Indeed - but then you can't say.."36 to eliminate 36 in 36!" 
| daj95376 wrote: |
[Edit: demoted "General" to "general" thanks to ronk keeping my feet planted on the ground. ] |
"I am the very model of a modern Major-General". |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Sun May 30, 2010 9:35 am Post subject: |
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| daj95376 wrote: | Thanks Mogulmeister for catching the general Remote Pair and giving me a chance to verify some tests in my chains() routine.
To me, a general Remote Pair is two concurrent chains -- or a single chain with additional constraints.
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I have in the past found instances where the double elimination is needed to solve the puzzle - but I didn't keep them. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon May 31, 2010 4:42 am Post subject: |
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| Same as Ted; XY-Wing (263), flightless, with pincer transport. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon May 31, 2010 11:05 am Post subject: |
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| Quote: | | To me, a general Remote Pair is two concurrent chains -- or a single chain with additional constraints. |
Danny, can you explain this one in your terms? I see only one chain (on 6).
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon May 31, 2010 4:08 pm Post subject: |
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| keith wrote: | Danny, can you explain this one in your terms? I see only one chain (on 6).
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Here are the two concurrent chains from my post above.
| Code: | (3=6)r3c1 - r6c1 = r5c3 - (6=3)r5c6 => r3c6<>3
( 6)r3c1 = r6c1 - r5c3 = (6 )r5c6 => r3c6<>6
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In the first chain, I assume that r3c1<>3 and derive r5c6=3.
In the second chain, I assume that r3c1<>6 and derive r5c6=6.
The combined effect is r3c6<>36.
I'm unaware of any single chain that can explain a general (or traditional) Remote Pair. In each case, it's 2x concurrent chains that account for the eliminations.
Note: As ronk mentioned, this is concurrently a W-Wing and a Kite in the same cells. Of course, if more than four cells exist in the general Remote Pair, then this description has to be altered slightly.
Regards, Danny |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon May 31, 2010 5:51 pm Post subject: |
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Danny,
You wrote:
( 6)r3c1 = r6c1 - r5c3 = (6 )r5c6 => r3c6<>6
As written, ONE OR BOTH of r3c1 and r5c6 is <6>
However, in this example, the link r6c1 r5c3 is strong:
( 6)r3c1 = r6c1 = r5c3 = (6 )r5c6 => r3c6<>6
ONE of r3c1 and r5c6 is <6>. The other is <>6. Therefore one of them is <3>. You do not need another chain.
Keith |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Mon May 31, 2010 8:42 pm Post subject: |
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| keith wrote: | ( 6)r3c1 = r6c1 - r5c3 = (6 )r5c6 => r3c6<>6
As written, ONE OR BOTH of r3c1 and r5c6 is <6>
However, in this example, the link r6c1 r5c3 is strong:
( 6)r3c1 = r6c1 = r5c3 = (6 )r5c6 => r3c6<>6
ONE of r3c1 and r5c6 is <6>. The other is <>6. Therefore one of them is <3>. You do not need another chain. |
If you do that, you'll end up using the same '=' symbol for both strong inferences and conjugate links (your 'strong links' apparently) That's bound to cause confusion. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon May 31, 2010 9:52 pm Post subject: |
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| keith wrote: | Danny,
You wrote:
( 6)r3c1 = r6c1 - r5c3 = (6 )r5c6 => r3c6<>6
As written, ONE OR BOTH of r3c1 and r5c6 is <6>
However, in this example, the link r6c1 r5c3 is strong:
( 6)r3c1 = r6c1 = r5c3 = (6 )r5c6 => r3c6<>6
ONE of r3c1 and r5c6 is <6>. The other is <>6. Therefore one of them is <3>. You do not need another chain.
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| I wrote: | To me, a general Remote Pair is two concurrent chains -- or a single chain with additional constraints.
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Okay, I see your point and realize that the discrepancy is in the use of the word chain. I've relied on AICs for so long that I almost forgot that other chain logic exists. In my AIC ...
| Code: | ( 6)r3c1 = r6c1 - r5c3 = (6 )r5c6 => r3c6<>6
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... it guarantees that at least one of r3c1=6 or r5c6=6 is true, but it does not exclude the possibility that both might be true. Thus the need for a separate chain for <3>. Your chain is based on strong links ...
| Code: | ( 6)r3c1 = r6c1 = r5c3 = (6 )r5c6 => r3c6<>6
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... and it's impossible for both r3c1=6 and r5c6=6 to be true. Thus, you force r3c1=3 or r5c6=3 as a defacto situation because these cells are identical bivalue cells. To my knowledge, your chain can't be expressed as an AIC without an additional constraint -- namely that all weak inferences are supported by strong links. Without the additional constraint, it takes 2x AICs. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon May 31, 2010 11:39 pm Post subject: |
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Danny,
I think we agree!
Now, I suppose you could argue that the chain of strong links is actually two; One in each direction. You have to prove A implies not A in both directions.
(Somehow, you are connecting two cells with bivalue candidates AB.)
Which is different than proving A implies not A, and also B implies not B in the same direction.
From a VERY stormy SE Michigan.
Keith |
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