quick colors question

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quick colors question

Postby lovethepirk » Wed Mar 01, 2006 11:30 pm

*-----------*
|.6.|.1.|...|
|..3|4.7|16.|
|1..|6.8|..2|
|---+---+---|
|9.8|...|321|
|...|...|...|
|716|...|4.5|
|---+---+---|
|8..|9.6|..3|
|.27|1.3|9..|
|...|.7.|.1.|
*-----------*


*-----------*
|.6.|.1.|...|
|.83|4.7|169|
|17.|6.8|5.2|
|---+---+---|
|9.8|76.|321|
|.3.|..1|...|
|716|...|4.5|
|---+---+---|
|8.1|9.6|..3|
|627|1.3|9..|
|39.|.7.|.1.|
*-----------*


*-----------------------------------------------------------*
| 245 6 2459 | 235 1 259 | 78 3478 478 |
| 25 8 3 | 4 25 7 | 1 6 9 |
| 1 7 49 | 6 39 8 | 5 34 2 |
|-------------------+-------------------+-------------------|
| 9 45 8 | 7 6 45 | 3 2 1 |
| 245 3 245 | 58 4589 1 | 678 789 678 |
| 7 1 6 | 238 2389 29 | 4 89 5 |
|-------------------+-------------------+-------------------|
| 8 45 1 | 9 245 6 | 27 457 3 |
| 6 2 7 | 1 458 3 | 9 458 48 |
| 3 9 45 | 258 7 245 | 268 1 468 |
*-----------------------------------------------------------*

This sudoku is from simple sudoku, "Expert", cause that's what I am, just kidding.
Thanks for your time.

I found the "colors" solution starting with cell R4C2. I understand that eventually the 4
in cell R7C5 must go but Simple sudoku has it getting removed immediately and the 4 in R5C5 is
getting removed later on. I would think this would be the opposite.

Regardless, I finished the puzzle, but is Simple Sudoku just skipping steps and getting to a faster
solution?

Thanks,

LTP
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Postby emm » Thu Mar 02, 2006 3:04 am

Code: Select all
 *-----------------------------------------------------------*
 | 245   6     2459  | 235   1     259   | 78    3478  478   |
 | 25    8     3     | 4     25    7     | 1     6     9     |
 | 1     7     49    | 6     39    8     | 5     34    2     |
 |-------------------+-------------------+-------------------|
 | 9     45+   8     | 7     6     45-   | 3     2     1     |
 | 245   3     245   | 58    4589+ 1     | 678   789   678   |
 | 7     1     6     | 238   2389  29    | 4     89    5     |
 |-------------------+-------------------+-------------------|
 | 8     45-   1     | 9     245   6     | 27    457   3     |
 | 6     2     7     | 1     458   3     | 9     458   48    |
 | 3     9     45+   | 258   7     245+  | 268   1     468   |
 *-----------------------------------------------------------*


By my reckoning they go at the same time.

The 4 at r7c5 goes because it intersects with a (+) and a (-) and all the (4+) go because there are two (+) in row 9.

Maybe Simple Sudoku's way is more interesting?
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Postby TKiel » Thu Mar 02, 2006 3:25 am

LTP,

I don't see any way to exclude only the 4 at r5c5 at this time with colours.

As em pointed out, they do disappear at the same time if the chain is constructed in the manner outlined.

Tracy
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Postby ravel » Thu Mar 02, 2006 10:40 am

You can do it with 2 turbot fishes (at the same time)
r5c5,r4c6,r4c2,r7c2,r7c5 eliminates the 4 in r7c5.
From
r4c6,r4c2,r7c2,r9c3,r9c5 you get r4c6=4

So Simple Sudoku maybe just found them in this order.
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Postby lovethepirk » Thu Mar 02, 2006 7:59 pm

Thank you all....getting better:)

LTP
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Postby TKiel » Fri Mar 03, 2006 12:27 am

Uh oh, I'm getting confused again. I thought 'Turbot fish' was only a specific pattern of colouring, but R7c2 and r7c5 aren't conjugates, so it seems like they couldn't be used in a 'Turbot Fish'. What am I not understanding?

Tracy
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Postby emm » Fri Mar 03, 2006 3:42 am

Hi Tracy - Turbot fish has an unconditional link - to a cell where there are more than two of that number in the group - as well as conjugate links.

I liked the way this was explained on Havard’s thread on strong links

A and B are conjugates, C and D are conjugates, A and C are buddies => either B or D are true => any cell that intersects with B and D is false.

Code: Select all

 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+------
 . 4A-------/4C| . . .
 . | . | . 4D. | . . .
 . | . | . | . | . . .
---|---+---|---+------
 . 4B------* . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .


[r7c5]-4-[r7c2]=4=[r4c2]-4-[r4c6]=4=[r5c5]-4-[r7c5]

Code: Select all
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+------
 . 4A--------4B| . . .
 . | . | . . | | . . .
 . | . | . . | | . . .
---|---+-----|-+------
 . 4C. | . . | | . . .
 . .\. | . . | | . . .
 . . 4D------* | . . .


[r9c6]-4-[r9c3]=4=[r7c2]-4-[r4c2]=4=[r4c6]-4-[r9c6]
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Postby TKiel » Sun Mar 05, 2006 4:16 pm

em,

Thanks for the explanation. I think what also confused me is that the cell with the value to be excluded is included in the 'Turbot-fish' pattern, whereas most of the time in colouring the exclusion takes place outside the chain.

It seems from the diagrams you used as illustrations, that the 'Turbot-fish' pattern could be constructed from either one four-cell chain or from two two-cell chains. Is that correct?

Tracy
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Postby tarek » Sun Mar 05, 2006 4:37 pm

The answer also maybe that it used the finned fish techniques:

Code: Select all
*--------------------------------------------------------*
| 245   6     2459 | 235   1     259  | 78    3478  478  |
| 25    8     3    | 4     25    7    | 1     6     9    |
| 1     7     49   | 6     39    8    | 5     34    2    |
|------------------+------------------+------------------|
| 9    *45    8    | 7     6    *45   | 3     2     1    |
| 245   3     245  | 58    4589  1    | 678   789   678  |
| 7     1     6    | 238   2389  29   | 4     89    5    |
|------------------+------------------+------------------|
| 8    #45    1    | 9     245   6    | 27    457   3    |
| 6     2     7    | 1     458   3    | 9     458   48   |
| 3    *9    -45   | 258   7    *245  | 268   1     468  |
*--------------------------------------------------------*
Eliminating 4 From r9c3 (Finned XWing in Columns 26)


which again can be concluded with above techniques.


Tarek
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Postby ronk » Sun Mar 05, 2006 5:31 pm

em wrote:A and B are conjugates, C and D are conjugates, A and C are buddies => either B or D are true => any cell that intersects with B and D is false.
Code: Select all
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+------
 . 4A-------/4C| . . .
 . | . | . 4D. | . . .
 . | . | . | . | . . .
---|---+---|---+------
 . 4B------* . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .

[r7c5]-4-[r7c2]=4=[r4c2]-4-[r4c6]=4=[r5c5]-4-[r7c5]

A very small point: One can determine which links are the strong links from your description, from your nice loop, from your color designators, and even from the '*' on your diagram, but ... it is customary in this forum to show the dashed lines for the strong links only.

OTOH, I do like the fact that one can pretty much just rotate the colors to produce other layouts, e.g., ...
Code: Select all
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+------
 . 4C-------/4D| . . .
 . | . | . * . | . . .
 . | . | . | . | . . .
---|---+---|---+------
 . 4A------4B. | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .

Hmm, Ron
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