Sudokus with an original rare shape

Everything about Sudoku that doesn't fit in one of the other sections

Postby udosuk » Tue Jul 04, 2006 11:26 am

No wonder... I see... I did solve it to a point that a few cells are down to 2 candidates, one leading to contradiction (after a long branch) and one leading to the unique solution...

Perhaps Carcul or others will show a Nice-loop or other fancy techniques?
udosuk
 
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Postby ravel » Wed Jul 05, 2006 1:41 pm

Code: Select all
5     3679  3679  |  1      67  6789  |  6789  2    4         
679   4     8     |  5679   2   5679  |  1     36   3567       
679   2     1     |  56789  4   3     |  6789  68   5678   
---------------------------------------------------------   
4     1     67    |  678    5   2     |  3     9    68         
368   5     36    |  4      9   1     |  68    7    2         
6789  679   2     |  678    3   678   |  5     4    1         
---------------------------------------------------------   
2     6789  679   |  3      1   679   |  4     5    678       
3679  3679  4     |  5679   8   5679  |  2     1    367       
1     3678  5     |  2      67  4     |  678   368  9       
r9c7=7 (=> r8c7<>7) (=> r47c9=68 => r8c9<>6) =>
{r7c9=8 => r9c2=8 => r9c8=3 => r8c9<>3 or
r7c9=6 => r4c9=8 => r5c7=6 => r5c1=8 => r8c1=3 => r8c9<>3}
=> r8c9 is empty => r9c7<>7

Brings us here:
Code: Select all
5     3679  3679  |  1      67  8     |  79    2    4         
679   4     8     |  5679   2   5679  |  1     36   356       
679   2     1     |  5679   4   3     |  79    68   568       
---------------------------------------------------------   
4     1     67    |  678    5   2     |  3     9    68         
368   5     36    |  4      9   1     |  68    7    2         
6789  679   2     |  678    3   67    |  5     4    1         
---------------------------------------------------------   
2     6789  679   |  3      1   679   |  4     5    678       
3679  3679  4     |  5679   8   5679  |  2     1    367       
1     3678  5     |  2      67  4     |  68    368  9           
r1c3=9 => (r1c7=7 => r9c5=7) => r1c2=3 => r8c1=3 (r9c8=3 => r2c8=6 => r2c1=7 => r6c6=7) => r6c1=9 => r6c4=8 => r6c2=6
r1c3=9 => (r1c2=3 => r1c5=6 => r9c5<>6) => r8c1=3 (=> r9c8=3 => r9c8<>6) => r6c1=9 => r5c1=8 => r5c7=6 => r9c7<>6 => r9c2=6
=> r1c3<>9

It solves with UR type 1, 2x coloring(2SL) and xy-wing then.
ravel
 
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Postby daj95376 » Wed Jul 05, 2006 4:34 pm

After 22 Hidden Singles and Locked Candidates in [b3] & [b7], you get to the following grid.

Code: Select all
*--------------------------------------------------------------------*
| 5      3679   3679   | 1      67     6789   | 6789   2      4      |
| 679    4      8      | 5679   2      5679   | 1      36     3567   |
| 679    2      1      | 56789  4      3      | 6789   68     5678   |
|----------------------+----------------------+----------------------|
| 4      1      67     | 678    5      2      | 3      9      68     |
| 368    5      36     | 4      9      1      | 68     7      2      |
| 6789   679    2      | 678    3      678    | 5      4      1      |
|----------------------+----------------------+----------------------|
| 2      6789   679    | 3      1      679    | 4      5      678    |
| 3679   3679   4      | 5679   8      5679   | 2      1      367    |
| 1      3678   5      | 2      67     4      | 678    368    9      |
*--------------------------------------------------------------------*

At this point, there are several exposed backdoor singles, but their co-candidates are not easy to eliminate. The easiest backdoor single for my solver to uncover was [r4c9]=6. However, determining that [r4c9]<>8 is a nightmare. So, my solver resolved [r4c3]<>6 followed by [r4c4]<>6, instead. Send me a PM if you'd like to see the particulars or want me to add them to this post. They involve chains of (boring) Naked/Hidden Singles that lead to contradictions in [b2] & [r9], respectively.

Now I know that simply using an initial backdoor single is in bad taste, but does that mean it's wrong to take advantage of exposed backdoor singles once other techniques in your solver are exhausted? Mike Barker has ~100 techniques listed for his solver. There's no way that many of us are ever going to match that. However, I'm adding more -- just as soon a I get done playing with Ruud's Templates idea. (Similar to Myth Jellies POM w/rookeries.)
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Postby udosuk » Thu Jul 06, 2006 5:44 am

Thanks mates... I'll try ravel's chains... But daj's "backdoor singles" seems too complicated for me to comprehend... Well, one can only learn so many techniques... And vanilla sudoku is never my love interest... (Prefer killers more...)
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Another Solution for Claudiarabia's Puzzle

Postby Carcul » Fri Jul 07, 2006 4:37 pm

Claudiarabia wrote:Here I produced another one which may be a bit harder. You will take resort to the dancing links I suppose.

Code: Select all
5 . . 1 . . . . 4
. . 8 . 2 . . . .
. 2 . . . 3 . . .
4 . . . . . 3 . .
. 5 . . 9 . . 7 .
. . 2 . . . . . 1
. . . 3 . . . 5 .
. . . . 8 . 2 . .
1 . . . . 4 . . 9 


This is a very good puzzle, and yes, it is harder than the previous one, but there is no need to dance.:D

Udosuk wrote:Perhaps Carcul or others will show a Nice-loop or other fancy techniques?


Here is a possible solution for this puzzle:

Code: Select all
 *--------------------------------------------------------------------*
 | 5      3679   3679   | 1      67     6789   | 6789   2      4      |
 | 679    4      8      | 5679   2      5679   | 1      36     3567   |
 | 679    2      1      | 56789  4      3      | 6789   68     5678   |
 |----------------------+----------------------+----------------------|
 | 4      1      67     | 678    5      2      | 3      9      68     |
 | 368    5      36     | 4      9      1      | 68     7      2      |
 | 6789   679    2      | 678    3      678    | 5      4      1      |
 |----------------------+----------------------+----------------------|
 | 2      6789   679    | 3      1      679    | 4      5      678    |
 | 3679   3679   4      | 5679   8      5679   | 2      1      367    |
 | 1      3678   5      | 2      67     4      | 678    368    9      |
 *--------------------------------------------------------------------*

1. [r13c7]-8-[r5c7]=8=[r5c1]=3=[r8c1]-3-[r9c2]=3=[r9c8]=8=[r3c8]-8-
[r13c7], => r1c7/r3c7<>8.

2. [r8c1]=3=[r5c1]-3-[r5c3]=3=[r1c3]=9=[r7c3]-9-[r8c1], => r8c1<>9.

3. [r3c9]=5=[r2c9]=3=[r8c9]-3-[r8c1]=3=[r5c1]=8=[r5c7]=6=[r4c9]-6-
[r2c9|r3c9], => r2c9/r3c9<>6.

4. [r1c7]-6-[r1c5]=6=[r9c5]-6-[r9c78]=6=[r78c9]-6-[r4c9]=6=[r5c7]-6-
[r1c7], => r1c7<>6.

5. [r8c1]=3=[r5c1]=8=[r5c7]=6=[r4c9]-6-[r78c9]=6=[r9c78]-6-[r9c5]
=6=[r1c5]-6-[r1c23]=6=[r23c1]-6-[r5c1|r8c1], => r5c1/r8c1<>6.

6. [r3c9]=5=[r2c9]=3=[r8c9]-3-[r8c1]=3|6=[r23c1]-6-[r1c23]=6=[r1c5]
=7=[r9c5]-7-[r9c7]=7=[r13c7]-7-[r2c9|r3c9], => r2c9/r3c9<>7.

7. [r7c9]-8-[r4c9]=8=[r5c7]-8-[r5c1]-3-[r8c1]-7-[r8c9]=7=[r7c9], =>
r7c9<>8.

8. [r8c6]=5=[r2c6]-5-[r2c9]=5=[r3c9]=8=[r4c9]-8-[r4c4]=8=[r6c4]-8-
[r6c1]=8=[r5c1]=3=[r5c3]-3-[r1c3]-{ATILA(6,7): r4c3|r4c4|r6c6|(r7c6)
|r9c5|r1c5|(r1c3)}-9-[r7c3]=9=[r8c2]-9-[r8c6], => r8c6<>9.

9. [r7c3]=9=[r7c6](-9-[r2c6])-9-[r8c4]=9=[r8c2]-9-[r6c2]=9=[r6c1](-9-
[r2c1])=8=[r5c1]=3=[r8c1]-3-[r9c2]=3=[r9c8]-3-[r2c8](-6-[r2c6])-6-
[r2c1]-7-[r2c6]-5-[r8c6]-{TILA(6,7): r9c5|r9c2|r6c2|r6c6|r8c6}, => r7c3=9.

10. [r4c9]-8-[r4c4]={ATILA(6,7): r4c3|(r4c4)|r6c6|r7c6|r9c5|r1c5|(r1c3)}
=8|3=[r1c3]-3-[r5c3]-6-[r5c7]-8-[r4c9], => r4c9<>8 and the puzzle is solved.

Carcul
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Re: Another Solution for Claudiarabia's Puzzle

Postby claudiarabia » Fri Jul 07, 2006 8:34 pm

Carcul wrote:This is a very good puzzle, and yes, it is harder than the previous one, but there is no need to dance.:D



I'm happy this puzzle was challenging a bit. And your hope, our soccer teams will meet comes true tomorrow though not in the final.

Cheers

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Postby udosuk » Sun Jul 09, 2006 12:55 pm

Congrats Claudia with Germany winning the bronze... Too bad for Carcul about Portugal... Hope they'll have a better result 4 years later!

Carcul, I was following your solution, until this step which puzzles me:

Carcul wrote:6. [r3c9]=5=[r2c9]=3=[r8c9]-3-[r8c1]=3|6=[r23c1]-6-[r1c23]=6=[r1c5]
=7=[r9c5]-7-[r9c7]=7=[r13c7]-7-[r2c9|r3c9], => r2c9/r3c9<>7.


In that particular stage, 6 has already been eliminated from r8c1 in the previous steps, and r6c1 could still be 6... I couldn't follow the chains from there...

Elaboration please? Thanks!
udosuk
 
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Postby ravel » Mon Jul 10, 2006 10:56 am

A way to repair it:
... r8c9=3 => r8c1=7 => r23c1<>7 => r1c23=7 => r1c5=6 ...
(... [r8c9]-3-[r8c1]-7-[r23c1]=7=[r1c23]=6=[r1c5] ...)

Edit: i should have written "another way to write" instead of "repair", since it was correct. For people, who dont use it themselves, sometimes this notation seems to make things more difficult as they are (i spotted the above chain faster than i understood the ALS-notation, and i needed some time to see the elimination r2c9<>7, because for this i had to leave out the first link)
Last edited by ravel on Mon Jul 10, 2006 8:32 am, edited 1 time in total.
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Postby Carcul » Mon Jul 10, 2006 11:44 am

Udosuk wrote:Congrats Claudia with Germany winning the bronze... Too bad for Carcul about Portugal... Hope they'll have a better result 4 years later!


Yes, congratulations to Claudia and Germany, because their team played better than Portugal. Too bad that Nuno Gomes didn't enter the game early... Well, let's see what will happen in South Africa.

Udosuk wrote:In that particular stage, 6 has already been eliminated from r8c1 in the previous steps, and r6c1 could still be 6...


That has nothing to do with the chain. The link "[r8c1]=3|6=[r23c1]" exists because of the ALS in cells r238c1, in which if r23c1 are not "6" then r8c1 is "3", and if r8c1 is not "3" then one of r23c1 must be "6". Let's now have a closer look to the chain 6:

6. [r3c9]=5=[r2c9]=3=[r8c9]-3-[r8c1]=3|6=[r23c1]-6-[r1c23]=6=[r1c5]
=7=[r9c5]-7-[r9c7]=7=[r13c7]-7-[r2c9|r3c9], => r2c9/r3c9<>7.

If any of r23c9 is "7" then r8c9 is "3", which eliminates "3" from the ALS in r238c1 and so one of r23c1 is "6". But this means that both r1c23 cannot be "6" and so r1c5 must be "6", implying that r9c5 is "7". But in column 7, candidate "7" can be in only two places: r9c7 and r13c7. In our chain, this means, as r9c5 is "7", that one of r13c7 is "7". But we have started with the hypothesis that any of r23c9 is "7", and so we have a contradiction. So, both r23c9 cannot be "7".

Carcul
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Postby algernon » Mon Jul 17, 2006 2:58 pm

Ruud wrote:This is the largest empty rectangle possible: 7x7

It has a unique solution, but the diagonals must also contain digits 1-9. Sudoku-X boldly goes where no classic sudoku has gone before.:D

Here is a version with less clues, symmetry type I and it solves with singles only. ...



Hmmm. I just modified my solver to use diagonals, too.
It can solve the 2nd sudoku, but spits blood on the first one.
Seems you need very advanced methods, AIC, APE, simple
Coloring won't suffice:(
As my solver works on arbitrary topologies, I am eager to find
a sudoku with an X-Wing with diagonal/row vs. col/col. Are there
similar lists like your famous benchmark list anywhere?

If not, I'd have to implement brute force and write a generator:)

Michael
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Postby ravel » Thu Jul 20, 2006 7:38 am

One i found with gsf's solver, which is fine to use for pattern search. It needs (at least) a short chain to solve.
Code: Select all
 +-------+-------+-------+
 | . . . | . 1 . | . . . |
 | . . . | . 5 . | . . . |
 | 8 . . | . 9 . | . . 6 |
 +-------+-------+-------+
 | . 1 . | . 3 . | . 4 . |
 | . . 7 | . 2 . | 9 . . |
 | . . . | 4 6 7 | . . . |
 +-------+-------+-------+
 | 4 9 1 | 6 8 5 | 2 7 3 |
 | . . . | 3 . 1 | . . . |
 | . . 5 | . . . | 8 . . |
 +-------+-------+-------+

[Added:]
This pattern is much more common and gives some "Carcul nice" puzzles (increasing difficulty according to Explainer)
Code: Select all
 +-------+-------+-------+
 | . . . | . 2 . | . . . |
 | 6 . . | . 7 . | . . 3 |
 | . 1 . | . 4 . | . 8 . |
 +-------+-------+-------+
 | . 9 . | . 8 . | . 2 . |
 | . . 7 | . 9 . | 5 . . |
 | . . . | 1 5 4 | . . . |
 +-------+-------+-------+
 | . 8 1 | 5 . 7 | 3 4 . |
 | 2 . . | 8 . 9 | . . 6 |
 | . . 6 | . . . | 8 . . |
 +-------+-------+-------+
....1....5...8...2.2..7..6..7..3..9...4.5.3.....926....482.153.1..7.3..8..2...9..
....1....8...3...7.5..9..1..8..6..9...4.7.6.....582....918.756.2..1.3..9..8...3..
....8....3...4...5.1..6..4..9..7..6...7.2.1.....591....857.963.7..2.8..1..9...8..
....2....1...3...9.3..6..4..9..4..5...7.9.8.....687....219.478.5..2.6..4..4...2..
....3....2...4...1.9..1..5..8..5..7...5.8.4.....291....193.482.7..9.8..6..8...9..
....3....9...1...8.4..2..9..7..6..2...3.8.1.....593....213.985.7..1.8..2..5...9..
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Postby JPF » Thu Jul 20, 2006 11:56 am

What about this pattern included in yours :
Code: Select all
 . . . | . . . | . . .
 x . . | . . . | . . x
 . x . | . . . | . x .
-------+-------+-------
 . x . | . . . | . x .
 . . x | . x . | x . .
 . . . | x . x | . . .
-------+-------+-------
 . x x | x . x | x x .
 x . . | x . x | . . x
 . . . | . . . | . . .

This pattern is valid ; for example this 13-stepper :
Code: Select all
 . . . | . . . | . . .
 5 . . | . . . | . . 4
 . 1 . | . . . | . 9 .
-------+-------+-------
 . 3 . | . . . | . 1 .
 . . 9 | . 3 . | 2 . .
 . . . | 5 . 1 | . . .
-------+-------+-------
 . 9 6 | 8 . 2 | 3 4 .
 2 . . | 4 . 5 | . . 7
 . . . | . . . | . . .


I’m assuming, but I don’t know if it is true, that if 2 valid patterns PT and PT’ are such that PT<PT’ then there are (in proportion) more difficult PT-puzzles than PT’-puzzles.
At the same time, there are less PT-puzzles than PT’-puzzles...

JPF
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Postby ravel » Thu Jul 20, 2006 3:01 pm

Very nice pattern, JPF (and hard to find puzzles with it). I am not sure about your assumption, that subpatterns tend to have more difficult puzzles. I suppose this is not the case for low clue puzzles.

Now something for p&p solvers, who like puzzles a bit harder than typically in newspapers.
Many cells are easily filled and all can be solved with at most x(yz)-wing, UR, turbot fish (2 strong links/coloring) and BUG.
Code: Select all
 +-------+-------+-------+
 | . . . | . 8 6 | 3 4 . |
 | . . 4 | 3 7 . | . . . |
 | . 3 1 | . . . | . . . |
 +-------+-------+-------+
 | . . 7 | 4 . . | . . . |
 | . . . | 7 3 5 | . . . |
 | . . . | . . 2 | 4 . . |
 +-------+-------+-------+
 | . . . | . . . | 8 5 . |
 | . . . | . 9 8 | 7 . . |
 | . 9 5 | 1 2 . | . . . |
 +-------+-------+-------+
....4273...156.....28........92........973........68........45.....981...7461....
....4375...817.....24........65........319........41........47.....586...1742....
 +-------+-------+-------+
 | . 9 . | . 8 . | . . . |
 | 6 1 . | 7 . . | . 5 . |
 | . . 5 | . . . | . . 1 |
 +-------+-------+-------+
 | . 2 . | 9 . . | . . 8 |
 | 1 . . | . 6 8 | 9 7 2 |
 | . . . | . 4 1 | . . . |
 +-------+-------+-------+
 | . . . | . 2 . | . . . |
 | . 8 . | . 1 . | . . . |
 | . . 9 | 4 5 . | . . . |
 +-------+-------+-------+
.1..2....28.7...1...4.....6.9.6....33...19874....85.......3.....5..4......289....
.9..3....73.6...5...2.....4.7.4....93...69741....83.......7.....8..5......491....
 +-------+-------+-------+
 | . . . | 5 4 7 | . . . |
 | . 8 . | . . . | . 5 . |
 | 1 . . | . 9 . | . . 7 |
 +-------+-------+-------+
 | 3 6 7 | . . . | 8 9 2 |
 | 2 . . | 9 . 8 | . . 4 |
 | . . . | 3 . 6 | . . . |
 +-------+-------+-------+
 | . . 8 | . . 5 | . . . |
 | . . 6 | . . 9 | . . . |
 | . . . | 4 1 . | . . . |
 +-------+-------+-------+
...496....9.....2.4...5...1152...3848..2.5..7...1.3.....6..4.....9..7......82....
...821....7.....3.8...5...9594...8726..5.4..3...9.2.....3..6.....7..5......24....
 +-------+-------+-------+
 | . . . | 8 2 3 | . . . |
 | . 1 . | . 4 . | . 3 . |
 | 6 . . | . . . | . . 2 |
 +-------+-------+-------+
 | . . . | 5 8 1 | . . . |
 | . 3 . | . 7 . | . 1 . |
 | 4 . . | . . . | . . 9 |
 +-------+-------+-------+
 | . . . | 4 5 7 | . . . |
 | . 7 . | . 1 . | . 4 . |
 | 8 . . | . . . | . . 7 |
 +-------+-------+-------+
...516....9..4..1.1.......4...839....8..7..9.2.......6...781....6..9..2.7.......3
...158....9..4..3.5.......7...489....4..3..9.1.......5...695....2..1..6.7.......9
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Postby JPF » Thu Jul 20, 2006 11:01 pm

ravel wrote:I am not sure about your assumption, that subpatterns tend to have more difficult puzzles. I suppose this is not the case for low clue puzzles.

You are right. This general statement doesn’t make sense.
example : 17 clues, singles only.
Sorry.
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The Easy Beauty

Postby claudiarabia » Mon Jul 24, 2006 10:57 am

JPF wrote:
This pattern is valid ; for example this 13-stepper :
Code: Select all
 . . . | . . . | . . .
 5 . . | . . . | . . 4
 . 1 . | . . . | . 9 .
-------+-------+-------
 . 3 . | . . . | . 1 .
 . . 9 | . 3 . | 2 . .
 . . . | 5 . 1 | . . .
-------+-------+-------
 . 9 6 | 8 . 2 | 3 4 .
 2 . . | 4 . 5 | . . 7
 . . . | . . . | . . .
JPF

This is a real beauty worth do develop a more difficult pattern.
Here is another 21-clue Sudoku:
Code: Select all
4 . . . 1 . . . 9
. . . 2 . 3 . . .
. . 8 . . . 5 . .
. 2 . 1 . . . 3 .
. . . . 7 . . . .
. 6 . . . 5 . 8 .
. . 3 . . . 6 . .
. . . 8 . 2 . . .
5 . . . 4 . . . 1


Claudia
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