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

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