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Medusa 3: Crossed Blades III -- a new? pattern

 
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Bob Hanson

Joined: 05 Oct 2005
Posts: 187
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Location: St. Olaf College

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PostPosted: Tue Nov 08, 2005 7:26 pm    Post subject: Medusa 3: Crossed Blades III -- a new? pattern Reply with quote

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:

                        |
---------1-----------1--+-------
         .            . |
         .             .|
         .              1
         .              |
         .              |
         .              |
         .              |
         (*)............1
                        |
                        |

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
| | | || | | || | |
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r2 | 8 | 25 | 25 || 4 | 9 | 67 || 157 | 3 | 156
| | | || | | || | |
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r3 | 359 | 7 | 6 || 38 | 2 | 1 || 4589 | 489 | 4589
| | | || | | || | |
===========================||=======================||=======================
r4 | 2579 | 1 | 4 || 6 | 578 | 2578 || 3 | 289 | 589
| | | || | | || | |
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r5 | 6 | 2358 | 2358 || 28 | 1458 | 9 || 1458 | 1248 | 7
| | | || | | || | |
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r6 | 2579 | 2589 | 2589 || 278 | 14578 | 3 || 6 | 12489 | 14589
| | | || | | || | |
===========================||=======================||=======================
r7 | 239 | 2389 | 1 || 23789 | 3678 | 4 || 789 | 5 | 689
| | | || | | || | |
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r8 | 4 | 6 | 2589 || 2789 | 578 | 2578 || 1789 | 1789 | 3
| | | || | | || | |
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r9 | 359 | 3589 | 7 || 1 | 3568 | 568 || 2 | 4689 | 4689
| | | || | | || | |
-----------------------------------------------------------------------------[/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.)
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St. Olaf College
Northfield, MN
http://www.stolaf.edu/people/hansonr
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Ruud
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Joined: 17 Sep 2005
Posts: 708
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Location: Netherlands

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PostPosted: Tue Nov 08, 2005 7:43 pm    Post subject: Reply with quote

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
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Location: St. Olaf College

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PostPosted: Tue Nov 08, 2005 8:18 pm    Post subject: Reply with quote

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



Code:
 
   |---c1--|---c2--|---c3--||---c4--|---c5--|---c6--||---c7--|---c8--|---c9--
-----------------------------------------------------------------------------
r1 |     1 |     4 |    39 ||     5 |   378 |   678 ||   789 |  6789 |     2
   |       |       |       ||       |       |       ||       |       |       
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r2 |     8 |    25 |    25 ||     4 |     9 |    67 ||    17 |     3 |    16
   |       |       |       ||       |       |       ||       |       |       
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r3 |    39 |     7 |     6 ||    38 |     2 |     1 ||    45 |   489 |  4589
   |       |       |       ||       |       |       ||       |       |       
===========================||=======================||=======================
r4 |   279 |     1 |     4 ||     6 |   578 |  2578 ||     3 |   289 |    89
   |       |       |       ||       |       |       ||       |       |       
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r5 |     6 |  2358 |  2358 ||    28 |    14 |     9 ||    45 |  1248 |     7
   |       |       |       ||       |       |       ||       |       |       
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r6 |  2579 |  2589 |  2589 ||   278 |    14 |     3 ||     6 | 12489 | 14589
   |       |       |       ||       |       |       ||       |       |       
===========================||=======================||=======================
r7 |   239 |  2389 |     1 || 23789 |  3678 |     4 ||   789 |     5 |   689
   |       |       |       ||       |       |       ||       |       |       
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r8 |     4 |     6 |  2589 ||  2789 |   578 |  2578 ||  1789 |  1789 |     3
   |       |       |       ||       |       |       ||       |       |       
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r9 |   359 |  3589 |     7 ||     1 |  3568 |    58 ||     2 |  4689 |  4689
   |       |       |       ||       |       |       ||       |       |       
-----------------------------------------------------------------------------

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Professor of Chemistry
St. Olaf College
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http://www.stolaf.edu/people/hansonr
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