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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Sat Apr 02, 2011 8:04 pm Post subject: Aha! Slow Learner |
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After two and a half years, I think I finally understand something re'born tried to explain to me. Try this one:
| Code: | Puzzle: M5151065sh18WW
+-------+-------+-------+
| . 8 3 | . . . | . . . |
| . . 9 | . 4 . | . . . |
| . 7 . | . 6 2 | . . 3 |
+-------+-------+-------+
| . . . | . 5 . | . . . |
| . . . | . . 3 | . 2 1 |
| . 2 . | . 8 . | 9 . . |
+-------+-------+-------+
| . 3 . | 4 . . | . . . |
| 1 . 2 | . . . | 4 . 7 |
| . 4 7 | 9 . . | . . 8 |
+-------+-------+-------+
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Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Apr 03, 2011 1:33 am Post subject: |
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OK, after basics: | Code: | +----------------+----------------+----------------+
| 256 8 3 | 17 179 1579 | 1567 1457 2456 |
| 256 16 9 | 3 4 157 | 1567 8 256 |
| 4 7 15 | 8 6 2 | 15 9 3 |
+----------------+----------------+----------------+
| 379 16 8 | 2 5 1479 | 367 347 46 |
| 79 5 4 | 6 79 3 | 8 2 1 |
| 37 2 16a | 17 8 147 | 9 3457 456 |
+----------------+----------------+----------------+
| 8 3 56 | 4 127 167 | 125 15 9 |
| 1 9 2 | 5 3 8 | 4 6 7 |
| 56 4 7 | 9 12 16b | 1235 135 8 |
+----------------+----------------+----------------+ |
The <16> cells marked a and b are a remote pair. What eliminations do they make?
If you don't like calling them a remote pair, let's call them Stephen. Or, even better, a re'mote pair. 
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Apr 03, 2011 2:05 am Post subject: |
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| keith wrote: | OK, after basics: | Code: | +----------------+----------------+----------------+
| 256 8 3 | 17 179 1579 | 1567 1457 2456 |
| 256 16 9 | 3 4 157 | 1567 8 256 |
| 4 7 15 | 8 6 2 | 15 9 3 |
+----------------+----------------+----------------+
| 379 16 8 | 2 5 1479 | 367 347 46 |
| 79 5 4 | 6 79 3 | 8 2 1 |
| 37 2 16a | 17 8 147 | 9 3457 456 |
+----------------+----------------+----------------+
| 8 3 56 | 4 127 167 | 125 15 9 |
| 1 9 2 | 5 3 8 | 4 6 7 |
| 56 4 7 | 9 12 16b | 1235 135 8 |
+----------------+----------------+----------------+ |
The <16> cells marked a and b are a remote pair. What eliminations do they make?
If you don't like calling them a remote pair, let's call them Stephen. Or, even better, a re'mote pair.
Keith |
OK, I'll walk into the trap. As a W-Wing, r6c6<>1. With a transport, r2c6<>1. With another transport, r9c7<>1. With yet another transport, r1c78<>1. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Apr 03, 2011 2:18 am Post subject: |
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| Marty R. wrote: | | keith wrote: | OK, after basics: | Code: | +----------------+----------------+----------------+
| 256 8 3 | 17 179 -1579 | 1567 1457 2456 |
| 256 16 9 | 3 4 -157 | 1567 8 256 |
| 4 7 15 | 8 6 2 | 15 9 3 |
+----------------+----------------+----------------+
| 379 16 8 | 2 5 1479 | 367 347 46 |
| 79 5 4 | 6 79 3 | 8 2 1 |
| 37 2 16a | 17 8 -147 | 9 3457 456 |
+----------------+----------------+----------------+
| 8 3 56 | 4 127 -167 | 125 15 9 |
| 1 9 2 | 5 3 8 | 4 6 7 |
| 56 4 7 | 9 12 16b | 1235 135 8 |
+----------------+----------------+----------------+ |
The <16> cells marked a and b are a remote pair. What eliminations do they make?
If you don't like calling them a remote pair, let's call them Stephen. Or, even better, a re'mote pair.
Keith |
OK, I'll walk into the trap. As a W-Wing, r6c6<>1. With a transport, r2c6<>1. With another transport, r9c7<>1. With yet another transport, r1c78<>1. |
Marty, not a trap. The surprising answer is the eliminations of <1> in C6, shown in my edit of the quote above. No transport needed.
The other question is, I have said they are a remote pair, and you have found half of the answer, that they are a W-wing.
(Hint: Note WW in the title of this thread.)
I'll explain and expand tomorrow. (It's late here now, and I need to be careful to check the accuracy of what I post.)
Again, that Sonoma juice problem!
Keith |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Apr 03, 2011 2:41 am Post subject: |
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The eliminations are due to it being a continuous AIC loop.
(1=6)r6c3 - (6)r7c3=(6)r9c1 - (6=1)r9c6 - ER[(1)r46c6=(1)r6c46] - Loop
All of the links become conjugate. This means that the ERI cell, r6c6, cannot be <1> since it prevents the ER from being conjugate. (Or, you can consider it a direct elimination due to the Remote Pair.) This leaves (1)r9c6 and (1)r4c6 as the conjugate pair of <1>s in c6 and all other c6 <1>s are eliminated. (All the other links in the loop were already conjugate so there are no other eliminations.) |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Apr 03, 2011 3:21 am Post subject: |
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Asellus,
I do not understand anything beyond the "ER" in your chain notation.
Yes, a and b are connected by strong links in 1: R4, and in 6: R7 or B7. I do not understand your proposition.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Apr 03, 2011 3:51 am Post subject: |
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If you wish to bypass the ERI logic -- or maybe add two of Marty's elimination:
| Code: | (1=6)r6c3 - r7c3 = r9c1 - (6=1)r9c6 - r4c6 = (1)r4c2 - loop => r1267c6 <>1
(1=6)r6c3 - r7c3 = r9c1 - (6=1)r9c6 - r79c5 = r1c5 - r1c4 = (1)r6c4 - loop => r1267c6,r1c78<>1
________________________________________________________________________________________________
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I was trapped in an ugly discussion in another forum on the notation and properties of an ERI in a loop. I'm going to keep my nose out of the upcoming discussions! |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Apr 03, 2011 3:53 am Post subject: |
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| I hope so. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sun Apr 03, 2011 3:54 am Post subject: |
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| Quote: | | I'm going to keep my nose out of the upcoming discussions! |
excellent idea
me too. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Apr 03, 2011 4:54 am Post subject: |
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| Keith wrote: | | Yes, a and b are connected by strong links in 1: R4, and in 6: R7 or B7. I do not understand your proposition. |
I just happened to see the ER first. But if you prefer the strong inference in r4 to that of the ER in b5, then:
(1=6)r6c3 - (6)r7c3=(6)r9c1 - (6=1)r9c6 - (1)r4c6=(1)r4c2 - Loop
The result is exactly the same but avoids use of the ER inference. The weak inference (1)r9c6 - (1)r4c6 becomes conjugate, eliminating all other <1>s in c6. It just so happens that it was re'born who long ago was among the first to point out continuous AIC loops to me.
I don't know why the ER inference would be controversial. It is very straightforward. "(1)r46c6=(1)r6c46" essentially means "one of the <1>s in c6 of b5 is true and/or one of the <1>s in r6 of b5 is true". Both sides of the inference would be true if (and only if) the <1> in the ERI cell r6c6 is true. But once such an ER inference finds itself in a continuous AIC loop, it must be conjugate (that is, it is now impossible for both sides to be true) so the ERI cell candidate must be false.
Most of the time we only concern ourselves with the weak inferences creating eliminations as they become conjugate in a continuous AIC loop. But this ERI elimination within an ER strong inference is an example of an elimination that can result from a strong inference becoming conjugate within such a loop. In fact, it is the only case that I have encountered where an elimination results from a strong inference within a continuous AIC loop. It is a nice one to know about. I have encountered such cases a few times and I recall seeing a solution posted by Myth Jellies in which he used it. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sun Apr 03, 2011 12:12 pm Post subject: |
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| Asellus wrote: | | But this ERI elimination within an ER strong inference is an example of an elimination that can result from a strong inference becoming conjugate within such a loop. In fact, it is the only case that I have encountered where an elimination results from a strong inference within a continuous AIC loop. |
Within a continuous loop, the non-linking digits of an ALS also cause eliminations. Moreover, only one of the ALS linking digits is ultimately true, so the ALS may also be said to "become conjugate." |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Apr 03, 2011 3:32 pm Post subject: |
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| ronk wrote: | | Within a continuous loop, the non-linking digits of an ALS also cause eliminations. Moreover, only one of the ALS linking digits is ultimately true, so the ALS may also be said to "become conjugate. |
Very true. Thanks for pointing out a second case where a strong inference becoming conjugate within a continuous AIC loop can cause eliminations. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Apr 03, 2011 3:49 pm Post subject: |
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| Asellus wrote: | | I don't know why the ER inference would be controversial. |
It's not controversial. I just didn't see it at the time.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Apr 03, 2011 5:30 pm Post subject: |
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After basics: | Code: | +----------------+----------------+----------------+
| 256 8 3 | 17 179 -1579 | 1567 1457 2456 |
| 256 16 9 | 3 4 -157 | 1567 8 256 |
| 4 7 15 | 8 6 2 | 15 9 3 |
+----------------+----------------+----------------+
| 379 16c 8 | 2 5 1479d| 367 347 46 |
| 79 5 4 | 6 79 3 | 8 2 1 |
| 37 2 16a | 17 8 -147 | 9 3457 456 |
+----------------+----------------+----------------+
| 8 3 56f | 4 127 -167e | 125 15 9 |
| 1 9 2 | 5 3 8 | 4 6 7 |
| 56 4 7 | 9 12 16b | 1235 135 8 |
+----------------+----------------+----------------+ |
a and b are a W-wing eliminating 6 (strong link on 1 in R4).
a and b are a W-wing eliminating 1 (strong link on 6 in R7 or B7).
So they are a double W-wing and a remote pair, or a Stephen if you don't accept that use of the term "remote pair".
What re'born (and maybe Bud) tried to point out is that the two W-wings combine to from a closed chain, in this case a-c-d-b-e-f-a. As Asellus and ronk have already noted in this thread, all the links become strong in such a closed chain (loop).
In particular, the strong link b-d eliminates 1 in C6 as shown.
I only realized what re'born was saying recently, when I went to fix a broken link to Bud's thread. Here it is:
http://Forum.EnjoySuDoku.com/viewtopic.php?p=64249#64249
By the way, has anyone solved this puzzle? I found it at Menneske - it is not lifted from another discussion thread.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Apr 03, 2011 8:15 pm Post subject: |
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Maybe we should call it George? (As in Dubya.)
Anyway, after the WW: | Code: | +----------------+----------------+----------------+
| 256 8 3 | 17a 179b 5-79 | 567 457 2456 |
| 256 16 9 | 3 4 5-7 | 1567 8 256 |
| 4 7 15 | 8 6 2 | 15 9 3 |
+----------------+----------------+----------------+
| 379 16 8 | 2 5 1479 | 367 347 46 |
| 79 5 4 | 6 79c 3 | 8 2 1 |
| 37 2 16 | 17 8 47 | 9 3457 456 |
+----------------+----------------+----------------+
| 8 3 56 | 4 127 67d | 25 15 9 |
| 1 9 2 | 5 3 8 | 4 6 7 |
| 56 4 7 | 9 12 16 | 235 135 8 |
+----------------+----------------+----------------+ |
(The following move is in the after basics grid.)
Any cell that sees a, b, and c cannot be 7. c can be transported to d, making the eliminations shown, and solving the puzzle. 
In the after basics grid, without the WW, this reveals an X-wing that makes almost all the eliminations of the WW, and solves the puzzle.
Are these things common, or am I just a freak who happened to find two of them in as many days. (Rhetorical question! Please do not answer!)
I suppose this is a transported XYZ-wing, or simply a transported triple.
Keith |
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