hardest 6x6?

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

Re: hardest 6x6?

Postby 999_Springs » Wed Apr 24, 2019 1:09 am

i had trouble getting the se-modified-for-6x6 thing set up, so i decided to convert what i could from the big pile of 542257 unique not-singles sudokus into 9x9s. i managed to convert 375052 of them into 9x9's (maybe another 1% or so is possible - my code is a bit buggy). i then rated them all with skfr as it's faster than se for now, and then double-checked the top end with se.

here is the distribution of 6x6s by clue count, and how many that were able to be converted to 9x9s
Code: Select all
clues, unique 6x6s, convertible to 9x9s
8  0      0
9  103    2
10 5323   1630
11 38778  19053
12 84895  49736
13 101229 64816
14 98356  68931
15 82129  61720
16 58576  46568
17 35903  29937
18 19622  16934
19 9715   8389
20 4613   4093
21 2075   1737
22 625    573
23 242    215
24 59     58
25 14     14

here is the distribution by skfr rating. note that there may be some differences between skfr and se, such as most or all skfr 6.9's being se 7+ (haven't found one that's not yet) and some 7.7's being 7.8, a few 8.2's being 8.3 and so on.
Code: Select all
1.7 1456
2.0 31165
2.5 1173
2.6 19633
2.8 1301
3.0 2857
3.2 3068
3.4 378
3.6 15
3.8 56
4.2 101278
4.4 6682
4.5 7002
4.6 1372
4.7 18
5.6 12372
5.7 2854
5.8 43
6.2 505
6.5 2157
6.6 102638
6.7 4603
6.8 4571
6.9 5057
7.0 3318
7.1 46282
7.2 12858
7.3 64
7.5 2
7.6 44
7.7 24
7.8 4
8.2 44
8.3 149
8.4 9

here is the distribution of top ratings by clue count. the top line refers to clue count in the converted 9x9s, the next line to the original 6x6s
Code: Select all
se\cl9 54     55     56     57     58     59     60     61     62     63     64     65
se\cl6 9      10     11     12     13     14     15     16     17     18     19     20     total
-------------------------------------------------------------------------------------------------
8.4                         8                           1                                  9
8.3           4      25     71     17     15     10     7                                  149
8.2                  42     2                                                              44
7.8                                4                                                       4
7.7                                3      7      12     2                                  24
7.6           2      4      14     12     10            2                                  44
7.5                  2                                                                     2
7.3                  34     8      18     4                                                64
7.2           110    1423   3459   3019   2295   1531   686    255    58     19            12858
7.1           374    5589   11268  10186  8677   5383   2846   1257   600    60     14     46282

and finally here are the nine SE 8.4's. the top one is the 16-clue and is a (non-minimal) diamond that solves in one step. the other 8 are 12-clue puzzles that have ED=3.0 but have a much longer solve path, and i wonder if they're all basically isomorphic. numbers 1 and 5-8 are new; the others were found in the previous batch by 1to9only twice each, as there are two places to get rid of an initial single in each one.
original 6x6 format:
Code: Select all
1...56...1..21...5.35..13.1.6..62.1.
....5.4....3...5.1...34.3.2.1..6..3.
.2......61..2.4...61.....4.6.5.6..3.
.2.4....6...2.4...61......2..5..123.
.....64...2.23...1..5..2...61....2.4
1....6....2..3..6.6.5.4....61....2.4
..3....5.1....456...5..234....5.1...
..34...5.....3..6..1.3.234....5.1...
1...5......3...5.1...34...2..556...4

converted 9x9s:
Code: Select all
8...19567...7..81919785623498...1725.15..79833729856417.1.6.398.68.9.172239178456
....8.9579....7834487953126...8.9571...37.4898795412637.8.9.312.6..3.798392718645
.8....927..97..8162671893459.8...47271....689624897153.7.6.8594.9..3.768846975231
.8.9..247..7...8969264871358.9...47267....981214879563..8..5729..279.318791238654
.....89679...7.82448792613583...2719..9..7582275891346...78.691...2.9478798614253
8....9167....7.892197826345.8..9.6737.9.6.458635748921...68.719...9.7284978214536
..8...937.9.7..815357189246..957.468..5..879287496215398....3747.1...589543897621
..89..347.7....895953487126.8..9.673.3.7.821971936245889....7345.7...981341879562
8...9.157.....7893197853246...9.8571...37.984978541632..9..572878...9465562784319

a summary of hardest high-clue puzzles has been posted to my "maximum clues for each se rating" thread.
i'm not sure what to do with the remaining 167205 non-convertibles. maybe i'll leave the task of re-rating the entire batch with se-modified-for-6x6s to 1to9only to work his magic :P
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Re: hardest 6x6?

Postby qiuyanzhe » Wed Apr 24, 2019 9:49 am

999_Springs wrote:
Code: Select all
....5.4....3...5.1...34.3.2.1..6..3.
.2......61..2.4...61.....4.6.5.6..3.
.2.4....6...2.4...61......2..5..123.
.....64...2.23...1..5..2...61....2.4
1....6....2..3..6.6.5.4....61....2.4
..3....5.1....456...5..234....5.1...
..34...5.....3..6..1.3.234....5.1...
1...5......3...5.1...34...2..556...4

Yes, these 12-clue 8.4 puzzles are isomorphic.
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Re: hardest 6x6?

Postby jco » Sun May 22, 2022 9:25 pm

First time solving (manually) a puzzle 6x6 (using chess notation for this one).
Probably missed a shorter or simpler path

Code: Select all
....4.
.1.3.5
...2..
..3...
6.2.5.
.5....  SE 7.3

Code: Select all
.---------------.
| . . . | . 4 . |
| . 1 . | 3 . 5 |
|-------+-------|
| . . . | 2 . . |
| . . 3 | . . . |
|-------+-------|
| 6 . 2 | . 5 . |
| . 5 . | . . . |
'---------------'


(mentioned by 999_Springs » Sun Dec 30, 2018 in this thread)
----------------------
After basics

Code: Select all
.---------------------------------------.
|a23-5  236  f56    |e16    4     126   | 6
| 24    1     46    | 3     26    5     | 5
|-------------------+-------------------|
| 145   46    1456  | 2     136   346   | 4
| 124   246   3     |*5     16    46    | 3
|-------------------+-------------------|
| 6    c34    2     |d14    5     13    | 2
|b134   5     14    | 46    236   236   | 1
'---------------------------------------'
  a     b     c        d     e     f

1. (3)a6 = (3)a1 - (3=4)b2 - (4=1)d2 - (1=6)d6 - (6=5)c9 => -5 a6
----
Code: Select all
.-----------------------------------------.
|  v23    236   56    | 16    4     126   | 6
|  v24    1     46    | 3    b26    5     | 5
|---------------------+-------------------|
|   145  B46    1456  | 2     136   346   | 4
|uAa124  B246   3     |*5    b16    46    | 3
|---------------------+-------------------|
|   6    B34    2     | 14    5     13    | 2
|   14-3  5     14    | 46   b236   236   | 1
.-----------------------------------------.
    a     b     c        d     e     f

2. Kraken Cell (124)a3 => -3 a1 [8 placements]
||(1)a3 - (1=623)e351
||(2)a3 - (2=463)b342
||(4)a3 - (4=23)a56
----
Code: Select all
.---------------------------------------.
|*3     26   *5     |*1     4     26    | 6
| 24    1    f6-4   | 3    e26    5     | 5
|-------------------+-------------------|
|*5     46    146   | 2     136   346   | 4
|c124   246   3     |*5    d16    46    | 3
|-------------------+-------------------|
| 6    *3     2     |*4     5    *1     | 2
|b14    5    a14    |*6     23    23    | 1
'---------------------------------------'
  a     b     c       d     e      f

3. (4=1)c1 - (1)a1 = (1)a3 - (1=6)e3 - (6)e5 = (6)c5 => -4 c5; ste
Last edited by jco on Mon May 23, 2022 9:53 pm, edited 1 time in total.
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Posts: 498
Joined: 09 June 2020

Re: hardest 6x6?

Postby jco » Sun May 22, 2022 9:43 pm

Re: Re: hardest 6x6? Postby 1to9only » Tue Jan 01, 2019
- the highest rated grid is:

..3...4.....2..3.5.....1.6.5.45...1. ED=8.3/8.3/6.6

Code: Select all
+-------+-------+
| . . 3 | . . . |
| 4 . . | . . . |
+-------+-------+
| 2 . . | 3 . 5 |
| . . . | . . 1 |
+-------+-------+
| . 6 . | 5 . 4 |
| 5 . . | . 1 . |
+-------+-------+

---------------
Just one more

Code: Select all
.----------------------------------.
|c16   125  3    | 1246 456-2  d26 | 6
| 4    125  1256 | 126  356-2  236 | 5
|----------------+-----------------|
| 2    14   146  | 3    46     5   | 4
| 36   345  456  | 246  246    1   | 3
|----------------+-----------------|
|b13   6    12   | 5   a23     4   | 2
| 5    234  24   | 26   1      36-2| 1
'----------------------------------'
  a    b    c      d    e      f

1. (2=3)e2 - (3=1)a2 - (1=6)a6 - (6=2)f6 => -2 f1, -2 e56 [& lc elimination]
---
Code: Select all
.-----------------------------------.
| c16  b125   3    | 146  456  26   | 6
|  4   b125   1256 | 16   356  236  | 5
|------------------+----------------|
|  2   a14   u164  | 3   A46   5    | 4
| C36   345   56-4 |B246 B246  1    | 3
|------------------+----------------|
|Dd13   6   Ee12   | 5    23   4    | 2
|  5    234 Ff24   | 26   1    36   | 1
'-----------------------------------'
   a    b     c      d    e    f

2. Kraken Row (4)bce4 => -4 c3
(4-1)b4 = (1)b56 - (1)a6 = (1)a2 - (1=2)c2 - (2=4)c1
||
(4)c4
||
(4)e4 - (4=26)de3 - (6=3)a3 - (3=1)a2 - (1=2)c2 - (2=4)c1
---
Code: Select all
.---------------------------------.
|a16  A125  3    |u146 v456  26   | 6
| 4    125  1256 | 16   356  236  | 5
|----------------+----------------|
| 2   B14   14-6 | 3  wC46   5    | 4
|c36   345  56   | 246  24-6 1    | 3
|----------------+----------------|
|b13   6    12   | 5    23   4    | 2
| 5    234  24   | 26   1    36   | 1
'---------------------------------'
  a    b    c      d    e    f

3. Kraken Row (1)abd6 => -6 c4,e3 [& basics]
(1)a6 - (1=3)a2 - (3=6)a3
(1)b6 - (1=4)b4 - (4=6)e4
(1-4)d6 = (4)e6 - (4=6)e4
---
Code: Select all
.---------------------------------.
| 16   125  3    | 46   45   26   | 6
| 4    251  6-5  | 16  a35   236  | 5
|----------------+----------------|
| 2    14   14   | 3   *6    5    | 4
|c36   35  d56   | 24   24   1    | 3
|----------------+----------------|
|b13   6    12   | 5   b23   4    | 2
| 5    34   24   | 26   1    36   | 1
'---------------------------------'
  a    b    c      d    e    f

4. (5=3)e5 - (3)e2 = (3)a2 - (3=6)a3 - (6=5)c3 => -5 c5; ste
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Posts: 498
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Re: hardest 6x6?

Postby jco » Sat May 28, 2022 11:01 pm

I solved a nice 6x6 today (Source: Re: hardest 6x6? Postby 999_Springs » Sat Jan 12, 2019 1:12 pm).

Code: Select all
    ..3..6
    ...23.
    ..1.4.
    .4.3..
    .12...
    5..1..

SE 8.2/6.6/6.6
----
Code: Select all
.-------------------------------------.
| a14-2 25   3    | 45   15      6    | 6
| b146  56   456  | 2    3      c145  | 5
|-----------------+-------------------|
|  236  2356 1    | 56   4       25   | 4
|eA26   4    56   | 3   E156(2) d125  | 3
|-----------------+-------------------|
| B346  1    2    | 456  56      345  | 2
|  5   C36  C46   | 1   D26      234  | 1
'-------------------------------------'
   a    b    c      d    e       f

1. Almost L2-wing (2=6)a3 - (6)a2 = (6)bc1 - (6=2)e1 - (2*)e3 = [(1)a6 = (1)a5 - (1)f5 = (1-2)f3 =* (2)a3] => -2 a6

[+2 b6 & LC(5)bc5 => -5 f5]
-----
Code: Select all
.----------------------------------.
| 14   2    3    |a45   15    6    | 6
| 146  56   456  | 2    3    b14   | 5
|----------------+-----------------|
| 236  356  1    | 6-5  4    c25   | 4
| 26   4    56   | 3    1256 c125  | 3
|----------------+-----------------|
| 346  1    2    | 456  56    345  | 2
| 5    36   46   | 1    26    234  | 1
'----------------------------------'
  a    b    c      d    e    f

2. (5=4)d6 - (4=1)f5 - (1=25)f34 => -5 d4 [+6 d4]
------
Code: Select all
.---------------------------------.
| 14   2    3    | 45   15   6    | 6
| 146 A56   456  | 2    3    14   | 5
|----------------+----------------|
| 23 f 3-5  1    | 6    4   a25   | 4
| 26   4   d56   | 3    125  125  | 3
|----------------+----------------|
| 346  1    2    | 45   56   345  | 2
| 5   B36  c46   | 1    26  b24(3)| 1
'---------------------------------'
  a    b    c      d    e    f

3. Almost XY-Chain (5=6)b5 -(6=3)b1 - (3*)f1 = [(5=2)f4 - (2 =* 4)f1 - (4=6)c1 - (6=5)c3] => -5 b4; ste
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Re: hardest 6x6?

Postby jco » Sat Jun 04, 2022 12:30 pm

I have solved a nice puzzle proposed by tarek in this thread [Re: hardest 6x6? Postby tarek » Thu Jan 03, 2019 3:46 pm]
Again I use chess notation. I did not find the one-trick-pony way, but enjoyed especially the AUR in step 3.

Code: Select all
+-------+-------+
| 4 2 . | . 1 . |
| . . . | . . 2 |
+-------+-------+
| . . . | . . . |
| 1 . . | . . 4 |
+-------+-------+
| . . 3 | 5 . . |
| . 5 . | . . . |
+-------+-------+

42..1......2......1....4..35...5.... ED=6.8/6.6/2.6

After basics

Code: Select all
.---------------------------------------.
| 4     2    c56    | 36    1    d356   | 6
|b35    136   156   | 46    456   2     | 5
|-------------------+-------------------|
|a35    346   2456  | 1236  2356  136-5 | 4
| 1     36    256   | 236   2356  4     | 3
|-------------------+-------------------|
| 26    14    3     | 5     246   16    | 2
| 26    5     14    | 12346 2346  136   | 1
'---------------------------------------'
  a     b     c       d     e     f

1. (5): a4 = a5 - c6 = f6 => -5 f4 [+5 f6, +6 c6, +3 d6]
---
Code: Select all
.---------------------------------------.
| 4     2     6     | 3     1     5     | 6
| 35    13   c15    | 4-6  g46    2     | 5
|-------------------+-------------------|
| 35    346   245   | 126   235-6 136   | 4
| 1     36   b25    |a26    235-6 4     | 3
|-------------------+-------------------|
| 26   e14    3     | 5    f246   16    | 2
| 26    5    d14    | 1246  2346  136   | 1
'---------------------------------------'
  a     b     c       d     e     f

2. (6=2)d3 - (2=5)c3 - (5=1)c5 - (1)c1 = (1-4)b2 = (4)e2 - (4=6)e5 => -6 d5, -6 e34
---
Code: Select all
.------------------------------.
| 4   2    6   | 3    1    5   | 6
| 35  13   15  | 4    6    2   | 5
|--------------+---------------|
| 35  346 c245#| 126 d235# 136 | 4
| 1   36   25# | 26  d235# 4   | 3
|--------------+---------------|
| 26  14   3   | 5    24   16  | 2
| 26  5   b14  | 126 a24-3 136 | 1
'------------------------------'
  a   b    c      d   e    f

3. (4)e1 = (4)c1 - (4)c4 = UR(25)c34e34 = (3)e34 => -3 e1 [+3 f1]

NP(24)e12 => -2 e34, -2 d1
NP(35)ae4 => -3 b4, -5 c4
---
Code: Select all
.------------------------------.
| 4   2    6   | 3    1    5   | 6
| 35  13   15  | 4    6    2   | 5
|--------------+---------------|
| 35 b46   24  | 126  35  c16  | 4
| 1   36   25  | 26   35   4   | 3
|--------------+---------------|
| 26 a14   3   | 5    24   6-1 | 2
| 26  5    14  | 16   24   3   | 1
'------------------------------'
  a   b    c     d    e    f

4. Y-wing (1=4)b2 - (4=6)b4 - (6=1)f6 => -1 f2; ste
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Re: hardest 6x6?

Postby jco » Fri Jun 10, 2022 10:53 pm

Re: hardest 6x6? Postby tarek » Thu Jan 03, 2019
My last venture (possibly :D ) into one-trick-pony land:

.3..6...5..4.4....2....13......1.2.. ED=7.1/7.1/7.1
tarek

---------
After no basics

Code: Select all
.-----------------------------------------.
|  14     3     F14-2  | 15    6    a25#  | 6
|  16    v26     5     | 13    123   4    | 5
|----------------------+------------------|
|  156    4     F136   | 356   235   2356 | 4
|  2     u5(6)  F36    |E3456 D345   1    | 3
|----------------------+------------------|
|  3      256  cA26(4)#|B1456 B145  b56#  | 2
|  456    1      46    | 2    C345   356  | 1
'-----------------------------------------'
  a       b      c       d     e     f

1. Almost Almost Y-wing
(6&)b3 - (6=2)b5 [tags u,v]
||
(4*)c2 - (4)de2 = (4)e1 - (4)e3 = (4-6)d3 =& (631)c346 [tags A ... F]
||
[Y-wing (2=5)f6 - (5=6)f2 - (6 =*2)c2] [tags a,b,c]

=> -2 c6 [& basics]
---
Code: Select all
.-----------------------------.
| 14  3   14  | 5    6    2   | 6
| 6   2   5   | 13   13   4   | 5
|-------------+---------------|
|c15  4   136 | 36   2   d35  | 4
| 2   56  36  | 346  45-3 1   | 3
|-------------+---------------|
| 3   56  2   | 14   14   56  | 2
|b45  1   46  | 2   a35   56-3| 1
'-----------------------------'
  a   b   c     d    e    f

2. W-wing (3=5)e1 - (5)a1 = (5)a4 - (5=3)f4 => -3 f1; ste

Nice puzzle!
JCO
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Posts: 498
Joined: 09 June 2020

Re: hardest 6x6?

Postby jco » Thu Jun 16, 2022 10:08 pm

My last post in this very nice thread.
Re: hardest 6x6?
Postby 999_Springs » Wed Apr 24, 2019 1:09 am
(...)
1...56...1..21...5.35..13.1.6..62.1.
(...)

SE = 8.4
Code: Select all
.---------------------------------.
|  1    24  c34  |d234  5    6    | 6
|  456  245  346 | 1   d234 e234  | 5
|----------------+----------------|
|  2    1   b46  | 346 c34   5    | 4
| a46   3    5   | 246  24   1    | 3
|----------------+----------------|
|  3    45   1   | 245  6    24   | 2
|  5-4  6    2   | 345  1   f34   | 1
'---------------------------------'
   a    b    c     d    e    f

1. (4)a3 = (4)c4 - (4)c6|(4)e4 = (3)c6 & (3)e4 - (3)d6.e5 = (3)f5 - (3=4)f1 => -4 a1; ste
--------------------
Re: hardest 6x6?
Postby 999_Springs » Wed Apr 24, 2019 1:09 am
(...)
1....6....2..3..6.6.5.4....61....2.4
(...)

SE = 8.4
--
Code: Select all
.------------------------------------------.
|   1        245   234  | 345 e*35    6    | 6
|fed*35(4) CB46(5) 346  |f1345  2    f135  | 5
|-----------------------+------------------|
|  c24       3     124  | 15    6    b125  | 4
|   6       B12    5    | 13    4   aA2-13 | 3
|-----------------------+------------------|
|   2345     245   234  | 6     1    i35   | 2
|ge*35      B16    16   | 2  he*35    4    | 1
'------------------------------------------'
    a        b     c      d     e     f

1. [(2)f3 = (2)f4 - (2=4)a4 - (4)a5 = [RP(35)a15.e16] - (3|5 =& 1*45)adf5 - (5=3)a1 - (3)e1 = (3)f2] = (5& - 6)b5 = (6-1)b1 = (1-2)b3 = (2)f3
=> -13 f3 [6 placements]
(summary in words: either (5)b5 is true (implying +2 f3), or the chain [(2)f3 = ... = (3)f2] is valid. But this chain implies -13 f3)
----
Code: Select all
.---------------------------------.
| 1    245  234  | 45   35   6    | 6
| 345  45   6    | 145  2    135  | 5
|----------------+----------------|
| 24   3    24   | 15   6    15   | 4
| 6    1    5    | 3    4    2    | 3
|----------------+----------------|
| 2345 245  234  | 6    1    35   | 2
| 35   6    1    | 2    35   4    | 1
'---------------------------------'
  a    b    c      d    e    f


2. Skyscraper (3): c6 = e6 - e1 = a1 => -3 c2, a5

Nice puzzle!

EDIT: For the second puzzle, I found an interesting solution in two steps that replaces
an incorrect simplification of a complex two-stepper (hidden).
Hidden Text: Show
After basics
Code: Select all
.------------------------------------.
| 1    245  V2(3)4| 34-5 WD35   6    | 6
| 345  456 a(3)46 | 134-5  2    135  | 5
|-----------------+------------------|
| 24   3    c124  |d15     6    125  | 4
| 6    12    5    | 13     4    123  | 3
|-----------------+------------------|
| 2345 245  A2(3)4| 6      1    35   | 2
|B35   16   b16   | 2     C35   4    | 1
'------------------------------------'
  a    b     c      d      e    f

1. Kraken Column (3)c256
(3)c2 - (3)a1 = (3)e1 - (3=5)e6 [tags A ... D]
||
(3-6)c5 = (6-1)c1 = (1)c4 - (1=5)d4 [tags a ... d]
||
(3)c6 - (3=5)e6 [tags V, W]
=> -5 d56
----
Code: Select all
.---------------------------------------.
|  1     245   V234  |  V34  A5-3  6    |
|dC34(5) 456    346  |   134  2   B135  |
|--------------------+------------------|
| c24    3     b124  |   5    6    12   |
|  6     12     5    |   13   4    123  |
|--------------------+------------------|
|  2345  245 auU234  |   6    1    35   |
|ev35    16     16   |   2  fw35   4    |
'---------------------------------------'

2. (5)e6 = (5)f5 - (5*)a5 = Kraken Cell (234)c2 [tags A,B,C]
Kraken Cell (234)c2
(2)c2 - (2=43)cd6 [tags U,V]
(3)c2 - (3)a1 = (3)e1 [tags u,v,w]
(4)c2 - (4)c4 = (4)a4 - (4=*3)a5 - (3)a1 = (3)e1 [tags a ... f]

=> -3 e6; ste
JCO
jco
 
Posts: 498
Joined: 09 June 2020

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