Need some help on next step / rule

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Need some help on next step / rule

Postby dbldbl » Sat Mar 25, 2006 6:44 pm

Trying to solve this one from the Milwaukee Journal/Sentinel on Saturday March 25, 2006 with 6 stars (out of 6) with logic and rules - any guidance is appreciated --- dbldbl


Code: Select all
x   5   4   x   2   x   1   3   x
1   2   3   4   x   x   x   9   8
x   6   8   x   3   1   4   5   2
8   4   1   3   x   2   x   7   5
6   7   x   x   4   x   x   1   x
5   3   x   1   x   7   x   x   4
                         
4   9   7   2   1   x   x   x   x
3   8   6   x   x   4   x   2   1
2   1   5   x   x   x   x   4   x
[/url]
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Postby tarek » Sun Mar 26, 2006 1:36 am

hi dbldbl,

Where should I start, first of all, I do not know exactly where you have reached in your solution. a candidate grid with pencilmarks would be helpful. consult the "help in posting puzzles" sticky thread.....

As this is an advanced puzzle, it needs advanced techniques.

My solution has:
Hidden doubles
Finned X-wing
XY wing
XYZ wing
Uniquness
Almost locked sets XY (4 nodes)......
(Not all required)

so where are you exaactly in the middle of this ?

Tarek
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Postby dbldbl » Sun Mar 26, 2006 5:29 am

hello Tarek - I am having difficulty in pasting the candidate grid with the pencilmarks into this reply. I am using an Excel format as my source and all my attempts are ending up being very poorly aligned in this reply.

I also could not locate the Sticky with the instructions you suggested in your response - if you could send me the link to that site it would be appreciated. I am not a 'techie' but will continue to try to have the detailed grid completed and sent to you --- dbldbl.
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Postby tarek » Sun Mar 26, 2006 10:01 am

here is the link: http://forum.enjoysudoku.com/viewtopic.php?t=2664.

It is also worth saying what techniques you're familiar with & how advanced are you in solving sudokus.

Tarek
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Need some help on next step/rule

Postby Cec » Sun Mar 26, 2006 11:14 am

dbldbl wrote:"...I am not a 'techie' but will continue to try to have the detailed grid completed and sent to you --"

Hi dbldbl,
If you are still having trouble in posting a Candidate" grid then clicking on this THREAD may help you. If you don't have the Simple Sudoku program then type your original puzzle as described in the above link mentioned by Tarek and then follow the remaining steps suggested.
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Postby Carcul » Sun Mar 26, 2006 12:11 pm

Code: Select all
 *--------------------------------------------------------------------*
 | 79     5      4      | 6789   2      689    | 1      3      67     |
 | 1      2      3      | 4      57     56     | 67     9      8      |
 | 79     6      8      | 79     3      1      | 4      5      2      |
 |----------------------+----------------------+----------------------|
 | 8      4      1      | 3      69     2      | 69     7      5      |
 | 6      7      29     | 589    4      589    | 2389   1      39     |
 | 5      3      29     | 1      689    7      | 2689   68     4      |
 |----------------------+----------------------+----------------------|
 | 4      9      7      | 2      1      3568   | 3568   68     36     |
 | 3      8      6      | 579    579    4      | 579    2      1      |
 | 2      1      5      | 6789   789    3689   | 36789  4      3679   |
 *--------------------------------------------------------------------*

[r5c9]{-3-[r5c7]-(Unique Rectangle: r5c3/r6c3/r5c7/r6c7/r6c8)-6-[r4c7](-9-[r8c7])=6=[r4c5]-6-[r6c5]}-3-[r7c9]-6-[r1c9]=6=[r2c7]=7=[r2c5](-7-[Naked Pair:r6c5|r9c5]-9-[r8c5])-7-[r3c4]-9-[r8c4]

and we would have no place for candidate "9" in row 8 if r5c9=3. So, r5c9 cannot be "3" and it solve the puzzle.
However, if this looks too complicated, a technique that can be applied is the bilocation/bivalue plot for the identification of Nice Loops. An example of a Nice Loop is:

[r5c9]-3-[r7c9]-6-[r1c9]-7-[r2c7]-6-[r4c7]-9-[r5c9]

which implies r9c9<>3,6; r6c7/r7c7/r9c7<>6; r5c7/r6c7<>9.

Please try yourself. Refer here for a good thread about Nice Loops. In any case, read this post for an explanation about the notation used.

Regards, Carcul
Last edited by Carcul on Fri Mar 31, 2006 7:12 am, edited 1 time in total.
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Postby QBasicMac » Sun Mar 26, 2006 7:30 pm

A good case for T&E

Guess r2c7=7 leads easily via singles to a solution
Guess r2c7=6 leads easily via singles to this
Code: Select all
+----------+--------------+--------------+
| 9  5  4  | 68  2    68  | 1    3   7   |
| 1  2  3  | 4   7    5   | 6    9   8   |
| 7  6  8  | 9   3    1   | 4    5   2   |
+----------+--------------+--------------+
| 8  4  1  | 3   6    2   | 9    7   5   |
| 6  7  29 | 5   4    89  | 28   1   3   |
| 5  3  29 | 1   {8}  7   | 28   68  4   |
+----------+--------------+--------------+
| 4  9  7  | 2   1    368 | 38   68  {6} |
| 3  8  6  | 7   9    4   | 5    2   1   |
| 2  1  5  | 68  {8}  368 | 378  4   69  |
+----------+--------------+--------------+

Impossible due to 2 8's in column 5.

Thus the puzzle has one solution.

Mac
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Postby dbldbl » Wed Mar 29, 2006 4:01 am

Hello to all - thanks for your responses - one question of carcul: When you give your solution

[r5c9]{-3-[r5c7]-(Unique Rectangle: r5c3/r6c3/r5c7/r6c7/r6c8)-6-[r4c7](-9-[r8c7])=6=[r4c5]-6-[r6c5]}-3-[r7c9]-6-[r1c9]=6=[r2c7]=7=[r2c5](-7-[r6c5|r9c5]-9-[r8c5])-7-[r3c4]-9-[r8c4]


and,
[r5c9]-3-[r7c9]-6-[r1c9]-7-[r2c7]-6-[r4c7]-9-[r5c9]


could you provide me with a basic thread that tells me how to interpret your coding string. I do understand some parts of the equation(s) but not all --- thank you --- dbldbl.
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Postby re'born » Wed Mar 29, 2006 7:27 am

Carcul,

I presume that r6c8 should not be a part of your UR, but is a part of the next step where you use it along with the quantum cell (r5c7/r6c7)<68> to eliminate 6 from r4c7. Was this actually a typo, or is that standard notation for this situation?

Also, I'm not clear how you eliminate 9 from r8c5. I can see that once you deduce r2c5 = 7, then r8c5 is pinned to 5, but that is not what I am reading in your loop. Please explain.

In the end, it seems that you don't even need the UR and can just use:

(5,9)3 > (7,9)6 > (1,9)7 > (2,7)6 ( > (4,7)9 > (8,7)!9 ) > (2,5)7 ( > (8,5)5 ) > (3,4)9 > (8,4)!9.
Last edited by re'born on Wed Mar 29, 2006 6:41 pm, edited 1 time in total.
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Postby TKiel » Wed Mar 29, 2006 1:28 pm

Rep'nA,

Not sure if you're asking how 9 can be eliminated from r8c5 in general or specifically in carcul's loop, but once the 7 is excluded from r9c5 (by colouring) there is either a naked triple or hidden double in column 5, which does it.

Tracy
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Postby ravel » Wed Mar 29, 2006 5:13 pm

Rep'nA,
in Carculs chain the UR in the 5 cells is one of type 2 (i think): You know that either 6 or 8 has to go into one of r56c7 to avoid the unique pattern and also into r6c8, so you have something like a hidden pair in 3 cells and can eliminate 6 and 8 from the rest of the block. So the answer is "standard notation", because Carcul defines the standard (see here - still hard to read in Mozilla/Firefox)
The elimination of the 9 in r8c5 comes from the 89-pair in column 5 (r6c5<>6,r9c5<>7).
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Postby re'born » Wed Mar 29, 2006 10:39 pm

TKiel wrote:Rep'nA,

Not sure if you're asking how 9 can be eliminated from r8c5 in general or specifically in carcul's loop, but once the 7 is excluded from r9c5 (by colouring) there is either a naked triple or hidden double in column 5, which does it.

Tracy


I am referring to Carcul's loop. At the end of my post, I offered a different proof that (8,5)!9 (under the assumption (5,9)3 ), so that isn't the problem for me.

ravel wrote:Rep'nA,
in Carculs chain the UR in the 5 cells is one of type 2 (i think): You know that either 6 or 8 has to go into one of r56c7 to avoid the unique pattern and also into r6c8, so you have something like a hidden pair in 3 cells and can eliminate 6 and 8 from the rest of the block.


Yes, I figured that out already...

rep'nA wrote:I presume that r6c8 should not be a part of your UR, but is a part of the next step where you use it along with the quantum cell (r5c7/r6c7)<68> to eliminate 6 from r4c7.



ravel wrote:So the answer is "standard notation", because Carcul defines the standard (see here - still hard to read in Mozilla/Firefox)


I looked through it again and I could not find any unique rectangle that had 5 cells in the notation. If such an example exists there, could you please direct me to it?

ravel wrote:The elimination of the 9 in r8c5 comes from the 89-pair in column 5 (r6c5<>6,r9c5<>7).


Thank you, that is what I wasn't seeing. One thing I would to suggest to those who set the notation standards is that this loop (as Carcul has done it) might be easier to follow if there was some reference to the naked pair [r69c5]<89> at the point in the chain where it is being used.
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Postby Carcul » Fri Mar 31, 2006 11:10 am

Dbldbl wrote:could you provide me with a basic thread that tells me how to interpret your coding string.


I have already done that in my previous post: please read this post for an explanation about the notation I have used.

Rep'nA wrote:In the end, it seems that you don't even need the UR and can just use:


Yes, it may not be necessary, but I have started by loking to cell r5c9 because of its relation with the AUR, and so I thought it would be fair to use the AUR in the deduction, even if there is a much more simpler way of proving the same. Also, its more elegant for me to use such a pattern as an AUR, even if it is more complicated.

Rep'nA wrote:I looked through it again and I could not find any unique rectangle that had 5 cells in the notation. If such an example exists there, could you please direct me to it?


Please check this post about Almost Unique Rectangles.

Rep'nA wrote:One thing I would to suggest to those who set the notation standards is that this loop (as Carcul has done it) might be easier to follow if there was some reference to the naked pair [r69c5]<89> at the point in the chain where it is being used.


Good suggestion. Normally I don't care to write such information in a deduction because when following it I think its obvious when a naked set arises (and also to not over-complicate the notation), but this might not be the case. Anyway, deduction edited.

Regards, Carcul
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