#7 from the top95

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#7 from the top95

Postby 999_Springs » Tue Aug 26, 2008 4:16 pm

Code: Select all
6     4789  2     |14789 5    479  |1389 179   39
1789  5789  15789 |1789  169  3    |1689 4     2
13789 4789  13489 |14789 1469 2    |1689 15679 569
------------------+----------------+--------------
4     3     5679  |15679 2    8    |169  1569  569
789   1     56789 |34579 349  45679|2    3569  48
289   25689 5689  |13459 1349 4569 |7    13569 48
------------------+----------------+--------------
5     4689  134689|2     7    149  |3469 69    369
279   24679 4679  |3459  349  459  |4569 8     1
139   49    1349  |6     8    1459 |3459 2     7


I know that the top95 provides many puzzles that can be solved with a few hidden pairs. But once in a while they throw in some extremely evil puzzle in which you can't get anywhere. This seems to be one of the latter. The sheer number of candidates is intimidating. Help!
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Re: #7 from the top95

Postby tarek » Tue Aug 26, 2008 4:31 pm

999_Springs,

2 things:

1st: The candidate 6 in r4c4 is hurting my eyes, allow me to remove it:D
Code: Select all
6     4789  2     |14789 5    479  |1389 179   39
1789  5789  15789 |1789  169  3    |1689 4     2
13789 4789  13489 |14789 1469 2    |1689 15679 569
------------------+----------------+--------------
4     3     5679  |15-679 2   8    |169  1569  569
789   1     56789 |34579 349  45679|2    3569  48
289   25689 5689  |13459 1349 4569 |7    13569 48
------------------+----------------+--------------
5     4689  134689|2     7    149  |3469 69    369
279   24679 4679  |3459  349  459  |4569 8     1
139   49    1349  |6     8    1459 |3459 2     7

2nd: I'm also stuck:(

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Postby ttt » Tue Aug 26, 2008 11:15 pm

Hi 999_Springs,
Looked at your very nice solution http://forum.enjoysudoku.com/viewtopic.php?t=6267 and I don’t think you need help for this:D , you have no time?
I only come to below :

Code: Select all
                    -----------------(7)r2c3
                   /                  ||
(hp27)r8c12=(7)r8c3—(7)r45c3=(7)r5c1-(7)r2c1
                   \                  ||
                    -(7)r7c3=(7)r4c4-(7)r2c4
                                      ||
                                     (7-5)r2c2=(5-2)r6c2=(2)r8c2 (edit)
=> r8c2<>469


Sorry, I can’t use NL notation on my diagram, explanation :
1- if r8c3<>7 => pair (27) at r8c12 => r8c2<>469
2- if r8c3=7 => r5c1=7 & r4c4=7 => (r2c3,r2c1,r2c4)<>7 => r2c2=7 (on row) => r6c2=5 => r8c2=2 => r8c2<>469 (edit: I only saw triple 489 at r139c2 => r8c2<>49 then don't see bilocation 5's & 2's on col.2)

BTW, If use AALS (46789)r79c2/r8c3 then can eliminate r8c2=49

ttt
Last edited by ttt on Sun Aug 31, 2008 7:38 pm, edited 1 time in total.
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Postby daj95376 » Wed Aug 27, 2008 12:57 am

No help here with Hidden Pairs. However, I did use Naked Pairs and a Naked Triple.

Code: Select all
 +--------------------------------------------------------------------------------+
 |  6       4789    2       |  14789   5       479     |  1389    179     39      |
 |  1789    5789    15789   |  1789    169     3       |  1689    4       2       |
 |  13789   4789    13489   |  14789   1469    2       |  1689    15679   569     |
 |--------------------------+--------------------------+--------------------------|
 |  4       3       5679    |  1579    2       8       |  169     1569    569     |
 |  789     1       56789   |  34579   349     45679   |  2       3569    48      |
 |  289     25689   5689    |  13459   1349    4569    |  7       13569   48      |
 |--------------------------+--------------------------+--------------------------|
 |  5       4689    134689  |  2       7       149     |  3469    69      369     |
 |  279     24679   4679    |  3459    349     459     |  4569    8       1       |
 |  139     49      1349    |  6       8       1459    |  3459    2       7       |
 +--------------------------------------------------------------------------------+
 # 164 eliminations remain

SIN:          7r1c6 7r3c8 5r3c9 6r23c7 6r7c89 489r137c2 [r9c2]=EMPTY             =>  [r1c6]<>7

Forcing Net:  9r1c6 3r1c9,7r5c6 7r4c3,6r6c6 6r5c3 49b7 13b7 8r7c3 6r7c2 ~9r7c89  =>  [r1c6]<>9

SSTS:         Singles, Naked Pair

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Last edited by daj95376 on Fri Aug 29, 2008 11:46 am, edited 2 times in total.
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Postby ttt » Wed Aug 27, 2008 1:32 am

Hi Daj,
Very nice solution...! But r1c6<>7 then singles to the end, why you need more forcing net?

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Postby daj95376 » Wed Aug 27, 2008 2:35 am

ttt wrote:Hi Daj,
Very nice solution...! But r1c6<>7 then singles to the end, why you need more forcing net?

Hello ttt,

I was working with output from my old solver -- which indicated that [r1c6]=4 would crack the puzzle with basic SSTS. So, I set out to eliminate 7 and 9 from that cell. I was unaware that the elimination [r1c6]<>7 would lead to Singles and two Naked Pair cracking the puzzle. Thanks for letting me know!
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Postby eleven » Thu Aug 28, 2008 5:40 am

daj95376 wrote:SIN: 7r1c6 7r3c8 5r3c9 6r34c7 6r7c89 489r137c2 [r9c2]=EMPTY => [r1c6]<>7
Suppose, it should be 6r23c7.
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Postby daj95376 » Thu Aug 28, 2008 10:43 am

eleven wrote:
daj95376 wrote:SIN: 7r1c6 7r3c8 5r3c9 6r23c7 6r7c89 489r137c2 [r9c2]=EMPTY => [r1c6]<>7

Thanks ... and corrected!!!
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Postby ronk » Thu Aug 28, 2008 12:10 pm

daj95376 wrote:SIN: 7r1c6 7r3c8 5r3c9 6r23c7 6r7c89 489r137c2 [r9c2]=EMPTY => [r1c6]<>7

Nice find ... which can be "linearized" to a chain using two ALSs, an ER and a grouped SL.
Code: Select all
 6     B4789   2      |  14789  5      49-7   | D1389  D179   D39
A1789  A5789  A15789  | A1789   169    3      | D1689   4      2
 13789 B4789   13489  |  14789  1469   2      | D1689   15679  569
----------------------+-----------------------+----------------------
 4      3      5679   |  1579   2      8      |  169    1569   569
 789    1      56789  |  34579  349    45679  |  2      3569   48
 289    25689  5689   |  13459  1349   4569   |  7      13569  48
----------------------+-----------------------+----------------------
 5     B4689   134689 |  2      7      149    | C3469  C69    C369
 279    24679  4679   |  3459   349    459    | C4569   8      1
 139   B49     1349   |  6      8      1459   |  3459   2      7

               A                   B                 C                    D
r1c6 -7- r2c4 =7= r2c123 -7- ALS:r1379c2 -6- r7c789 =6= r78c7 -6- ALS:[r23c7,r1c789] -7- r1c6 ==> r1c6<>7

Verbosely:
r1c6 -7- r2c4 =7= r2c123 -7- ALS:(r13c2,r9c2 =7|489|6= r7c2) -6- r7c789 =6= r78c7 -6- ALS:(r23c7 =6|1389|7= r1c789) -7- r1c6
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Postby 999_Springs » Thu Aug 28, 2008 3:29 pm

Thanks for all the help with the puzzle. I was extremely tired when I started it so I didn't find very much... (this explains the 6 in r4c4)

ttt wrote:Looked at your very nice solution http://forum.enjoysudoku.com/viewtopic.php?t=6267

I believe that luck has a large role with finding neat chain eliminations. I wrote about that in that thread. I still believe that I got lucky with my eliminations, and the solution just happened to be neat.
Here is an example of When My Luck Turns Really Bad.

It looks like I will need more luck if I am going to complete all the top95 by hand.
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Postby hobiwan » Fri Aug 29, 2008 1:44 pm

daj95376 wrote:
Code: Select all
 
Forcing Net:  9r1c6 3r1c9,7r5c5 7r4c3,6r6c6 6r5c3 49b7 13b7 8r7c3 6r7c2 ~9r7c89  =>  [r1c6]<>9


Looks like a major solver upgrade:D

7r5c6?
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Postby daj95376 » Fri Aug 29, 2008 3:52 pm

hobiwan wrote:Looks like a major solver upgrade:D

7r5c6?

Hello Bernhard,

I wish it was a major solver upgrade. The SIN is from my new solver, but a typo was introduced somehow during transcription.

The Forcing Net is even more complicated. My old solver does several forms of Forcing Nets, but only lists the starting cell and the results. I have to manually reconstruct its actions. Obviously, my transcribing the results had a typo as well. Maybe my next solution will have fewer mistakes.:D

Regards, Danny
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Postby 999_Springs » Fri Aug 29, 2008 4:00 pm

What is the point of having both #7 and #9 of the top95? The puzzles are completely identical except that the 3 and 4 in r2 have been switched. Their solving paths are near-identical and so are their difficulty levels. From the solution of #7 it is just an easy task to simply find the 12-cell unavoidable containing that 3 and that 4 and no other clues (just take the 3 and 4 in blocks 2, 3, 5, 6, 8 and 9) and switch those numbers round, and then copy out the rest of the solution. It is completely pointless to include both puzzles. How were the top95 designed?
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Postby gsf » Sat Aug 30, 2008 8:20 am

999_Springs wrote:What is the point of having both #7 and #9 of the top95? The puzzles are completely identical except that the 3 and 4 in r2 have been switched. Their solving paths are near-identical and so are their difficulty levels. From the solution of #7 it is just an easy task to simply find the 12-cell unavoidable containing that 3 and that 4 and no other clues (just take the 3 and 4 in blocks 2, 3, 5, 6, 8 and 9) and switch those numbers round, and then copy out the rest of the solution. It is completely pointless to include both puzzles. How were the top95 designed?

they were compiled by dukosu in 2005
based on statistical analysis of the behavior of a simple randomized backtrack solver
its amazing how that simple (as in uncomplicated) analysis still holds for a large number of the topn collections
see http://magictour.free.fr/sudoku.htm for details
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Postby 999_Springs » Sun Aug 31, 2008 12:11 pm

gsf wrote:they were compiled by dukosu in 2005
based on statistical analysis of the behavior of a simple randomized backtrack solver
its amazing how that simple (as in uncomplicated) analysis still holds for a large number of the topn collections

I have little knowledge in Su-Doku programming - could you please explain further?

ttt wrote:2- if r8c3=7 => r5c1=7 & r4c4=7 => (r2c3,r2c1,r2c7)<>7

I presume you mean r2c4?
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