The hardest sudokus (new thread)

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

Quads backdoors

Postby dobrichev » Wed Jul 18, 2012 5:56 pm

ronk wrote:Andrew Stuart has proposed the number of quads backdoors of maximum size as a new metric for difficult puzzles.

"Quads backdoors" means, in addition to the backdoors guesses, the techniques used are singles, locked candidates, naked and hidden subsets (pairs, triples, and quads).


The best I found in this proposal is the analogy with fish-hooks. The weaker the hook is, the larger numeric symbol is used. Stronger than "0" are hooks "00", "000", etc.

Usability of such a system highly depends on the family of the "basic" techniques used.

From the perspective of the solver it is an estimation of wrong guess expectation rate. But guessing usually is made on "best" candidates, where best are bi-value cell and/or bi-position digit in house(s). IMO counting only the "best" guessing candidates takes more sense. Further, the rating could be scaled according to whether 2/3/4 value/position is the best available at respective guessing level.
Further, the "right" and "wrong" guess could have much different continuation paths and if uniqueness is not assumed then both subtrees must be estimated.

Probably some of the popular rating systems use similar approach but with different "basic" techniques family?
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Re: The hardest sudokus (new thread)

Postby champagne » Fri Jul 20, 2012 1:46 am

This is an update of an original post published Sat Oct 15, 2011 12:15 pm
The only change in that post is that 11 puzzles disappeared after multi fish patterns have been found;
The data base has meantime more than doubled, I'll make ASAP an update of that list

====================================================================


This is my current short list of potential hardest.

The list has not changed that much since the last post despite the fact that the database has now more than 18000 puzzles.
The link to my website will be updated soon.

The main changes come from a lower cut off.

The puzzle 5416 formerly in the list has been cleared after a multi fish has been shown.

The items in the list are

puzzle;
seq number in my database
Family code
id code in the family (could be the name)
ER (serate)
EP
ED
code 9 to 1 (see below)
most promissing floor group
index of difficulty (print size) found by my solver

The code 9 to 1 gives an idea of the chances for the puzzle to stay in the list

9 no evidence of a potential in a multi floors "Allan Barker mode" approach
1 good chance to find a multi floor pattern not seen by my solver

In between, I made the choice regarding potential eliminations
Most of the puzzles having a low "code" should be discarded later;

champagne

Hidden Text: Show
..34......5...9...7...2...62...7..1..9...5......3....8..1.6...78......21......4..;4024;elev;L406;11.10;11.10;3.40;9;;881
1.......9.5.1...3...8..34...1.5.......9..8..2....6..7.3....4..8..2.......8..7..6.;3411;elev;3174;11.10;11.10;10.80;9;;785
1.......9..67...2..8....5.......83.....2...64..7.4..1...462....5..8......9...3...;889;elev;L59;11.30;11.30;9.50;9;;607
1..4..7....7.8...6.9.......2..3......4...71....5.4..2..3.9..4......6...8..2....5.;7417;elev;H193;10.80;10.80;10.80;9;;592
98.7.....65....4....3.6....7..5..8......2..5......1..6.4.8..9....9.....3....1..2.;10216;GP;22ky5;10.70;10.70;3.40;9;;580
..3.5.....5.1....68....7....6..9...57....2.4...5...1........8.......4.2...9.3...1;1362;elev;413;11.30;1.20;1.20;9;;505
.2.4.......7.8...6.....3.5...9.6...1.....23.....5...4...1...8..6...1...797.......;243;elev;258;11.40;11.40;11.30;8;23459;884
...45.........9.3.6...375...4....1....8.....29...6..7.3....5.9...2...8...1..7....;620;elev;890;11.30;11.30;10.60;8;12348;829
..3..6.8.4.....2......3.5....89...3.5...7...4.....1....6.8...9.7...2......1..3...;2780;elev;1126;11.20;1.20;1.20;8;12457;790
....5...94..1...3..6.7..1....59......8..7.......5.2..73......6...8.9...2.1....4..;2051;elev;1452;11.20;11.20;9.90;8;13456;542
98.7.....6.....9....5....7..4..3..2...85..4.......4..1..69..5......2...3.....1.4.;35;GP;H4;11.70;11.70;11.30;7;1234;852
1...5.7..........6..83...4...4.....7.3.2....4......92......15..7...9......26....8;3909;elev;2788;11.10;11.10;9.40;7;1579;529
98.7.....7...6......5..97..5....69....43...6.....2...1.5...48.....6...3.....1...2;14596;GP;kz1a;11.40;11.40;11.30;7;1236;525
1....6....5.........82....4..98..3...6...5.7.........27....2.1...2.4.9.3...3.....;1102;elev;837;11.30;11.30;2.60;4;12567;619
.2.4....9..7......8....2.1...1..5.7..6..9...5...2..........8.5....36...2.3..2.6..;4993;elev;2354;11.10;1.20;1.20;3;1578;730
98.7.....7...6......5..87..5....69....43...6.....2...1.5...48.....6....3....1..2.;12120;GP;kz0;11.70;11.70;11.30;3;1236;637
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Re: The hardest sudokus (new thread)

Postby Leren » Sat Jul 21, 2012 6:00 am

I ran Champagne's latest list of potential hardest puzzles through my solver and found almost Multifish patterns in all but 4 of them.

The table below compares the floors I found with Champagne's
most promising
floors - at the moment I only use 4 digit floors
so the agreement is't too bad. I also found Exocet's in puzzles 35, 14596 and 12120.

Leren

Hidden Text: Show
Puzzle Champagne Leren
4024 - 3459
3411 - -
889 - 2467
7417 - -
10216 - 1236
1362 - 2345
243 23459 2345
620 12348 1248
2780 12457 1689
2051 13456 -
35 1234 1234
3909 1579 -
14596 1236 1236
1102 12567 1567
4993 1578 1578
12120 1236 1236
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Re: The hardest sudokus (new thread)

Postby Leren » Sat Jul 21, 2012 6:14 am

That last post was my first ever in a forum and I got a bit too clever for myself with the hidden text.

Hopefully the table will be readable this time.

Leren

Puzzle Champagne Leren
4024 - 3459
3411 - -
889 - 2467
7417 - -
10216 - 1236
1362 - 2345
243 23459 2345
620 12348 1248
2780 12457 1689
2051 13456 -
35 1234 1234
3909 1579 -
14596 1236 1236
1102 12567 1567
4993 1578 1578
12120 1236 1236

[ronk-moderator edit: reply and follow-on discussion moved here]
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Re: The hardest sudokus (new thread)

Postby champagne » Wed Jul 25, 2012 3:19 pm

There has been a lot of activity on that topic and I can have missed some findings.
This is the status of my old list of potential hardest I have after the last updates (5 more cleared)

I am working on the next update of the data base.
The last step of the update will be to produce a revised list of these candidates for the "hardest puzzle" award
====================================================================


This is my current short list of potential hardest.

The list has not changed that much since the last post despite the fact that the database has now more than 18000 puzzles.
The link to my website will be updated soon.

The main changes come from a lower cut off.

The puzzle 5416 formerly in the list has been cleared after a multi fish has been shown.

The items in the list are

puzzle;
seq number in my database
Family code
id code in the family (could be the name)
ER (serate)
EP
ED
code 9 to 1 (see below)
most promissing floor group
index of difficulty (print size) found by my solver

The code 9 to 1 gives an idea of the chances for the puzzle to stay in the list

9 no evidence of a potential in a multi floors "Allan Barker mode" approach
1 good chance to find a multi floor pattern not seen by my solver

In between, I made the choice regarding potential eliminations
Most of the puzzles having a low "code" should be discarded later;

champagne

Hidden Text: Show
..34......5...9...7...2...62...7..1..9...5......3....8..1.6...78......21......4..;4024;elev;L406;11.10;11.10;3.40;9;;881
1.......9.5.1...3...8..34...1.5.......9..8..2....6..7.3....4..8..2.......8..7..6.;3411;elev;3174;11.10;11.10;10.80;9;;785
1.......9..67...2..8....5.......83.....2...64..7.4..1...462....5..8......9...3...;889;elev;L59;11.30;11.30;9.50;9;;607
1..4..7....7.8...6.9.......2..3......4...71....5.4..2..3.9..4......6...8..2....5.;7417;elev;H193;10.80;10.80;10.80;9;;592
98.7.....65....4....3.6....7..5..8......2..5......1..6.4.8..9....9.....3....1..2.;10216;GP;22ky5;10.70;10.70;3.40;9;;580
..3.5.....5.1....68....7....6..9...57....2.4...5...1........8.......4.2...9.3...1;1362;elev;413;11.30;1.20;1.20;9;;505
...45.........9.3.6...375...4....1....8.....29...6..7.3....5.9...2...8...1..7....;620;elev;890;11.30;11.30;10.60;8;12348;829
..3..6.8.4.....2......3.5....89...3.5...7...4.....1....6.8...9.7...2......1..3...;2780;elev;1126;11.20;1.20;1.20;8;12457;790
....5...94..1...3..6.7..1....59......8..7.......5.2..73......6...8.9...2.1....4..;2051;elev;1452;11.20;11.20;9.90;8;13456;542
1...5.7..........6..83...4...4.....7.3.2....4......92......15..7...9......26....8;3909;elev;2788;11.10;11.10;9.40;7;1579;529
1....6....5.........82....4..98..3...6...5.7.........27....2.1...2.4.9.3...3.....;1102;elev;837;11.30;11.30;2.60;4;12567;619 7
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Re: The hardest sudokus (new thread)

Postby champagne » Fri Jul 27, 2012 3:14 pm

last update of the data base of potential hardest is available
The link is unchanged

here


The data base has now 38 106 puzzles
Analysis of specific properties has been done for all puzzles
except symmetry of given for part of them

many files have changed after the work done on exotic patterns
nearly 95% of the puzzles have now an identified exotic pattern.

Is included in the file my updated list of candidates that could be the hardest


champagne
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Re: exocet pattern in hardest puzzles

Postby daj95376 » Sat Jul 28, 2012 1:31 am

Champagne released his latest version of "Hard11.zip".

File "04b Jexocet.txt" contains the puzzles that champagne's solver considers to be JExocet puzzles. However, 426 of these puzzles aren't found by my QExocet analyzer -- which should find all JExocet puzzles. Consider the first JExocet in this puzzle:

Code: Select all
........1......234..1..2.56..3..4.2..5..7....8..9.......6..3.1..7..5....9..8.....;32943;dob;2012_04;2

;r1c7 r1c8   r2c1 r3c1   r2c5 r3c5    789
;r1c7 r3c7   r5c8 r5c9   r9c8 r9c9    789;;

     b5  Naked  Quad                     <> 1568 r5c4,r6c5
     b7  Naked  Quad                     <> 2458 r8c1,r9c2

 +--------------------------------------------------------------------------------+
 |  234567  234689  245789  |  34567   34689   56789   | B789    B789     1       |
 | Q567     689     5789    |  1567   R1689    156789  |  2       3       4       |
 | Q347     3489    1       |  347    R3489    2       |  789     5       6       |
 |--------------------------+--------------------------+--------------------------|
 |  167     169     3       |  156     168     4       |  156789  2       5789    |
 |  1246    5       249     |  23      7       168     |  134689  4689    389     |
 |  8       1246    247     |  9       23      156     |  134567  467     357     |
 |--------------------------+--------------------------+--------------------------|
 |  245     248     6       |  247     249     3       |  45789   1       25789   |
 |  13      7       248     |  1246    5       169     |  34689   4689    2389    |
 |  9       13      245     |  8       1246    167     |  34567   467     2357    |
 +--------------------------------------------------------------------------------+
 # 163 eliminations remain
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Re: exocet pattern in hardest puzzles

Postby ronk » Sat Jul 28, 2012 3:59 am

daj95376 wrote:Champagne released his latest version of "Hard11.zip".

File "04b Jexocet.txt" contains the puzzles that champagne's solver considers to be JExocet puzzles. However, 426 of these puzzles aren't found by my QExocet analyzer -- which should find all JExocet puzzles. Consider the first JExocet in this puzzle:

Code: Select all
........1......234..1..2.56..3..4.2..5..7....8..9.......6..3.1..7..5....9..8.....;32943;dob;2012_04;2

There's an sk-loop, which always produces more exclusions than an exocet. I suspect a bookkeeping error.

Code: Select all
     16 Truths = {5789R4 5789R7 5789C3 5789C6}
     16 Links = {12n3 12n6 47n7 47n9 5b57 7b48 8b57 9b48}
     9 Eliminations --> r12c6<>6, r1c3<>24, r4c7<>16, r2c6<>1, r7c9<>2, r7c7<>4
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Re: exocet pattern in hardest puzzles

Postby Leren » Sat Jul 28, 2012 4:49 am

I also don't see Exocets in puzzles 32943 and 32942 in Champagne's new 04b Jexocet.txt file.

Another query relates to the following, a bit further on in the same file.

........7..4..83..1...3..6....9.4.....9.8.2...5...2...6...4...1..38..4..7......5.;206;tarx;tarx0077;2;r6c4 r6c5 r4c1 r5c1 r4c7 1367;r4c5 r6c5 r2c4 r8c6 1567;;

The 1567 Exocet is OK but the first one looks spurious - in fact r4c1 = 2 and r5c1 = 4

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Re: exocet pattern in hardest puzzles

Postby champagne » Sat Jul 28, 2012 5:42 am

ronk wrote:
daj95376 wrote:Champagne released his latest version of "Hard11.zip".

File "04b Jexocet.txt" contains the puzzles that champagne's solver considers to be JExocet puzzles. However, 426 of these puzzles aren't found by my QExocet analyzer -- which should find all JExocet puzzles. Consider the first JExocet in this puzzle:

Code: Select all
........1......234..1..2.56..3..4.2..5..7....8..9.......6..3.1..7..5....9..8.....;32943;dob;2012_04;2

There's an sk-loop, which always produces more exclusions than an exocet. I suspect a bookkeeping error.


that puzzle is flagged as having a SK loop and a multi-fish pattern.

I checked the process for Jexocets and got the same results.

This is not a book keeping error, but seems to be a bug to find and fix.
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Re: exocet pattern in hardest puzzles

Postby Leren » Sat Jul 28, 2012 6:08 am

Champagne,

I've found other oddities in your Jexocet file

for example:

.......35.....1..9..9.5..6...8.3...6.7...2...1..4.......3.8..9..2.7..8.......4...;7594;col;H437;2;r2c7 r2c8 r3c2 r1c2 r1c5 2478;r1c7 r2c7 r4c8 r7c9 1247;;

and

.......354......6...3.6.8....8.9...6.1...2...7..4.......9.3..5..2...1......7..9..;2983;col;H178;2;r2c7 r2c9 r3c2 r1c2 r3c4 r1c4 1279;r1c7 r2c7 r4c8 r7c9 1247;;

in each case the first Exocet does not resolve properly.

I'd also take a look at 5099, 1501 & 1504.

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Re: The hardest sudokus (new thread)

Postby champagne » Sat Jul 28, 2012 11:14 am

I am somehow lost with posts moved here and there.

I confirm I found not one, but 2 bugs in my code with the example given on puzzle 32943

Meantime I had to take care of my lobster pots and fishing net.

I should find the time to fix them properly to-day or to morrow and to re do the Jexocet process.

I'll then update the file to ease the cross checking process.

EDIT first result to check, I lost 483 puzzles compared to 426 missing in danny's process

EDIT2 all the puzzles shown above have been fixed.
I prepare an update of the file limited to the file 04b Jexocet
The other data will be updated in the next revision that should take place in about one and half month and include some 25 clues puzzles.

EDIT 3 revision of the file done.
I noticed that in the previous one some files where likely missing (not included in the zip file)
Last edited by champagne on Sat Jul 28, 2012 1:20 pm, edited 3 times in total.
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Re: The hardest sudokus (new thread)

Postby ronk » Sat Jul 28, 2012 12:38 pm

champagne wrote:I am somehow lost with posts moved here and there.

Just doing my job. I'm sure you can see why posts triggered by a flawed "hardest sudokus" file are more appropriate here, rather than the exocet thread.

champagne wrote:
ronk wrote:There's an sk-loop, which always produces more exclusions than an exocet. I suspect a bookkeeping error. the puzzle is flagged as having a SK loop and a multi-fish pattern. I checked the process for Jexocets and got the same results. This is not a book keeping error, but seems to be a bug to find and fix.

"Bug" was my actual thought, but I thought "bookkeeping error" sounded kinder.

BTW a reply to my post was not necessary.
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Re: exocet pattern in hardest puzzles

Postby daj95376 » Sat Jul 28, 2012 3:44 pm

There are 37 puzzles in the latest "04b Jexocet.txt" that my QExocet analyzer doesn't recognize. This is the first:

Code: Select all
98.7.....7.....9....6....5..4..3..2...98..........4..1.3..1..4...83..6.......2..3

;10238;GP;22ky5;1

;r3c1 r3c2 r2c4 r1c7    1234;;;

 +--------------------------------------------------------------------------------+
 |  9       8       12345   | Q7       2456    1356    | R1234    136     246     |
 |  7       125     12345   | Q12456   24568   13568   | R9       1368    2468    |
 | B1234   B12      6       |  1249    2489    1389    |  123478  5       2478    |
 |--------------------------+--------------------------+--------------------------|
 |  1568    4       157     |  1569    3       15679   |  578     2       56789   |
 |  12356   12567   9       |  8       2567    1567    |  3457    367     4567    |
 |  23568   2567    2357    |  2569    25679   4       |  3578    36789   1       |
 |--------------------------+--------------------------+--------------------------|
 |  256     3       257     |  569     1       56789   |  2578    4       25789   |
 |  1245    12579   8       |  3       4579    579     |  6       179     2579    |
 |  1456    15679   1457    |  4569    456789  2       |  1578    1789    3       |
 +--------------------------------------------------------------------------------+
 # 184 eliminations remain

 r3c1=3 => r6c3=3 => this grid ... where I can't force r1c7=3
 +-----------------------------------+
 |  .  . -3  |  .  .  3  | ?3  3  .  |
 |  .  . -3  |  .  .  3  |  .  3  .  |
 | =3  .  .  |  .  . -3  | -3  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  3  .  |  .  .  .  |
 | -3  .  .  |  .  .  .  |  3  3  .  |
 | -3  . =3  |  .  .  .  | -3 -3  .  |
 |-----------+-----------+-----------|
 |  .  3  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  3  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  3  |
 +-----------------------------------+
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Re: exocet pattern in hardest puzzles

Postby champagne » Sat Jul 28, 2012 4:13 pm

daj95376 wrote:There are 37 puzzles in the latest "04b Jexocet.txt" that my QExocet analyzer doesn't recognize. This is the first:

Code: Select all
98.7.....7.....9....6....5..4..3..2...98..........4..1.3..1..4...83..6.......2..3

;10238;GP;22ky5;1

;r3c1 r3c2 r2c4 r1c7    1234;;;




clearly another bug in my code for downgraded forms.

I'll look at that to morrow.

Do you have some not found by my solver in that Jexocet process??
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