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ravel
Joined: 21 Apr 2006
Posts: 536
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 Posted: Fri Feb 29, 2008 8:41 pm Post subject: Almost remote pairs |
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| Code: | 1 . . | . 2 . | . . 3
. 4 . | . . . | . 5 .
. . . | 3 . 6 | . . .
- - - + - - - + - - -
. . 5 | . . . | 7 . .
4 . . | . 6 . | . . 1
. . 8 | . . . | 2 . .
- - - + - - - + - - -
. . . | 8 . 5 | . . .
. 9 . | . . . | . 1 .
8 . . | . 3 . | . . 4 TTHsieh |
>>> play online
There are at least 2 ways to solve it with a remote pair variant. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Feb 29, 2008 9:27 pm Post subject: |
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(I think we are all about to learn something.)
Working through the basics is a challenge on this one. You might get to here:
| Code: | +-------------------+-------------------+-------------------+
| 1 78 67 | 5 2 49 | 49 678 3 |
| 23 4 36 | 179 89 1789 | 19 5 26 |
| 5 278 9 | 3 14 6 | 14 278 278 |
+-------------------+-------------------+-------------------+
| 69 123 5 | 124 89 123 | 7 34 689 |
| 4 237 27 | 279 6 23789 | 5 389 1 |
| 679 1367 8 | 1479 5 1379 | 2 3469 69 |
+-------------------+-------------------+-------------------+
| 67 267 14 | 8 14 5 | 3 279 279 |
| 23 9 34 | 6 7 24 | 8 1 5 |
| 8 5 127 | 129 3 129 | 6 27 4 |
+-------------------+-------------------+-------------------+ |
I will now see if I can take it further.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Feb 29, 2008 9:34 pm Post subject: |
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There is a UR with strong links on <69> in R46C16. R4C9 cannot be <9>, R6C1 cannot be <6>. Leading to an XY-wing, leading to here:
| Code: | +-------------------+-------------------+-------------------+
| 1 78 67 | 5 2 49 | 49 678 3 |
| 23 4 36 | 179 89 1789 | 19 5 26 |
| 5 278 9 | 3 14 6 | 14 278 278 |
+-------------------+-------------------+-------------------+
| 69 123 5 | 124 89 123 | 7 34 68 |
| 4 237 27 | 279 6 23789 | 5 389 1 |
| 79 1367 8 | 147 5 137 | 2 3469 69 |
+-------------------+-------------------+-------------------+
| 67 267 14 | 8 14 5 | 3 279 279 |
| 23 9 34 | 6 7 24 | 8 1 5 |
| 8 5 127 | 129 3 129 | 6 27 4 |
+-------------------+-------------------+-------------------+
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HMMM ...  |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Feb 29, 2008 9:50 pm Post subject: |
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I have solved it!
The pattern will be found by Medusa multicoloring on <6> and <7>, but you do not have to resort to that. I am not sure I would have found this one without ravel's hints.
I'll wait a while to post the details.
And, ravel said there are two ways ...
Keith
(ravel, thank you! My kind of puzzle.) |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Feb 29, 2008 10:16 pm Post subject: |
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| Quote: |
The pattern will be found by Medusa multicoloring on <6> and <7> |
Not looking to open a can of worms here, but what is Medusa multicoloring? Is that something different from what I know as extended Medusa? |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Fri Feb 29, 2008 11:00 pm Post subject: |
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I found this one after exploring a Type 3 UR [23] in R28C13, and a Type 6 UR [69] in R46C19 which places <3> in R5C2.
When R2C9=|6| => R4C9≠|6| => R4C1=|6| => R6C1=|9| => R6C9=|6| <=> R2C9≠6 collapsing the puzzle
| Code: | +--------------------------+--------------------------+--------------------------+
| 1 78 67 | 5 2 49 | 49 678 3 |
| 23 4 236 | 179 89 1789 | 19 5 2|6| |
| 5 278 9 | 3 14 6 | 14 278 278 |
+--------------------------+--------------------------+--------------------------+
||6|9 123 5 | 124 89 123 | 7 34 -|6|89 |
| 4 237 27 | 279 6 23789 | 5 389 1 |
| 67|9| 1367 8 | 1479 5 1379 | 2 3469 |6|9 |
+--------------------------+--------------------------+--------------------------+
| 67 267 14 | 8 14 5 | 3 279 279 |
| 23 9 234 | 6 7 24 | 8 1 5 |
| 8 5 127 | 129 3 129 | 6 27 4 |
+--------------------------+--------------------------+--------------------------+ |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Feb 29, 2008 11:24 pm Post subject: |
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| Marty R. wrote: | | Quote: |
The pattern will be found by Medusa multicoloring on <6> and <7> |
Not looking to open a can of worms here, but what is Medusa multicoloring? Is that something different from what I know as extended Medusa? |
Marty,
Can of worms? Box of snakes?
Yes, it is different. A skyscraper is multi-coloring.
Suppose you have a skyscraper pattern. One skyscraper is green and red. The other is blue and orange. If green and blue are on the ground floor, red and orange are the peaks. Any cell that sees both red and orange cannot be true. Now, instead of just coloring the strong links, do Medusa coloring starting on each tower. Any cell that sees both red and orange cannot be true.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Feb 29, 2008 11:34 pm Post subject: |
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| Code: | +-------------------+-------------------+-------------------+
| 1 78 6g7r | 5 2 49 | 49 678 3 |
| 23 4 36r | 179 89 1789 | 19 5 26g |
| 5 278 9 | 3 14 6 | 14 278 278 |
+-------------------+-------------------+-------------------+
| 6o9 123 5 | 124 89 123 | 7 34 6b8 |
| 4 237 27 | 279 6 23789 | 5 389 1 |
| 79 1367 8 | 147 5 137 | 2 3469 69 |
+-------------------+-------------------+-------------------+
| 6b7o 267 14 | 8 14 5 | 3 279 279 |
| 23 9 34 | 6 7 24 | 8 1 5 |
| 8 5 12-7 | 129 3 129 | 6 27 4 |
+-------------------+-------------------+-------------------+
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There is a skyscraper on <6> in R24. One of R2C3 and R4C1 must be <6>. But, note the cells <67>. One of R1C3 and R7C1 must then be <7>.
Which takes out <7> in R9C3, solving the puzzle.
Keith
g - green
b - blue
r - red
o - orange |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Fri Feb 29, 2008 11:42 pm Post subject: almost |
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Is Johan's solution a "forcing chain?"
Keith's solution is essentially a w-wing, established by the pincers of the skyscraper (R2C3 and R4C1). But BOTH could be 6, which would not make a strong pair. Does that establish a w-wing? Just wondering.
Earl |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Mar 01, 2008 12:26 am Post subject: |
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| Quote: | | I found this one after exploring a Type 3 UR [23] in R28C13 |
Johan,
I admire your eye for uniqueness solutions... I just want to make sure of something... isn't that a type 4B in your quote?? |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Mar 01, 2008 12:52 am Post subject: |
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Marty,
multicoloring medusa chains allows you to make eliminations because you are making the same type of bridge that you can make when you muticolor a single candidate. requires much attention to detail and some of the bridged clusters can cover the entire board. |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Sat Mar 01, 2008 1:27 am Post subject: |
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| Quote: | isn't that a type 4B in your quote??
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Norm,
I think you're right about this one, it seems more difficult for me defining those varied UR types than dissecting them. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Mar 01, 2008 1:58 am Post subject: |
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Thanks Keith and Norm.
| Quote: | | Can of worms? Box of snakes? |
Maybe that should be promoted to Pandora's box. 
Let's see if I grasp this. When you have this situation, you start two Medusas, one with r-g and the other with b-o and see where it takes you, making sure that inferences follow the old rules, i.e., an inference from, say, a "g" also must be a "g."
Under this system, does this mean that an r-g or b-o trap is not allowed? That a trap only occurs between one color from each set? Could a trap result from each of r-b, r-o, g-b and g-o? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Mar 01, 2008 3:03 am Post subject: |
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| Marty R. wrote: | Thanks Keith and Norm.
| Quote: | | Can of worms? Box of snakes? |
Maybe that should be promoted to Pandora's box.
Let's see if I grasp this. When you have this situation, you start two Medusas, one with r-g and the other with b-o and see where it takes you, making sure that inferences follow the old rules, i.e., an inference from, say, a "g" also must be a "g."
Under this system, does this mean that an r-g or b-o trap is not allowed? That a trap only occurs between one color from each set? Could a trap result from each of r-b, r-o, g-b and g-o? |
Marty,
If I understand the question, the answer is "No". It is not that complicated.
To use my previous notation, suppose you start Medusa coloring on green-red. Any conclusions you make are valid. Suppose you do not get too far.
Suppose you start another Medusa coloring cluster in cells you have not yet used. Any conclusions you make for this cluster (blue - orange) are valid.
How do you connect the two? I suggest it is via the weak link, as in a skyscraper. As in the cells in C9 above. I believe the only conclusion between the two clusters is that a Medusa peer of both red and orange cannot be true.
Keith.
(Damn! Now I have to explain what a "Medusa peer" is.) |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Mar 01, 2008 4:47 am Post subject: |
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| Quote: | | If I understand the question, the answer is "No". |
I'm not sure I understand the question. But thanks, I'll try and play around with it. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sat Mar 01, 2008 11:56 am Post subject: |
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Nice, you have found, what i meant (and more), but in a different way.
My way to get to Keith's elimination of 7 in r9c3 was a w-wing, connected by 2 strong links for 6.
| Code: | +-------------------+-------------------+-------------------+
| 1 78 #67 | 5 2 49 | 49 @678 3 |
| 23 4 36 | 179 89 1789 | 19 5 26 |
| 5 278 9 | 3 14 6 | 14 278 278 |
+-------------------+-------------------+-------------------+
| 69 123 5 | 124 89 123 | 7 34 689 |
| 4 237 27 | 279 6 23789 | 5 389 1 |
| 679 @1367 8 | 1479 5 1379 | 2 @3469 69 |
+-------------------+-------------------+-------------------+
|#67 @267 14 | 8 14 5 | 3 279 279 |
| 23 9 34 | 6 7 24 | 8 1 5 |
| 8 5 12-7 | 129 3 129 | 6 27 4 |
+-------------------+-------------------+-------------------+ |
For those, who are not familiar with our terminology:
The 2 strong links for 6 in colums 2 and 8 form a skyskraper, one of r1c8 and r7c2 must be 6. Then one of r1c3 and r7c1 must be 7.
Johan's chain is exactly describing, what i saw as "half M-wing".
| Code: | +-------------------+-------------------+-------------------+
| 1 78 67 | 5 2 49 | 49 678 3 |
| 23 4 36 | 179 89 1789 | 19 5 2-6 |
| 5 278 9 | 3 14 6 | 14 278 278 |
+-------------------+-------------------+-------------------+
|#69 123 5 | 124 89 123 | 7 34 @68 |
| 4 237 27 | 279 6 23789 | 5 389 1 |
|@79 *1367 8 | 147 5 137 | 2 34-69 #69 |
+-------------------+-------------------+-------------------+
| 67 267 14 | 8 14 5 | 3 279 279 |
| 23 9 34 | 6 7 24 | 8 1 5 |
| 8 5 127 | 129 3 129 | 6 27 4 |
+-------------------+-------------------+-------------------+ |
r6c9=9 => r6c1<>9 => r4c1=9.
Now there is a strong link for 6 from r4c1 to r4c9. So we have either r6c9=6 or (r6c9=9 =>) r4c9=6.
Or you take the strong link to r6c2 to eliminate 6 in r6c8. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Mar 01, 2008 9:34 pm Post subject: |
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| Some fancy stuff... but, I saw that <6> elimination in r6c8 this way: Take the otherwise useless {679} XY Wing in r67c1|r6c9 and transport the <6> in r6c9 to r6c2 via r4c1. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Mar 02, 2008 7:58 am Post subject: |
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| storm_norm wrote: | Marty,
multicoloring medusa chains allows you to make eliminations because you are making the same type of bridge that you can make when you muticolor a single candidate. requires much attention to detail and some of the bridged clusters can cover the entire board. |
Norm,
I think I agree, if you just start coloring Medusa clusters, and then try to figure out the bridges (weak links).
However, if you establish the bridge first, as in my link of green - blue in C9 in the topic of this thread, the process is not that complicated, I think.
I simply note the colors in the margin: Eliminations can be made by red - green, blue - orange, AND by red - orange.
You do not have to use colors. I use a circle o and a solid dot first (red - green) then + and x (blue and orange).
Keith
PS: Thank you all. This, and other recent threads, are a great discussion. I've been having a good time! |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Mar 02, 2008 4:21 pm Post subject: |
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Marty asked
| Quote: | | Under this system, does this mean that an r-g or b-o trap is not allowed? That a trap only occurs between one color from each set? Could a trap result from each of r-b, r-o, g-b and g-o? |
Keith wrote
| Quote: | | I simply note the colors in the margin: Eliminations can be made by red - green, blue - orange, AND by red - orange. |
Keith, that's the answer I was looking for when I asked the question earlier in the thread. |
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