The hardest sudokus (new thread)

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

Re: The hardest sudokus (new thread)

Postby JC Van Hay » Wed Dec 02, 2015 1:37 pm

The simplest Rank 0 pattern in ........9.....1.35..3.9..6...5.3...6.7...2...1..4.......9.8..5..2.7.....4.....8.. ;321;col;H12;1;1247; ; ;X; ;;
Code: Select all
+-----------------------+-------------------------+-------------------------+
| 25678  14568  1247-68 | 23568    247-56  345678 | 1247    12478    9      |
| 26789  4689   247-68  | 268      247-6   1      | 247     3        5      |
| 2578   1458   3       | 258      9       4578   | 1247    6        12478  |
+-----------------------+-------------------------+-------------------------+
| 289    489    5       | 189      3       789    | 12479   1247-89  6      |
| 3689   7      (468)   | 5689-1   (156)   2      | 359-14  (1489)   (1348) |
| 1      3689   (268)   | 4        (567)   5689-7 | 359-27  (2789)   (2378) |
+-----------------------+-------------------------+-------------------------+
| 367    136    9       | 1236     8       346    | 123467  5        1247-3 |
| 3568   2      (168)   | 7        (1456)  3569-4 | 369-14  (149)    (134)  |
| 4      356-1  (167)   | 3569-12  (1256)  3569   | 8       (1279)   (1237) |
+-----------------------+-------------------------+-------------------------+
16 Cells Lizard (R5689C3589) :

16 Truths = {5689N3 5689N5 5689N8 5689N9}
16 Links  = {1r589 2r69 4r58 7r69 3c9 5c5 6c35 8c3 9c8 8b6}
22 Eliminations : (68)r12c3, (56)r12c5, (89)r4c8, 3r7c9,
                  (14)r5c47, (27)r6c67, (14)r8c67, (12)r9c24
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Re: The hardest sudokus (new thread)

Postby David P Bird » Wed Dec 02, 2015 3:47 pm

Yet another view...

........9.....1.35..3.9..6...5.3...6.7...2...1..4.......9.8..5..2.7.....4.....8.. ;321;col;H12;1;1247; ; ;X; ;;
Code: Select all
       *--------------------------*--------------------------*--------------------------*
       | 25678   14568   1247-68  | 23568   247-56  345678   | 1247    12478   <9>      |
       | 26789   4689    247-68   | 268     247-6   <1>      | 247     <3>     <5>      |
       | 2578    1458    <3>      | 258     <9>     4578     | 1247    <6>     12478    |
       *--------------------------*--------------------------*--------------------------*
(89)r4 | 289     489     <5>      | 189     <3>     789      | 12479   1247-89 <6>      | (24)b4
       | 3689    <7>     468      | 5689-1  156     <2>      | 359-14  1489    1348     | (17)b5
       | <1>     3689    268      | <4>     567     5689-7   | 359-27  2789    2378     |
       *--------------------------*--------------------------*--------------------------*
(36)r7 | 367     136     <9>      | 1236    <8>     346      | 123467  <5>     1247-3   | (17)b7
       | 3568    <2>     168      | <7>     1456    3569-4   | 369-14  149     134      | (124)b8
       | <4>     356-1   167      | 3569-12 1256    3569     | <8>     1279    1237     |
       *--------------------------*--------------------------*--------------------------*
                         (68)c3             (56)c5             (1247)c7

MS-NS:(89)r4,(36)r7,(68)c3,(56)c5,(1247)c7,(24)b4,(17)b5,(17)b7,(124)b8 (21 digit instances/cells)
=> 22 Elims:68r1c3, 56r1c5, 68r2c3, 6r2c5, 89r4c8, 1r5c4, 14r5c7, 7r6c6, 27r6c7, 3r7c9, 4r8c6, 14r8c7, 1r9c2, 12r9c4

This is an example of a 'rescuable' almost SK Loop through r47c35 which is spoilt because r9c6 doesn't contain (1) as a given.
This produces 16 cells needing to hold 17 digits - one of these digits is wrong and will be shown as an invalid elimination somewhere.

To attempt to rescue it, try to add an extra cover set consisting of the unsolved 'base' digits [1247] in either an external row or column where it will add x digits and x+1 cells to the MSNS. In this case it is (1247)c7 which adds 4 digits and 5 fully covered cells which gets the counts to match.

Note that (1247+?)r12347c7 is an almost naked set so that (9)r4c7 ^ (3|6)r7c7 as one of these digits was the invalid elimination.
Not all rescue attempts are successful however.

BTW This grid also has a JExocet

DPB

TAGdpbAlmostSKLoop

[Edit Added tag]
Last edited by David P Bird on Sun May 22, 2016 9:59 pm, edited 1 time in total.
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Re: The hardest sudokus (new thread)

Postby champagne » Thu Dec 24, 2015 11:48 am

I just made an update of the data base

as for all new files , that update is in my "google drive space" with the name ph_1512.zip

the link to that storage place is here



The file contains now 1 637 062 puzzles (1 583 095 in august)

the count per clue in the data base is the following

20 77 unchanged
21 10794
22 87176
23 351532
24 551787
25 409800
26 225713 unchanged


The count per er is the following
11.9 9 unchanged
11.8 53 unchanged
11.7 113 unchanged
11.6 187 +1
11.5 549 +4
11.4 1359 +6

so most additions were with ratings below 11.4
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