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ravel
Joined: 21 Apr 2006
Posts: 536
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 Posted: Sun Apr 06, 2008 12:25 pm Post subject: Generalised xy-wing |
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| Code: | . . 1 . . 2 3 . .
. 7 . . . . . 8 .
3 . . 6 . . . . 4
. . 3 9 . . . . 8
. . . . . . . . .
2 . . . . 5 1 . .
4 . . . . 3 . . 9
. 5 . . . . . 2 .
. . 6 8 . . 7 . . |
Nice puzzle by gsf, which also can be solved with a generalised xy-wing at the end. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sun Apr 06, 2008 2:42 pm Post subject: |
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"in the end" (took me a coloring elimination of 4 in r1c4 to arrive at this position), I guess, is here :
| Code: |
+--------------------------+--------------------------+--------------------------+
| 8 49 1 | 5 49 2 | 3 7 6 |
| 6 7 459 | 34 1349 19 | 59 8 2 |
| 3 29 259 | 6 78 78 | 59 1 4 |
+--------------------------+--------------------------+--------------------------+
| 5 16 3 | 9 167 167 | 2 4 8 |
| 17 1489 479 | 2 34 18 | 6 39 5 |
| 2 68 49 | 34 68 5 | 1 39 7 |
+--------------------------+--------------------------+--------------------------+
| 4 12 27 | 17 5 3 | 8 6 9 |
| 17 5 8 | 17 69 69 | 4 2 3 |
| 9 3 6 | 8 2 4 | 7 5 1 |
+--------------------------+--------------------------+--------------------------+
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Looking for xy-wings (there are two useless xy-wings pivoted in box 5) I found this baby:
pincers 69 in r8c5 and 19 in r2c6 connected by 68-81 in box 5.
Just a short xy-chain, but it solves the puzzle. |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Sun Apr 06, 2008 3:57 pm Post subject: |
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| Take it you mean a kite, or an ER, Nataraj, for that 4 - but what's in a name? ANd the 9s go from box 1, c3 - UR in 59s - but that doesn't seem to achieve much. Found the same XY-chain - waiting to hear what a generalised XY-wing is! |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sun Apr 06, 2008 6:46 pm Post subject: |
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| Victor wrote: | | Take it you mean a kite, or an ER, Nataraj, for that 4 - but what's in a name? |
Right, what's in a name. I can't remember which is which. I know what a scyscraper is (at least in real life  ). This isn't one. It looked like this:
| Code: |
* x
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*
.
.
*---*
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So that's a kite, great. Could also be a turbot fish or a hockey stick for all I know. ("Don't now much about history, don't know much trigonometry,...")
If there is an ER making the same elimination, I did not spot it... |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sun Apr 06, 2008 6:53 pm Post subject: |
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So this is what happens when one doen't follow the forum thoroughly for even one day! They dicover a new technique and I missed it. In fact I did see the thread but was too lazy to look at the details. 
I'll be better, promise. |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Sun Apr 06, 2008 7:00 pm Post subject: |
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| I'll try to be better too! I've thrown away my bit of paper, but I think the ER was based on the 4s in box 5: r6c4 sees it directly, while r5c5 sees it via 'mirrors' in boxes 4 & 1. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Apr 06, 2008 10:12 pm Post subject: |
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| nataraj wrote: | | Victor wrote: | | Take it you mean a kite, or an ER, Nataraj, for that 4 - but what's in a name? |
Right, what's in a name. I can't remember which is which. I know what a scyscraper is (at least in real life ). This isn't one. It looked like this:
| Code: |
* x
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*
.
.
*---*
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So that's a kite, great. Could also be a turbot fish or a hockey stick for all I know. ("Don't now much about history, don't know much trigonometry,...")
If there is an ER making the same elimination, I did not spot it... |
There is a classic paper by Havard, called "Strong Links for Beginners". Skyscraper, Kite, Turbot Fish, Fork, ... they are all the same, especially if you use the logic of two strong links.
http://www.sudoku.com/boards/viewtopic.php?t=3326
(If you approach them from the logic of the weak links, maybe there are differences. I don't know.)
Victor: Just to be pedantic -
1. Your diagram above is not correct. The cells that do not align with the elimination must be in the same box. You have them three rows apart.
2. NI is, I presume, Northern Ireland? The internet says Northern Ireland is NIR, NI is Nicaragua.
Best wishes,
Keith |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Sun Apr 06, 2008 11:13 pm Post subject: |
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Keith, to be pedantic in return:
| Quote: | | Your diagram above is not correct |
Not my diagram! - haven't got one in this thread. (Thank goodness - I seem to be error-prone these days, & so it's nice to find something I haven't done wrong.)
| Quote: | | NI is, I presume, Northern Ireland? |
Yep, this time.
| Quote: | | The internet says Northern Ireland is NIR, NI is Nicaragua |
I didn't know that (never thought about it indeed). NI is commonly used in the British Isles in an everyday sort of way. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Mon Apr 07, 2008 1:15 am Post subject: |
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a skyscraper is an elimination from mutlicoloring...
the term Kite is when two reds or two greens see each other in the same chain??
I also am not familiar with all the difference names given to the various coloring patterns.
I just see it as an elimination and not as a name.
but then again I wasn't part of the online sudoku community until late in the naming process. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Mon Apr 07, 2008 1:33 am Post subject: |
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| Code: | +--------------------------+--------------------------+--------------------------+
| 8 49 1 | 5 49 2 | 3 7 6 |
| 6 7 459 | 34 1349 19 | 59 8 2 |
| 3 29 259 | 6 G7R8 78 | 59 1 4 |
+--------------------------+--------------------------+--------------------------+
| 5 G1R6 3 | 9 -16R7 167 | 2 4 8 |
| 17 1489 479 | 2 34 18 | 6 39 5 |
| 2 G68 49 | 34 R6G8 5 | 1 39 7 |
+--------------------------+--------------------------+--------------------------+
| 4 12 27 | 17 5 3 | 8 6 9 |
| 17 5 8 | 17 69 69 | 4 2 3 |
| 9 3 6 | 8 2 4 | 7 5 1 |
+--------------------------+--------------------------+--------------------------+ |
using Nataraj's grid, you can see the 1 in r4c5 is eliminated using medusa from seeing a Green 1 when it has a Red 7 in its own cell. and that solves it also. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Mon Apr 07, 2008 6:50 am Post subject: |
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| keith wrote: | Just to be pedantic -
1. Your diagram above is not correct. The cells that do not align with the elimination must be in the same box. You have them three rows apart.
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I take the blame! It is my diagram, not Victor's.
When I drew it, I had no intention of showing actual distances as measured by the number of spaces or lines. I couldn't even remember exactly where the strong links were, only that one of them was vertical and the other horizontal and that there was a weak link (maybe a strong link even, but that would not be essential to the pattern) in a box. I should have drawn the box, but then I did not intend to write a textbook...
As a matter of fact, I never even look for these patterns but draw a diagram showing all the strong links for a given number and imagine the weak links in my head (the whole process is still multi-coloring). Sometimes the resulting elimination can be described as x-wing, sometimes as skyscraper, whatever, but basically they are all the same: strong links and weak links in an alternating pattern.
That's what the diagram was about, sorry for the wrong impression it created. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Apr 07, 2008 3:53 pm Post subject: |
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| Victor wrote: | Keith, to be pedantic in return:
| Quote: | | Your diagram above is not correct |
Not my diagram! - haven't got one in this thread. (Thank goodness - I seem to be error-prone these days, & so it's nice to find something I haven't done wrong.)
| Quote: | | NI is, I presume, Northern Ireland? |
Yep, this time.
| Quote: | | The internet says Northern Ireland is NIR, NI is Nicaragua |
I didn't know that (never thought about it indeed). NI is commonly used in the British Isles in an everyday sort of way. |
Victor, I'd been meaning to ask, but never got around to it. I had thought North Island, NZ might be a possibility, but I don't know if they commonly use those initials.
I had ruled out Northern Illinois and Northern Indiana.  |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Mon Apr 07, 2008 11:16 pm Post subject: |
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Yes, that's a clear description, Keith.
The original definitions of kite & skyscraper seem to be here:
http://www.sudoku.com/boards/viewtopic.php?t=2646
(Note the disapproval from some people over the introduction of yet more names.)
Can't say that I care much myself, one way or the other. (I think on the whole that it's quite nice to have distinct names for the simpler patterns that are around, but it's obviously not important.)
What perhaps is important is to distinguish simple colouring chains (which use exclusively conjugate links) from all those chains (x-cycles I think they're called, that start with skyscraper/kite) that have alternate strong & weak links. The ends of a colouring chain are related in a different way from those of any chain that includes a weak link. |
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