## The hardest sudokus (new thread)

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

### Re: The hardest sudokus (new thread)

champagne wrote:If I catch your point, your findings is that in these four columns you must have r1c6=6 r3c6=4 .....

Yes, this would follow from the eliminations
1) How did you come to that

Brute force random tries, as usual
2) If you don't have XSUDO, I'll try it for you

I dont have windows, so please.
3) you have to many rookeries, this is not something I am looking for in my solver

Yes, its all but easy to show, how the eliminations can be made. But e.g. in "champagne dry" there is a 4 unit elimination (if my propram is right), which i guess must be easier than ER's 11.8 step. If possible, i would like to classify puzzles with e.g. "can be solved with 5 units moves". I dont have a chance to check all possible 5 units moves, but i see good chances to find solutions with 6 unit moves in reasonable time for (almost ?) all puzzles. This is somewhat surprising for me. Before i thought, that hardest puzzles would need 8+ units for the hardest move.
eleven

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Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

eleven wrote:Since my program is very new and probably buggy, my question is, if someone can verify the eliminations in the 2 samples below (the second puzzle is from champagnes list of 18 hardest). Maybe this is possible with XSudo.
...
r1c6<>4, r1c6<>5, r1c6<>7, r1c6<>9, r1c8<>7, r1c8<>9, r1c9<>8, r3c6<>1, r3c6<>4, r3c6<>6, r3c6<>9, r3c9<>4, r3c9<>5, r3c9<>8, r4c6<>7, r4c6<>9, r4c8<>4, r4c9<>4, r5c6<>6, r6c8<>6, r6c8<>7, r7c6<>6, r8c2<>3, r8c2<>9, r8c6<>6, r8c6<>7, r8c6<>9, r8c9<>2, r8c9<>3, r9c2<>9, r9c8<>9

For your first puzzle, using only the unsolved cells in c2, c6, c8 and c9 as Xsudo truths (aka base sets, strong inference sets). XSUDO verifies all your eliminations.

Code: Select all
`+---------------------------+-------------------------+----------------------------+| 1       2          89-6   | 3     789-46  (+6-4579) | 789-45  (45-79)   (45-8)   || 4       (389)      5      | 2789  2789-1  (179)     | 6       (1379)    (138)    || 389     7          3689   | 89-6  1489-6  (+5-1469) | 89-45   2         (13-458) |+---------------------------+-------------------------+----------------------------+| 6       (589)      2789   | 1     279-4   (+4-79)   | 3       (57-4)    (258-4)  || 278-9   (189)      4      | 5     3       (79-6)    | 278     (167)     (1268)   || 2357    (135)      1237   | 267   267-4   8         | 2457    145-67    9        |+---------------------------+-------------------------+----------------------------+| 2789-3  (3689)     2789-3 | 4     5       (379-6)   | 1       (369)     (236)    || 23579   (1456-39)  12379  | 679   1679    (13-679)  | 2459    8         (456-23) || 359     (13456-9)  139    | 689   1689    2         | 459     (3456-9)  7        |+---------------------------+-------------------------+----------------------------+      27 Truths = {2456789N2 1234578N6 124579N8 1234578N9}     37 Links = {1r25 3r278 4r14 5r134 6r157 9r257 389c2 14679c6 79c8 238c9 6b2 134b3 9b4 4b5 6b6 3b8}     46 Eliminations, 3 Assignments --> r3578c6<>6, r1348c6<>9, r1c567<>4, r3c679<>4, r4c589<>4, r148c6<>7,      r1c67<>5, r1c35<>6, r3c79<>5, r3c45<>6, r7c13<>3, r8c29<>3, r9c28<>9,      r16c8<>7, r13c9<>8, r1c8<>9, r2c5<>1, r3c6<>1, r5c1<>9, r6c5<>4, r6c8<>6,      r8c9<>2, r8c2<>9,      r1c6=6, r3c6=5, r4c6=4`

IMO this scenario is unnecessarily complex. I say this because several of the base sets are not needed and because there are cannibalistic eliminations. In three cases, the cannibalistic eliminations cause XSUDO to assign naked singles for even more eliminations.

An interesting pattern is this embedded "0-rank logic set" with 16 base sets and 16 cover sets. As of now, I have no idea what makes this 0-rank pattern tick.
Code: Select all
`+-------------------------+----------------------+-----------------------+| 1       2        689    | 3     46789   456-79 | 45789  45-79   45-8   || 4       (389)    5      | 2789  2789-1  (179)  | 6      (1379)  (138)  || 389     7        3689   | 689   14689   1456-9 | 4589   2       1345-8 |+-------------------------+----------------------+-----------------------+| 6       (589)    2789   | 1     279-4   (479)  | 3      (457)   (2458) || 2789    (189)    4      | 5     3       (679)  | 278    (167)   (1268) || 2357    135      1237   | 267   2467    8      | 2457   1456-7  9      |+-------------------------+----------------------+-----------------------+| 2789-3  (3689)   2789-3 | 4     5       (3679) | 1      (369)   (236)  || 23579   13456-9  12379  | 679   1679    136-79 | 2459   8       3456-2 || 359     13456-9  139    | 689   1689    2      | 459    3456-9  7      |+-------------------------+----------------------+-----------------------+elev [22,232] 53 Candidates,      16 Truths = {2457N2 2457N6 2457N8 2457N9}     16 Links = {1r25 3r27 4r4 5r4 6r57 2c9 7c68 8c29 9c268}     18 Eliminations --> r138c6<>9, r1c68<>7, r7c13<>3, r9c28<>9, r13c9<>8, r1c8<>9, r2c5<>1,      r4c5<>4, r6c8<>7, r8c9<>2, r8c6<>7, r8c2<>9`

I'll update with an image later, after I figure out to use tinypic.com again.

In the case of the second puzzle, the logic set is apparently too big for XSUDO, and thus unable to verify your eliminations.
ronk
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### Re: The hardest sudokus (new thread)

eleven wrote:
Yes, its all but easy to show, how the eliminations can be made. But e.g. in "champagne dry" there is a 4 unit elimination (if my propram is right), which i guess must be easier than ER's 11.8 step. If possible, i would like to classify puzzles with e.g. "can be solved with 5 units moves". I dont have a chance to check all possible 5 units moves, but i see good chances to find solutions with 6 unit moves in reasonable time for (almost ?) all puzzles. This is somewhat surprising for me. Before i thought, that hardest puzzles would need 8+ units for the hardest move.

some comments:

1) champagne dry has an EXOCET pattern. This is usually a four floors structure, sometimes a three floors ("fata morgana", "trompe l'oeil"...)

2) The first puzzle is identified in my list as having a "rank 0 logic". In fact, my solver detected a "row based" rank 0 logic

sets 2789R2 2789R4 2789R5 2789R7
linksets 89C2 79C6 79C8 28C9 D2 E2 C4 E4 A5 G5 A7 C7

ronk seems to have another one. My solver does not look for that pattern

3) the second puzzle has a pure rank 0 logic but using 5 rows

here is XSUDO output for that logic

Code: Select all
`+---------------------------+--------------------------+---------------------------+| 16(9)   16(289)   3       | 4         (258)  6(25)   | 7        16(8)   16(589)  || 1467    5         678     | 378       38     9       | 148      2       1346-8   || 467(9)  467(289)  -7(289) | -37(258)  1      367(25) | -4(589)  346(8)  346(589) |+---------------------------+--------------------------+---------------------------+| 2       3         679     | 789       48     147     | 1489     5       1467-89  || 47(59)  47(9)     1       | -7(2589)  6      47(25)  | 3        47(8)   47(289)  || 8       467-9     5679    | 23579     2345   1347-25 | 1249     1467    1467-29  |+---------------------------+--------------------------+---------------------------+| 137(5)  17(28)    4       | 6         9      3(25)   | -1(258)  137(8)  137(258) || 1367-5  167-2     2567    | 235       2345   8       | 1245     9       1347-25  || 3(59)   (289)     (2589)  | 1         7      34(25)  | 6        34(8)   34(258)  |+---------------------------+--------------------------+---------------------------+`

Code: Select all
`72 Candidates,      19 Truths = {2R13579 5R13579 8R13579 9R1359}     19 Links = {59c1 289c2 25c6 8c8 2589c9 1n5 3n347 5n4 7n7 9n3}     18 Eliminations --> r3c34<>7, r6c69<>2, r6c29<>9, r8c29<>2, r8c19<>5, r24c9<>8, r3c4<>3,                          r3c7<>4, r4c9<>9, r5c4<>7, r6c6<>5, r7c7<>1,      `

EDIT : something is wrong in that table; Truths should appear as 2589 in rows 1;3;5;7;9
we have 19 truths
Links are ok

My solver does not look for more than 4 rows to build a SLG.

Here we have 5 rows, but the process is the same;

The floors used here are complementary to eleven's proposal.
Very often, when a group of floors is active, the complementary set is active also.

The 4 floors is easier to build and more efficient.

champagne
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### Re: The hardest sudokus (new thread)

Hi,

I had a look at the post where a short list of "potential hardest" was given.

Entry 5416 is shown with high potential for floors 2589 and floors 13467.

Likely other entries with similar potential will disappear as well.

Next update will include the filter for the found "rank 0 logic" for that puzzle.

champagne
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### Re: The hardest sudokus (new thread)

Thanks to Ron and champagne.

Now i have tested, if i could find 6 unit solutions for the 11.8+ and champagne's 18 puzzles. They were rather quickly found for all but this one (which i will try again later):
Code: Select all
`1.......9.5.1...3...8..34...1.5.......9..8..2....6..7.3....4..8..2.......8..7..6.;3411;elev;11.1;11.1;10.8;7`
eleven

Posts: 3107
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

champagne wrote:
Code: Select all
`19 Truths = {2R13579 5R13579 8R13579 9R1359}19 Links = {59c1 289c2 25c6 8c8 2589c9 1n5 3n347 5n4 7n7 9n3}18 Eliminations --> r3c34<>7, r6c69<>2, r6c29<>9, r8c29<>2, r8c19<>5, r24c9<>8, r3c4<>3,                     r3c7<>4, r4c9<>9, r5c4<>7, r6c6<>5, r7c7<>1,`

EDIT : something is wrong in that table; Truths should appear as 2589 in rows 1;3;5;7;9
we have 19 truths
Links are ok

I see nothing wrong in that table. Four candidate values in 5 rows would be 20 truths. R7c5 already holds digit <9>, leaving 19 truths.
ronk
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### Re: The hardest sudokus (new thread)

ronk wrote:
champagne wrote:
Code: Select all
`19 Truths = {2R13579 5R13579 8R13579 9R1359}19 Links = {59c1 289c2 25c6 8c8 2589c9 1n5 3n347 5n4 7n7 9n3}18 Eliminations --> r3c34<>7, r6c69<>2, r6c29<>9, r8c29<>2, r8c19<>5, r24c9<>8, r3c4<>3,                     r3c7<>4, r4c9<>9, r5c4<>7, r6c6<>5, r7c7<>1,`

EDIT : something is wrong in that table; Truths should appear as 2589 in rows 1;3;5;7;9
we have 19 truths
Links are ok

I see nothing wrong in that table. Four candidate values in 5 rows would be 20 truths. R7c5 already holds digit <9>, leaving 19 truths.

rigth

I am not so familiar with XSUDO notation and I misred the Truths

champagne
Last edited by champagne on Tue Sep 27, 2011 8:10 am, edited 1 time in total.
champagne
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### Re: The hardest sudokus (new thread)

The puzzle above (elev;11.1;11.1;10.8;7) also resisted 10 more tries to find a 6 unit solution. Only 8 candidates could be eliminated (7r1c2, 2r1c6, 2r1c6, 5r8c5, 7r2c1, 5r6c7, 9r7c7, 5r8c5). So in this respect it is the hardest known of the world

On the other hand for 10 of the 36 11.8+ puzzles (including 11.90;11.90;2.60;elev;1;5) and 6 of champagne's '18 hardest' solutions with 5 unit moves could be found in the first try.
eleven

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Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

eleven wrote:The puzzle above (elev;11.1;11.1;10.8;7) also resisted 10 more tries to find a 6 unit solution.

eleven, would you please clarify the meaning of "6 unit solution?" Six rows? Six columns? Six boxes? Any combination of six rows, columns and boxes? And how do candidates of one cell, as one strong-inference-set, fit into this picture?
ronk
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### Re: The hardest sudokus (new thread)

ronk wrote:
eleven wrote:The puzzle above (elev;11.1;11.1;10.8;7) also resisted 10 more tries to find a 6 unit solution.

eleven, would you please clarify the meaning of "6 unit solution?" Six rows? Six columns? Six boxes? Any combination of six rows, columns and boxes? And how do candidates of one cell, as one strong-inference-set, fit into this picture?

I mean subgrids, defined by 6 units (row/column/box), as i posted them in the 2 samples (with 4 units, could be boxes as well). Any candidate, for which it is not not possible to fill the subgrids according to the sudoku rules is eliminated.

E.g. this is a 4 unit subgrid (of champagne dry) consisting of box 1 and columns 3,4,7, where 8r2c4 can be eliminated.
Code: Select all
` *----------------------------------------------------------------------* | 9      8       12345  | 7      346    1246   | 1234    145    235    | | 7      1235    12345  | 12348  3489   12489  | 6       14589  23589  | | 1234   123     6      | 12348  5      12489  | 123478  14789  23789  | |-----------------------+----------------------+-----------------------| | 1268   4       129    | 168    678    5      | 278     3      26789  | | 12368  1236    7      | 9      3468   1468   | 5       468    268    | | 3568   3569    359    | 3468   2      4678   | 478     46789  1      | |-----------------------+----------------------+-----------------------| | 12346  12367   8      | 5      467    2467   | 9       167    367    | | 2356   235679  2359   | 268    1      26789  | 378     5678   4      | | 1456   15679   1459   | 468    46789  3      | 178     2      5678   | *----------------------------------------------------------------------*23 groups locked, 38 cells locked, 1/80 candidates could be eliminated *---------------------------------------------------* | 9     8     12345  | 7      .  .  | 1234    .  .  | | 7     1235  12345  | 12348  .  .  | 6       .  .  | | 1234  123   6      | 12348  .  .  | 123478  .  .  | |--------------------+--------------+---------------| | .     .     129    | 168    .  .  | 278     .  .  | | .     .     7      | 9      .  .  | 5       .  .  | | .     .     359    | 3468   .  .  | 478     .  .  | |--------------------+--------------+---------------| | .     .     8      | 5      .  .  | 9       .  .  | | .     .     2359   | 268    .  .  | 378     .  .  | | .     .     1459   | 468    .  .  | 178     .  .  | *---------------------------------------------------*r2c4<>8`

If a "subgrid" consists of all 9 rows (or columns/boxes), then all wrong candidates can be eliminated.
eleven

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Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

Hi all,

Apologies for not being up to speed with what has been posted here (work commitments ).

Can I propose that Champagne, eleven, .... use a single post which can be updated regulary by them to list what they/their solvers consider as hardest.

These posts can then can be easily accessed from a link in the 2nd post of this thread when I update it. (similar to what Ravel, JPF and others have done). The link would be something like "Champagne's hardest Sudoku puzzles ...."

tarek

P.S. I can understand champagne if you're too busy today to read this: Joyeux Anniversaire Ã  vous

tarek

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Joined: 05 January 2006

### Re: The hardest sudokus (new thread)

tarek wrote:Can I propose that Champagne, eleven, .... use a single post which can be updated regulary by them to list what they/their solvers consider as hardest.

I am not capable of rating puzzles. My statement "hardest in this respect" does not mean more than, that its best for this special "filter".
eleven

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### Re: special "filter"

eleven wrote:I am not capable of rating puzzles. My statement "hardest in this respect" does not mean more than, that its best for this special "filter".

Then I'll put a link to a list that categorizes hardest puzzles according this "filter" if you create one.

tarek

tarek

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Joined: 05 January 2006

### Re: The hardest sudokus (new thread)

eleven wrote:
ronk wrote:
eleven wrote:The puzzle above (elev;11.1;11.1;10.8;7) also resisted 10 more tries to find a 6 unit solution.

eleven, would you please clarify the meaning of "6 unit solution?" Six rows? Six columns? Six boxes? Any combination of six rows, columns and boxes? And how do candidates of one cell, as one strong-inference-set, fit into this picture?

I mean subgrids, defined by 6 units (row/column/box), as i posted them in the 2 samples (with 4 units, could be boxes as well). Any candidate, for which it is not not possible to fill the subgrids according to the sudoku rules is eliminated.

If a "subgrid" consists of all 9 rows (or columns/boxes), then all wrong candidates can be eliminated.

that's surely another way to find "nice logic". My solver works on floors.
It seems from "ronk example" that a set of cells can also be considered.

champagne
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### Re: The hardest sudokus (new thread)

tarek wrote:Hi all,

Apologies for not being up to speed with what has been posted here (work commitments ).

Can I propose that Champagne, eleven, .... use a single post which can be updated regulary by them to list what they/their solvers consider as hardest.

These posts can then can be easily accessed from a link in the 2nd post of this thread when I update it. (similar to what Ravel, JPF and others have done). The link would be something like "Champagne's hardest Sudoku puzzles ...."

tarek

P.S. I can understand champagne if you're too busy today to read this: Joyeux Anniversaire Ã  vous

hi tarek,

I have some days off, with other family events that just "anniversaire".

In principle, I have no problem to follow you.
In the data base I maintain, I'll add the file of "nothing special" with the appropriate evaluation of "forecast difficulty".

I can also put in a specific post the short list corresponding to these puzzles.

I'll be back home next Thursday and have then more time to open the discussion.

champagne
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