The hardest sudokus (new thread)

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Re: The hardest sudokus (new thread)

Postby tarek » Sat Jan 12, 2013 11:54 am

I encountered a discussion about an ArtoI sudoku creation here by chance here

Zapmeister (a.k.a. 999_Springs) -in his own way- giving his coments :D
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Re: The hardest sudokus (new thread)

Postby m_b_metcalf » Sat Jan 12, 2013 12:08 pm

tarek wrote:I encountered a discussion about an ArtoI sudoku creation here by chance here

Zapmeister (a.k.a. 999_Springs) -in his own way- giving his coments :D

Yes, he's incorrigible. He didn't reply to my most recent e-mail (below).

Regards,

Mike Metcalf


----- Original Message -----
From: [snip]
To: "Arto Inkala" <arto@aisudoku.com>
Sent: Monday, July 09, 2012 8:52 AM
Subject: Re: Hard puzzles?


> Dear Arto,
> Thank you for your thoughtful reply. It is widely agreed that rating is a
> difficult problem. That's why there is no commonly accepted methodology, but
> also why most people agree that, in the absence of a standard, Sudoku
> Explainer, for all its faults, at least provides a basis for comparison and
> discussion, especially as anyone can download it and use it. Further, in the
> Patterns Game, SE is used to provide each puzzle with a triple rating
> (hardest move/first cell solved/first elimination). This allows us to
> establish that a puzzle rated 10.0/10.0/10.0 is harder than 10.0/9.0/2.6
> even though asserting that it is easier that 10.1/1.2/1.2 might be less
> clear.
>
> In your case, you at least appear to design your own puzzles AND your own
> rating system, and then claim that your puzzles are the world's hardest.
> This is hardly the independent peer review that we are used to in the
> scientific world. Further, you use as comparisons some ancient puzzles that
> have long been superseded. Why not take the top dozen from champagne's list?
> This example, an isomorph of my own personal hardest, is from 2006:
>
> 001000200
> 090008050
> 600000007
> 000003040
> 000020000
> 080905000
> 700000006
> 050400030
> 002000100 SE=11.8/11.8/3.4
>
> How does that fare on your rating?
>
> I suggest that you do yourself a disfavour by not publishing your ideas for
> comment. This leads to
> postings such as these:
>
> the-hardest-sudokus-new-thread-t6539-420.html#p218972
>
> has-anyone-ever-tried-solved-the-ai-escargot-t30203-15.html
>
> Regards,
>
> Mike Metcalf
>
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Re: The hardest sudokus (new thread)

Postby 999_Springs » Sat Jan 12, 2013 5:45 pm

tarek wrote:I encountered a discussion about an ArtoI sudoku creation here by chance here

Zapmeister (a.k.a. 999_Springs) -in his own way- giving his coments :D


wow the internet is a small world

also don't ever play flash flash revolution unless you have too much spare time it's such a time-waster, you should play n instead

by the way can someone tell me what's been happening in the sudoku world in the last five-halves years because i haven't been following
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Once upon a time I was a teenager who was active on here 2007-2011
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Re: The hardest sudokus (new thread)

Postby 999_Springs » Sat Jan 19, 2013 7:59 pm

...... wow thanks for completely blanking my necrocomeback post guys

see you all in another five-halves years, and i fully expect to see a 16 or minimal 40 or se 12.0 by then
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Re: The hardest sudokus (new thread)

Postby champagne » Fri Mar 22, 2013 6:45 pm

We are end of March, it was time to produce, as announced the next update of the file of potential hardest. here

I added the file from Mladen Dobrichev I had in hands in January before departure for a 2 months break.
I also added the puzzles found in between in the 25 clues area.

Next month, may be after a new update, I'll study the exotic properties of the new puzzles.
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Re: The hardest sudokus (new thread)

Postby Obi-Wahn » Sat Apr 13, 2013 8:56 am

Hi, champagne,

I played around a bit with the multifish pattern and became quite good at manually spotting it. I tried one of your "nothing special" puzzles of the december update with the highest SE rating and found a rank 0 logic with 20 truths:

Code: Select all
98.7.....6..89......1..4...7...3.9....6...7....2....51.6..8.3.......5.4.........2;11.80;11.80;2.60;225580;col;2012_11_10;0


The way to find it is to look for a set of 4 digits that hardly mix with the non-set digits in rows and columns.

Code: Select all
 *-----------*
 |98.|7..|...|
 |6..|89.|...|
 |..1|..4|...|
 |---+---+---|
 |7..|.3.|9..|
 |..6|...|7..|
 |..2|...|.51|
 |---+---+---|
 |.6.|.8.|3..|
 |...|..5|.4.|
 |...|...|..2|
 *-----------*


In this case the digits 1,2,4 and 5 appear in the rows 3,6,8 and 9 and none of the other 5 digits do.
Now the 5 rows that don't contain 1,2,4,5 as given build the base set: 4 digits times 5 rows equals 20 truths. Afterwards I try to cover the base candidates columnwise either with column links or cell links, whichever takes less links. Basically the columns that contain digits from the set are covered by column links for the remaining digits and those columns that contain non-set digits as givens are covered by cell links for the empty cells in the base rows. If the number of links equals the number of truths it is a rank 0 logic and all covered candidates not part of the base can be eliminated.
In this case the 20 truths are 1245r12457 and the 20 links are 45c3, 12c6,12c8, 45c9, 1n57, 2n27, 4n24, 5n1245, 7n14 with 17 eliminations:

r1c57<>6, r2c2<>37, r3c8<>2, r3c9<>5, r4c4<>6, r5c1<>38, r5c2<>39, r5c4<>9, r7c4<>9, r9c3<>45, r9c68<>1

Actually, since the 4 truths in row 5 are covered by 4 cell links, you can remove them both from the pattern and get an easier multifish with 16 truths in 1245r1247 and only 12 eliminations.

Anyway, I believe this puzzle should be moved to the rank 0 only file.
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Re: The hardest sudokus (new thread)

Postby JasonLion-Admin » Mon Apr 15, 2013 2:21 pm

An extensive discussion of puzzles with backdoor size 3 and 4 has been moved to One flew over the backdoors.
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Re: The hardest sudokus (new thread)

Postby champagne » Mon Apr 15, 2013 3:19 pm

swu wrote:Hi, champagne,

I played around a bit with the multifish pattern and became quite good at manually spotting it. I tried one of your "nothing special" puzzles of the december update with the highest SE rating and found a rank 0 logic with 20 truths:

Code: Select all
98.7.....6..89......1..4...7...3.9....6...7....2....51.6..8.3.......5.4.........2;11.80;11.80;2.60;225580;col;2012_11_10;0


The way to find it is to look for a set of 4 digits that hardly mix with the non-set digits in rows and columns.
....
Anyway, I believe this puzzle should be moved to the rank 0 only file.


Sorry swu,

I just discovered your post after our admin cleaned the thread.

I'll have three days off, but I'll look at your post and come back end of this week for comments

A better place for such discussions would be here
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Re: The hardest sudokus (new thread)

Postby champagne » Mon Apr 15, 2013 5:15 pm

swu wrote:Hi, champagne,

I played around a bit with the multifish pattern and became quite good at manually spotting it. I tried one of your "nothing special" puzzles of the december update with the highest SE rating and found a rank 0 logic with 20 truths:

Code: Select all
98.7.....6..89......1..4...7...3.9....6...7....2....51.6..8.3.......5.4.........2;11.80;11.80;2.60;225580;col;2012_11_10;0

...
Anyway, I believe this puzzle should be moved to the rank 0 only file.


Finally it has not been too long to investigate that situation.

Some free comments

1) Congratulations, as a first post, you entered what was considered one year ago as an extremely difficult field.

2) I agree with you, although I don't spend that much time in manual solving, most of these big rank 0 logic are relatively easy to find for manual solvers.

3) Once you have found the rank 0 logic, you immediately find 7 assignments, and the residual difficulty is around ED 7.5 (serate mode), very far from the original 11.8


4) My solver starts with a 16 truths rank 0 logic (after easy eliminations) in the following position

Code: Select all
9     8     345    |7     1256 1236  |12456 136   3456   
6     23457 3457   |8     9    123   |1245  137   3457   
235   2357  1      |2356  256  4     |2568  36789 356789
--------------------------------------------------------
7     145   458    |12456 3    1268  |9     268   468   
1458  1459  6      |12459 1245 1289  |7     238   348   
348   349   2      |469   467  6789  |468   5     1     
--------------------------------------------------------
1245  6     4579   |1249  8    1279  |3     179   579   
1238  1237  3789   |12369 1267 5     |168   4     6789
13458 13457 345789 |13469 1467 13679 |1568  16789 2       




16 Truths = {1R1247 2R1247 4R1247 5R1247 }
16 Links = {1c68 2c68 4c39 5c39 1n57 2n27 4n24 7n14 }
15 elims 6r1c5 6r1c7 3r2c2 7r2c2 6r4c4 9r7c4 4r9c3 5r9c3 1r5c6 1r9c6 2r5c6 1r9c8 2r5c8 4r5c9 5r3c9

5) for sure this should be classified as a (pure ?) rank 0 logic.
In my data base, the last updates have not been analysed. That puzzle entered the data base after my last analysis of exotic properties.

I am currently working on another topic, The next update of the data base (in 2 or 3 weeks) should only include new puzzles. An update of exotic properties will come later;
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Re: The hardest sudokus (new thread)

Postby champagne » Mon Apr 15, 2013 9:21 pm

One more comment on swu's post.

I did not pay attention that swu constructed the rank 0 logic based on the given and not on the PM.

AFAIK it is the first time that somebody did it in that way and I must confess that it is very easy to follow in that case.

I am nearly sure that a process based on that view could replace my current process based on the PM.

In the last step, describing eliminations, the PM still helps.
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Re: The hardest sudokus (new thread)

Postby David P Bird » Tue Apr 16, 2013 9:49 am

Swu, yes as champagne said, an impressive first post!

I use the same way of trying to identify the multifish digits as you.

I then use the trial set as first cover set in one direction and the complementary set as the second set in the other, removing the known digits for each row and column. I'm doing this on spreadsheet and can flip the sets to find which one is more economical.

For this puzzle this produces these option:
Multi-sector Locked Set:(36)r1,(37)r2,(68)r4,(389)r5,(79)r7,(45)c3,(12)c6,(12)c8,(45)c9 19 digits/available cells
Multi-sector Locked Set:(25)r3,(4)r6,(12)r8,(145)r9,(38)c1,(379)c2,(369)c4,(67)c5,(68)c7, 20 digits/available cells

When there is an SK loop potential I look for 4 givens that match or nearly match this pattern of pairs
Code: Select all
| A . . | B . . |
| . A . | . B . |
| . . . | . . . |
-----------------
| B . . | A . . |
| . B . | . A . |
| . . . | . . . |

I then set these as cover sets for the 4 boxes and the complementary set for the 'unoccupied' rows and columns in the 4 boxes.

..7..1...6...9.2...3.5.....9.....6.8.......3.....8..922...4...9..13......5...7...;179;tax;tarek071223170000-;K;;;;G13

Code: Select all
. . 7 | . . 1 | . . .
6 . . | . 9 . | 2 . .
. 3 . | 5 . . | . . .
------| ------| ------
9 . . | . . . | 6 . 8
. . . | . . . | . 3 .
. . . | . 8 . | . 9 2
------| ------| ------
2 . . | . 4 . | . . 9
. . 1 | 3 . . | . . .
. 5 . | . . 7 | . . .

Here is a full blown SK loop with (15) & (37) in boxes 1278 fitting the pattern which gives:

Multi-sector Locked Set:(48)r2,(68)r7,(48)c1,(26)c5,(15)b1,(37)b2,(37)b7,(15)b8 16 digits/available cells
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Re: The hardest sudokus (new thread)

Postby logel » Fri Apr 19, 2013 3:31 pm

Because I used the large collection of very hard puzzles published in this thread, others might be interested in my results.
I scanned all puzzles with my permutation based solver.
All can be solved by assuming candidates TRUE and prove falsification with the following:
Repeatedly apply a sequence of eliminations with max 6 base lines until contradiction.

details see: universal-elimination-pattern
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Re: The hardest sudokus (new thread)

Postby ronk » Fri Apr 19, 2013 8:06 pm

David P Bird wrote:
Code: Select all
. . 7 | . . 1 | . . .
6 . . | . 9 . | 2 . .
. 3 . | 5 . . | . . .
------| ------| ------
9 . . | . . . | 6 . 8
. . . | . . . | . 3 .
. . . | . 8 . | . 9 2
------| ------| ------
2 . . | . 4 . | . . 9
. . 1 | 3 . . | . . .
. 5 . | . . 7 | . . .

Here is a full blown SK loop with (15) & (37) in boxes 1278 fitting the pattern which gives:

Multi-sector Locked Set:(48)r2,(68)r7,(48)c1,(26)c5,(15)b1,(37)b2,(37)b7,(15)b8 16 digits/available cells

I can't imagine describing a logic pattern without listing strong inference sets. Am I just overlooking them in your description?
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Re: The hardest sudokus (new thread)

Postby champagne » Sat Apr 20, 2013 3:21 am

David P Bird wrote:When there is an SK loop potential I look for 4 givens that match or nearly match this pattern of pairs
Code: Select all
| A . . | B . . |
| . A . | . B . |
| . . . | . . . |
-----------------
| B . . | A . . |
| . B . | . A . |
| . . . | . . . |

I then set these as cover sets for the 4 boxes and the complementary set for the 'unoccupied' rows and columns in the 4 boxes.

..7..1...6...9.2...3.5.....9.....6.8.......3.....8..922...4...9..13......5...7...;179;tax;tarek071223170000-;K;;;;G13

Code: Select all
. . 7 | . . 1 | . . .
6 . . | . 9 . | 2 . .
. 3 . | 5 . . | . . .
------| ------| ------
9 . . | . . . | 6 . 8
. . . | . . . | . 3 .
. . . | . 8 . | . 9 2
------| ------| ------
2 . . | . 4 . | . . 9
. . 1 | 3 . . | . . .
. 5 . | . . 7 | . . .



Hi David,


For sure, a "V" loop pattern (most often a SK loop) can also be seen on the given.

I am wondering, looking at your example whether it's not as easy to apply the full definition.

To have a "V" loop you need

Code: Select all
1) a rectangle in four boxes with four corners given and empty cells in the rows columns
  here the corners are 6r2c1 9r2c5 4r7c5 2r7c1

2) each pair of cells in the rows columns of the rectangle sees 5 given exactly
   r2c23 sees 763 29
   r13c1 sees 763 29
   r2c46 sees 195 26
   ....


IMO this is a necessary and sufficient condition to have a "V" loop.
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Re: The hardest sudokus (new thread)

Postby David P Bird » Sat Apr 20, 2013 9:22 am

The view I take on multi-sector locked sets isn't based on thinking in terms of base & cover or truth & link sets, although they can be used to confirm the results. Instead I'm looking for a balance in the sizes of a set of candidates and a set of cells.

As I select the resident candidates of interest in the various houses, the cells that are available for containing them are coloured in two colours by my spreadsheet: green when they are constrained to holding only residents, and orange when they can hold either residents or non residents

Let
R = total number of selected resident candidates
A = total number of available cells (green + orange)
C = total number of constrained cells (green)

If R = C then a naked locked set has been found
If R = A then a hidden locked set has been found

Depending on the result, either the resident candidates or the available cells can be considered to be the base set.

When a difference of one exists in either of these balances the potential eliminations can be examined to see if any external inferences can be employed to identify if some of them to be made – those that will apply regardless of whether the set becomes locked or not.

This works provided that no candidate in the pattern cells is counted as being resident in two different houses (an endo-fin situation).

This colouring tool can also be used to identify doubly linked ALSs and AHSs as in < this post >

Champagne, it's because I'm looking for the opportunities provided by near misses that I don't use the full pattern when deciding what's worth exploring.
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