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| Bob Hanson
| Joined: 05 Oct 2005 | Posts: 187 | : | Location: St. Olaf College | Items |
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Posted: Tue Nov 08, 2005 7:26 pm Post subject: Medusa 3: Crossed Blades III -- a new? pattern |
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OK, this one I do not think is new, but it is worth presenting in this context:
Just a simple crossed "blades" -- please do tell me what to call this! I hate the idea of introducing a new term like this....
Code: |
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---------1-----------1--+-------
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. 1
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(*)............1
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The idea here is that there are two weakly linked blades of the same candidate value. Then a weak corner positioned as shown can be eliminated.
Again, the ------1------1-------- just means "exactly two 1s in a row, column, or block.
Theory-- pretty simple -- we have two weakly connected strong chains:
[code]
blade-block-blade
1----1.....1----1
F--->T---->F--->T
or
T<---F<----T<---F
/code]
So the two ends are opposite parity and allow an elimination of any node weakly connected to both of them.
This one I have an example for:
[code] |---c1--|---c2--|---c3--||---c4--|---c5--|---c6--||---c7--|---c8--|---c9--
-----------------------------------------------------------------------------
r1 | 1 | 4 | 39 || 5 | 3678 | 678 || 789 | 6789 | 2
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---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r2 | 8 | 25 | 25 || 4 | 9 | 67 || 157 | 3 | 156
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---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r3 | 359 | 7 | 6 || 38 | 2 | 1 || 4589 | 489 | 4589
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===========================||=======================||=======================
r4 | 2579 | 1 | 4 || 6 | 578 | 2578 || 3 | 289 | 589
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---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r5 | 6 | 2358 | 2358 || 28 | 1458 | 9 || 1458 | 1248 | 7
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---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r6 | 2579 | 2589 | 2589 || 278 | 14578 | 3 || 6 | 12489 | 14589
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===========================||=======================||=======================
r7 | 239 | 2389 | 1 || 23789 | 3678 | 4 || 789 | 5 | 689
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---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r8 | 4 | 6 | 2589 || 2789 | 578 | 2578 || 1789 | 1789 | 3
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---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r9 | 359 | 3589 | 7 || 1 | 3568 | 568 || 2 | 4689 | 4689
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-----------------------------------------------------------------------------[/code]
There are two 7s in row 2 and two 7s in column 8. They are weakly connected via block 3. r8c6 cannot be 7.
Oh, there's another: 6s in row 2 and column 8 allow the elimination of r9c6#6. Although that's a bit stronger, because the two blades are actually one 4-node chain.
This is from
http://www.stolaf.edu/people/hansonr/sudoku?140500002800490030076021000014600300600009007000003600001004050460000003007100200
processed first with NO 3D Medusa checking to get to this point. Stepping through 3D Medusa from this point with the "edges only" option checked and with "+weak" (no hypothesis) selected does this elimination in a step or two.
Like I said, I'm sure this one is well recognized. It's too easy. Someone will tell us the name of this! (I know it's a form of X-cycle type 2 as described at http://www.research.att.com/~gsf/sudoku/, but it almost certainly has a name as well.) _________________ Bob Hanson
Professor of Chemistry
St. Olaf College
Northfield, MN
http://www.stolaf.edu/people/hansonr |
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| Ruud Site Admin
| Joined: 17 Sep 2005 | Posts: 708 | : | Location: Netherlands | Items |
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Posted: Tue Nov 08, 2005 7:43 pm Post subject: |
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This pattern is very common in coloring. It has 2 conjugate pairs (your "blades") that meet at one of the edges.
There are people who call this a "Turbot Fish" pattern.
Check this topic on the players forum: http://www.sudoku.com/forums/viewtopic.php?t=833 |
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| Bob Hanson
| Joined: 05 Oct 2005 | Posts: 187 | : | Location: St. Olaf College | Items |
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Posted: Tue Nov 08, 2005 8:18 pm Post subject: |
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Thanks! Right, OK. It makes sense that this would be common in coloring. Standard coloring, I think, is a way of handling X-cycles.
Oooh, that really got messed up. Sorry. I will try to remember to preview before posting. Here it is again -- the "Turbot Fish", for what it is worth. yes, conjugate pairs -- ok, but does that not also include a cell with just two candidates? Maybe not. I guess I got confused about the terminology in that respect.
The blade idea comes from the image of laying down crossed swords or something like that....
Code: |
blade-block-blade
1----1.....1----1
F--->T---->F--->T
or
T<---F<----T<---F
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Code: |
|---c1--|---c2--|---c3--||---c4--|---c5--|---c6--||---c7--|---c8--|---c9--
-----------------------------------------------------------------------------
r1 | 1 | 4 | 39 || 5 | 378 | 678 || 789 | 6789 | 2
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---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r2 | 8 | 25 | 25 || 4 | 9 | 67 || 17 | 3 | 16
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---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r3 | 39 | 7 | 6 || 38 | 2 | 1 || 45 | 489 | 4589
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===========================||=======================||=======================
r4 | 279 | 1 | 4 || 6 | 578 | 2578 || 3 | 289 | 89
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---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r5 | 6 | 2358 | 2358 || 28 | 14 | 9 || 45 | 1248 | 7
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---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r6 | 2579 | 2589 | 2589 || 278 | 14 | 3 || 6 | 12489 | 14589
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===========================||=======================||=======================
r7 | 239 | 2389 | 1 || 23789 | 3678 | 4 || 789 | 5 | 689
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---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r8 | 4 | 6 | 2589 || 2789 | 578 | 2578 || 1789 | 1789 | 3
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---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r9 | 359 | 3589 | 7 || 1 | 3568 | 58 || 2 | 4689 | 4689
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-----------------------------------------------------------------------------
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_________________ Bob Hanson
Professor of Chemistry
St. Olaf College
Northfield, MN
http://www.stolaf.edu/people/hansonr |
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