The New Sudoku Players' Forum

by **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

by **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.

by **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

by **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
----
EDIT (Nov 25, 2023): studying more this puzzle, I found:

1. (2=3)e2 - (3=1)a2 - (1=6)a6 - (6=2)f6 => -2 f1, -2 e56 [& lc elimination]
(same as before)
---

Code: Select all: .------------------------------------. |c16 *15(2) 3 | 1246 *45(6) c26 | 6 | 4 125 1256 | 126 356 236 | 5 |-----------------+------------------| | 2 *a14 a146 | 3 6-4 5 | 4 |b36 345 456 | 246 246 1 | 3 |-----------------+------------------| | 13 6 12 | 5 23 4 | 2 | 5 234 24 | 26 1 36 | 1 '------------------------------------' a b c d e f

2. Almost Y-wing (145)b46,e6

(4=16)bc4 - (6)a3 = (62)af6 - (2)b6|(6)e6 = Y-wing => -4 e4 [1 placement & NP(24)de3]
----

Code: Select all: .----------------------------------. | 16 a125 3 | 1246 b45 26 | 6 | 4 125 1256 | 126 c35 236 | 5 |----------------+-----------------| | 2 14 14 | 3 6 5 | 4 | 36 g3-5 56 | 24 24 1 | 3 |----------------+-----------------| | 13 6 12 | 5 d23 4 | 2 | 5 f234 24 | 26 1 e36 | 1 '----------------------------------' a b c d e f

3. (5)b6 = (5)e6 - (5=3)e5 - (3)e2 = (3)f1 - (3)b1 = (3)b3 => -5 b3; ste

by **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

by **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

by **jco** » Fri Jun 10, 2022 10:53 pm

Re: hardest 6x6? Postby tarek » Thu Jan 03, 2019
My last venture (possibly ) 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!

by **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

by **999_Springs** » Fri Oct 27, 2023 10:07 pm

4 years ago i took mathimagics's pile of 3703593 not-all-singles minimal 6x6 sudokus, did all the singles in them to get 542257 different puzzles (this is what mith now calls "singles-expanded forms"), converted about 70% of them to 9x9 sudokus and rated them with skfr, and the results are as above. i tried to get the java installation to work for 1to9only's modified sudokuexplainer for 6x6s, so i could see if the other 30% had any surprises in them, but never got around to it.

i finally got around to rating the whole batch of 542257 singles-expanded forms with sudoku6explainer. it took 3.5 hours

there are no new surprises. there remain only nine SE 8.4 puzzles and no more. this confirms that the SE 8.4 puzzles posted above are the hardest 6x6s available according to SE rating. a lot of new 8.3's popped up (130 of them). a lot of the skfr 7.7's turned into SE 7.8's but this is an already existing bug/feature known to skfr/SE

i suspect that, especially at the high-clue end, a lot of the puzzles will solve identically but not be isomorphic, by means of having multiple ways to fill in the complement of the puzzle in its solution grid - this looks like it's true for all 8 of the 12-clue 8.4's - this is something i briefly pointed out to mith when he was looking for high-clue hardest 9x9 puzzles, but applies to a much greater extent in the 6x6s

here is the complete table by SE rating and clue count

Code: Select all: clues 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 total ------------------------------------------------------------------------------------------------------------------- 8.4 8 1 9 8.3 6 63 123 35 28 16 8 279 8.2 42 3 45 7.8 13 2 2 1 18 7.7 2 5 14 6 12 5 44 7.6 2 12 25 18 12 2 71 7.5 2 2 7.3 7 34 12 36 4 93 7.2 4 389 3043 6398 5695 3774 2327 1128 434 155 19 23366 7.1 13 1075 10418 19396 16441 12522 7689 4014 1735 880 86 17 74286 7.0 5 72 152 188 143 117 23 700 6.9 2 114 336 241 322 94 28 21 11 2 1171 6.8 1 14 282 1111 1408 1163 874 380 180 58 4 5475 6.7 47 491 1357 1417 1232 1112 579 342 177 20 12 6786 6.6 8 1029 7270 18654 28193 29637 26889 20093 12693 7134 3530 1694 494 194 4 16 157532 6.5 8 20 82 228 424 550 425 282 291 156 82 24 2572 6.2 24 64 105 158 68 90 48 43 600 5.8 1 8 6 12 16 43 5.7 6 73 188 327 565 622 606 494 370 195 119 28 3593 5.6 6 76 474 1016 1799 2158 2417 2525 2355 1318 1283 513 733 114 133 14 6 16940 4.7 2 16 10 28 4.6 4 4 59 117 195 293 361 281 226 135 97 68 20 12 2 27 1901 4.5 94 558 1631 2135 2197 1809 1623 1147 882 362 239 156 32 10 12875 4.4 36 64 365 1051 1391 1583 1362 1068 640 194 124 56 7934 4.2 1 870 7206 18267 24750 24965 21719 16540 10217 6105 3260 1621 548 273 93 2 8 136445 3.8 4 7 19 16 9 2 57 3.6 2 6 4 4 16 3.4 2 74 96 148 109 27 8 10 474 3.2 124 462 527 700 620 481 237 158 40 6 3355 3.0 4 547 817 798 617 324 297 94 62 14 2 4 3580 2.8 25 276 470 468 196 193 91 32 6 2 1759 2.6 20 448 2766 5047 5237 4694 3469 2282 1521 740 256 110 48 26638 2.5 2 98 132 432 647 512 383 126 51 12 2395 2.0 4 409 3613 7112 7971 8991 7251 4905 2784 893 265 72 24 44294 1.7 96 322 679 1176 1632 1691 921 316 48 6881

this brings a somewhat anticlimactic conclusion to the question of what the hardest 6x6 puzzles are, if you're satisfied with using SE as a rating for these

for the manual solvers who like to do these tiny little puzzles for fun, here is a stratified random sample of 10% (rounded up) of the puzzles in each rating in the 7.3-8.3 range

random sample of hard 6x6s: Show

edit: the next stage after this, if anyone cares, is to determine how hard the hardest 6x6 pencilmark sudokus can be. for comparison, allowing arbitrary pencilmark grids moves the hardest known 9x9 sudoku from SE 11.9 to the 13+ range using nested dynamic chains, and possibly higher, if the implementation of SE allows for nested dynamic(+) (which i'm not sure if it does or not). for 4x4 sudokus, all the sudokus are doable with naked singles only or with hidden singles only, but the hardest known pencilmark 4x4 is SE 8.3. for the 6x6 ones, my guess is that there'll be something in the low 10's range with nested FC, but would be surprised to see anything higher

by **1to9only** » Sat Oct 28, 2023 11:15 am

This is the list of isomorphs in the list of 59 puzzles from the random sample of hard 6x6s.

6x6 isomorphs: Show

The #number is the puzzle number in the list. The last column shows the minlex form. My minlex program is here.

by **JPF** » Sat Oct 28, 2023 7:56 pm

1to9only wrote: My minlex program is here.

Thank you for these programs.
I tested the minlex 9x9 case. It seems to work for any series of digits from 0 to 9, whether valid puzzles or not.

JPF

by **jco** » Sat Oct 28, 2023 10:43 pm

999_Springs wrote: for the manual solvers who like to do these tiny little puzzles for fun, here is a stratified random sample of 10% (rounded up) of the puzzles in each rating in the 7.3-8.3 range

Thank you!!

I had my eyes on this:

Code: Select all: ..345..5..32.3..6.6.5.1.3...2.5...4. ED = 8.3/8.3/8.3

After no basics

Code: Select all: +----------------+--------------+ | 12 dc16(2) 3 | 4 5 d16 | 6 | 14 5 146 |d16 3 2 | 5 +----------------+--------------+ | 124 3 124 | 25 6 45 | 4 | 6 b24 5 |a2-3 1 34 | 3 +----------------+--------------+ | 3 146 146 | 156 2 156 | 2 | 5 dc16(2) 126 |e136 4 136 | 1 +----------------+--------------+ a b c d e f

1. (2)d3 = (2)b3 - (2)b16 = [RP(16): b1 = b6 - f6 = d5] - (1|6=3) d1 => - 3 d3 [9 placements]
----

Code: Select all: +--------------+-------------+ | 12 2-16 3 | 4 5 16 | 6 | 4 5 *16 |*16 3 2 | 5 +--------------+-------------+ | 12 3 12 | 5 6 4 | 4 | 6 4 5 | 2 1 3 | 3 +--------------+-------------+ | 3 *16 4 |*16 2 5 | 2 | 5 126 2-16| 3 4 16 | 1 +--------------+-------------+ a b c d e f

2. RP (16): b2 = d2 - d5 = c5 => -16 b6, c1; ste

EDIT: Nov 29, 2023 -> removed typo.

by **jco** » Sun Oct 29, 2023 2:34 pm

My solution for the last puzzle in the list of 9:

Code: Select all: 1...5......3...5.1...34...2..556...4 SE = 8.4

After [NP (26)af3 => -2b3, -6 c3]

Code: Select all: +-------------------+------------------+ | 1 B234 34-6 | 24-6 5 dA26 | 6 |a46(2) C245 456 | 1246 126 3 | 5 +-------------------+------------------+ | 2346 a'(2)34 34(6)| 5 26 1 | 4 |b26 C15 15 | 3 4 c26 | 3 +------------------+------------------+ | 34 D134 2 |E'16 136 5 | 2 | 5 6 E13 | 12 123 4 | 1 +-------------------+------------------+ a b c d e f (6")c4 || (2')a5,b4 - (2)a3 = (2)f3 - (2=6)f6 || (1=6)d2 || / (6=2)f6 - (2)b6 =' (25-1)b35 = (1)b2 \ (1=3)c1 - (3="4)c4 - (4='3)b4 - (3)b6 = (3)c6 => -6 c6, -6 d6; ste

My first approach was in two steps that could be put together

Hidden Text: Show

With no (2)b5, a w-wing would have solved it easily.

EDIT (Dez 03. 2023): I found a better way
After basics

Code: Select all: +------------------+-----------------+ | 1 234 346 | 246 5 *26 | 6 |A*26(4) 245 456 | 1246 *26(1) 3 | 5 +------------------+-----------------+ | 2346 234 346 | 5 26 1 | 4 | *26 15 15 | 3 4 *26 | 3 +------------------+-----------------+ |B 34 134 2 | 16 136 5 | 2 | 5 6 C13 | 12 23-1 4 | 1 +------------------+-----------------+ a b c d e f

1. Almost Bivalue Oddagon (26)e5, f6, f3, a3, a5

(1)e5 == (4)a5 - (4=31)a2.c1 => -1 e1
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Code: Select all: +------------------+----------------+ | 1 A(2)34 346 | 246 5 6-2 | 6 |A(2)46 B[2]45 456 | 1246 126 3 | 5 +------------------+----------------+ | 2346 234 346 | 5 F26 1 | 4 |A(2)6 C15 D15 | 3 4 GA(2)6 | 3 +------------------+----------------+ | 34 134 2 | 16 136 5 | 2 | 5 6 E13 | 12 E23 4 | 1 +------------------+----------------+ a b c d e f

2. Almost fish => -2 f6; ste

[(2): b6 = a5 - a3 = f3] = (2-5)b5 = (5)b3 - (5=1)c3 - (1=32)ce1 - (2)e4 = (2)f3

by **jco** » Sun Dec 10, 2023 5:33 pm

Source: Source: Re: 2 X 4 sudoku
Postby 999_Springs » Wed Nov 10, 2021 10:58 am
(...)
..34...5.....3..6..1.3.234....5.1... SE = 8.4
(...)

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After basics

Code: Select all: +-----------------+-------------------+ | 126 G*26 3 | 4 H125 156 | 6 | 1246 5 C*26(4)|B*26(1) 123 136 | 5 +-----------------+-------------------+ | 24 3 245 | A15 6 145 | 4 | 46 1 D46[5]| 3 4-5 2 | 3 +-----------------+-------------------+ | 3 4 E26 | 1256 H125 156 | 2 | 5 F*26 1 | G*26 34 34 | 1 +-----------------+-------------------+ a b c d e f

1. Almost chain with embedded Bivalue Oddagon (26) b16,c5,d15 using internals

Code: Select all: (5')c3 = [(5=1)d4 - (1)d5 =Odd= (4)c5 - (4='6)c3 - (6=2)c2 - (2)b1 = (2)d1,b6 - (2=15)e26] A B C D E F G H

=> -5 e3 [6 placements]
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Code: Select all: +----------------+----------------+ | 12 *26 3 | 4 125 *156 | 6 | 124 5 246 | 12-6 12 3 | 5 +----------------+----------------+ | 24 3 24 | 15 6 15 | 4 | 6 1 5 | 3 4 2 | 3 +----------------+----------------+ | 3 4 26 | 1256 125 15-6 | 2 | 5 *26 1 |*26 3 4 | 1 +----------------+----------------+ a b c d e f

2. Skyscraper (6): d1 = b1 - b6 = f6 => -6 f2, -6 d5; ste