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| Hafting
| Joined: 19 Dec 2006 | Posts: 12 | : | Location: Trondheim | Items |
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Posted: Thu Jan 25, 2007 12:39 pm Post subject: New addition to multicoloring? |
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I don't know if this is new, I just haven't seen it anywhere else.
An important part of multicoloring is to recognize interactions between different chains. I.e. when color "A" see color "B", then both can't be true, implying that at least one of their conjugates "a" and "b" must be true.
Now that is of course well known. Another coloring technique is to note that whan a color eliminates all candidates in a house, then that color must be false. And when it eliminates all but one, then that one candidate can be forced true by that color.
All this is stuff I have read about, and implemented. It also got me thinking - what if <i>two</i> colors together happens to eliminate all candidates in a house? Then those two colors can't both be true - just as if they see each other. Checking this for all houses and all combinations of colors not already seeing each other takes some time, but it solves more puzzles.
I haven't seen this particular technique described anywhere, so I post it in case it really is new.
Helge Hafting |
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| Ruud Site Admin
| Joined: 17 Sep 2005 | Posts: 708 | : | Location: Netherlands | Items |
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Posted: Thu Jan 25, 2007 7:11 pm Post subject: |
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You're in the territory of Grouped Turbot Chains with this technique.
In essence, your logic creates the following chain fragment:
Code: | a=A-(candidates seen by A)=(candidates seen by B)-B=b |
a and b can be end nodes (eliminating common peers) or part of a larger Turbot Chain.
To look at this from the coloring perspective is new AFAIK.
Ruud _________________ Meet me at sudocue.net |
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| rkral
| Joined: 21 Oct 2005 | Posts: 233 | : | | Items |
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Posted: Thu Jan 25, 2007 7:55 pm Post subject: Re: New addition to multicoloring? |
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Hafting wrote: | It also got me thinking - what if <i>two</i> colors together happens to eliminate all candidates in a house? Then those two colors can't both be true - just as if they see each other. Checking this for all houses and all combinations of colors not already seeing each other takes some time, but it solves more puzzles.
I haven't seen this particular technique described anywhere, so I post it in case it really is new. |
You mean like this?
Code: |
2.6953........2....8.....3......9......3..1...53.4..7.1.2........8.....1...4..65.
2 17 6 | 9 5 3 | 478 148 478
3479 1379 14579 | 1678 1678 2 | 579 169 5679
79 8 1579 | 167 167 4 | 2579 3 25679
----------------------+----------------------+---------------------
4678 127 147 | 25678 2678 9 | 23458 2468 234568
46789 279 479 | 3 2678 5678 | 1 24689 245689
689 5 3 | 1268 4 168 | 289 7 2689
----------------------+----------------------+---------------------
1 46 2 | 5678 39 5678 | 34789 489 34789
5 46 8 | 267 39 67 | 23479 249 1
379 379 79 | 4 128 18 | 6 5 28
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | B2 . b2
---------+----------+----------
. 2 . | 2 2 . | 2 2 2
. 2 . | . 2 . | . 2 2
. . . | 2 . . | 2 . 2
---------+----------+----------
. . . | . . . | . . .
. . . | A2 . . | 2 2 .
. . . | . a2 . | . . A2
Color A true implies color B true, which implies no candidates in row 6
Therefore color A is false |
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| daj95376
| Joined: 05 Feb 2006 | Posts: 349 | : | | Items |
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Posted: Fri Jan 26, 2007 12:15 am Post subject: |
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rkral,
Your example (a nice Sashimi Swordfish) reminds me of the Unified Coloring Technique, which I think now goes by the name X-Colors. (I hope this is an accurate depiction. I'm rusty on this technique.)
Code: | B G g g G g G
[r9c5]=[r9c9]-([r6c9],[r3c9])=[r3c7]-[r6c7]=[r6c4] => -([r45c5],[r8c4])
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | G2 . g2
---------+----------+----------
. 2 . | 2 -2 . | 2 2 2
. 2 . | . -2 . | . 2 2
. . . | G2 . . | g2 . g2
---------+----------+----------
. . . | . . . | . . .
. . . | -2 . . | 2 2 .
. . . | . B2 . | . . G2
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BTW: I have no idea if this is similar to what Hafting is describing! |
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| Myth Jellies
| Joined: 20 Sep 2005 | Posts: 14 | : | | Items |
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Posted: Fri Jan 26, 2007 8:49 am Post subject: |
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I think Hafting is approaching it from the other direction
Code: | . . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | B2 . b2
---------+----------+----------
. 2 . | 2 2 . | 2 2 2
. 2 . | . 2 . | . 2 2
. . . | 2 . . | 2 . 2
---------+----------+----------
. . . | . . . | . . .
. . . | A2 . . | 2 2 .
. . . | . a2 . | . . A2 |
Colors B and A eliminate all possibilities from row 6. Therefore colors A and B must exclude each other. Thus color a or b must be true which eliminates the 2 in r9c9. A very clever and satisfying way of looking at it. _________________ Myth Jellies |
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| rkral
| Joined: 21 Oct 2005 | Posts: 233 | : | | Items |
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Posted: Fri Jan 26, 2007 4:22 pm Post subject: |
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Myth Jellies wrote: | I think Hafting is approaching it from the other direction
(...)
Colors B and A eliminate all possibilities from row 6. Therefore colors A and B must exclude each other. Thus color a or b must be true which eliminates the 2 in r9c9. A very clever and satisfying way of looking at it. |
I suspect you're correct. And that might mean that none of the A-a colored candidates need see any of the B-b colored candidates. |
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| Myth Jellies
| Joined: 20 Sep 2005 | Posts: 14 | : | | Items |
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Posted: Fri Jan 26, 2007 5:00 pm Post subject: |
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Right.
Or, as Ruud put it...
Code: |
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | B2 . b2
---------+----------+----------
. 2 . | 2 2 . | 2 2 2
. 2 . | . 2 . | . 2 2
. . . | c2 . . | C2 . c2
---------+----------+----------
. . . | . . . | . . .
. . . | A2 . . | 2 2 .
. . . | . a2 . | . . A2
| b = B - C = c - A = a => b or a must be true _________________ Myth Jellies |
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| dpbobelisk
| Joined: 27 Apr 2006 | Posts: 16 | : | Location: Kettering,UK | Items |
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Posted: Sat Jan 27, 2007 10:37 am Post subject: |
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The example posted by rkral is resolved if we use the "weak colouring" extension of simple colouring http://www.sudopedia.org/wiki/Weak_Colors.
I'm not sure if this will be true in every case with Hafting's new way of looking at things though. Some more examples would be useful. |
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