The New Sudoku Players' Forum

by **Havard** » Fri May 05, 2006 11:43 pm

ronk wrote:
Havard wrote:And we see this leads to a contradiction, so the elimination is valid!

Sorry, I should have thought to tell you I don't consider "elimiination by contradiction" to be "logic". T&E can do as well.

ok, then... Do you remember these posts:
http://forum.enjoysudoku.com/viewtopic.php?p=24494
They have a very similar pattern that you accepted. (at least you did then... ) for the Jellyfish

Havard

by **Ocean** » Sat May 06, 2006 7:23 am

ab wrote:That wasn't my question. I have a program I can use to solve it by brute force. My question was how did you generate the puzzle?

A search through the specific pattern resulted in 53 non-equivalent minimal 20s, plus a number of non-minimals. All 53 are 'hard' to solve (at least hard for 'Simple Sudoku' and also my solver). In the previous post the 'vert hardest' was chosen (one of two puzzles where the solvers could not fix any extra cells). Among the non-minimals were both 'easy' and 'hard' ones.

Code: Select all: # # 48 M20s. Pattern: 0-9-6-0-0. Minimal puzzles with 20 clues, full symmetry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

Credit goes to ab for finding the first 20-clue puzzle in this pattern (as far as we know). Finding the first one is always most difficult. The search algorithm was not a complete search, it's based partly on input seed, and partly on random (- in effect a partial/limited search through the complete pattern). ab's 'first' puzzle (#08) was among the input seed, so it can be regarded as ancestor, or 'grandfather' to all (not 'father', since none of the minimals were 'first generation' results). The #01 ('almost similar' pattern) was also input to the process.

It's also possible more than these 53 were found. After a simple (incomplete) normalization process about 200 'different' puzzles were listed. But I could only separate with certainty the 53 listed above, so the rest are possible isomorphs.
[Edit: Five isomorphs taken out. Leaving the 48 non-equivalent puzzles.]

by ab » Sat May 06, 2006 7:42 am

That's interesting. I wonder if you can use a pseudo puzzle as the seed? As I said in an earlier post I have a pseudo puzzle for one 20 which we don't have yet:

Code: Select all: ...|...|... ...|6.5|... ..1|.3.|2.. ----------- .5.|.8.|.9. ..8|3.2|7.. .9.|.7.|.6. ----------- ..2|.1.|8.. ...|4.9|... ...|...|... 2 solutions

by **Ocean** » Sat May 06, 2006 8:33 am

ab wrote:That's interesting. I wonder if you can use a pseudo puzzle as the seed? As I said in an earlier post I have a pseudo puzzle for one 20 which we don't have yet:

Sure. Seemed to work. What about this:

Code: Select all: M20. [0-2-5-1-0]. Minimal full symmetric puzzle, 20 clues. *-----------* |...|...|...| |...|1.2|...| |..3|.4.|5..| |---+---+---| |.2.|.6.|.7.| |..6|4.5|8..| |.7.|.8.|.9.| |---+---+---| |..5|.3.|6..| |...|9.7|...| |...|...|...| *-----------*

The result came so fast, I just wondered what happened, and checked a litte more. It turns out that changing one clue in your pseudo is enough to make it a valid sudoku. For easier compare with the pseudo, here is the un-normalized version of the same puzzle:

Code: Select all: M20. (ab/Ocean) ...|...|... ...|6.5|... ..1|.3.|2.. ----------- .5.|.8.|.9. ..8|3.2|7.. .9.|.7.|.4. ----------- ..2|.1.|8.. ...|4.9|... ...|...|...

by ab » Sun May 07, 2006 12:41 am

We make a good team Ocean. You convert my pseudo puzzle into a valid 20 and I improve your puzzle in the inferior thread

Although my solver can handle xy-wings I've been having trouble trying to add them to my generator, so I might not have found that puzzle for myself :!:

by **JPF** » Sun May 07, 2006 10:07 am

ab wrote:That's interesting. I wonder if you can use a pseudo puzzle as the seed? As I said in an earlier post I have a pseudo puzzle for one 20 which we don't have yet:

Ocean wrote:Sure. Seemed to work. What about this...

Ocean, I have the same problem with 2 puzzles.
Both have 2 solutions :

Code: Select all: 20 clues ; 1-12-0-1-0 . . . | . 5 . | . . . . 7 2 | . . . | 3 6 . . 3 . | . . . | . 2 . -------+-------+------- . . . | . 9 . | . . . 5 . . | 3 . 8 | . . 1 . . . | . 4 . | . . . -------+-------+------- . 2 . | . . . | . 9 . . 6 3 | . . . | 7 4 . . . . | . 8 . | . . . 1-4-4-1-0 ; 1-12-0-1-0 ; 4-1-4-1-0 ; 8-8-1-1-0 ; 20-1-0-1-0 ; 24-0-1-1-0

ans this one, 21 clues, for which you just gave the associated 20 (#34 ab/Ocean) :

Code: Select all: 21 clues ; 2-0-5-1-1 . . . | 4 . 9 | . . . . . . | . . . | . . . . . 1 | . 5 . | 2 . . -------+-------+------- 1 . . | . 3 . | . . 4 . . 3 | 9 1 8 | 5 . . 6 . . | . 2 . | . . 7 -------+-------+------- . . 5 | . 8 . | 1 . . . . . | . . . | . . . . . . | 6 . 7 | . . . 0-2-5-1-1 ; 0-9-2-1-1 ; 2-0-5-1-1 ; 2-9-0-1-1 ; 17-0-2-1-1 ;17-2-0-1-1 PS : removing 1 in r5c5 gives 2517 solutions....

Could you do something for me ?

Thanks in advance.

JPF

by **Ocean** » Mon May 08, 2006 5:00 am

JPF wrote:Ocean, I have the same problem with 2 puzzles.
Both have 2 solutions :
(...)

and this one, 21 clues, for which you just gave the associated 20 (#34 ab/Ocean) :
(...)
Could you do something for me ?
Thanks in advance.

JPF

The first pseudo did not give any immediate results.
A slight modification of the second pseudo gives this minimal 21:

Code: Select all: M21 ; 2-0-5-1-1 (JPF/Ocean) . . . | 4 . 2 | . . . . . . | . . . | . . . . . 1 | . 5 . | 8 . . -------+-------+------- 1 . . | . 3 . | . . 4 . . 3 | 9 1 8 | 5 . . 6 . . | . 2 . | . . 7 -------+-------+------- . . 5 | . 8 . | 2 . . . . . | . . . | . . . . . . | 6 . 7 | . . . 0-2-5-1-1 ; 0-9-2-1-1 ; 2-0-5-1-1 ; 2-9-0-1-1 ; 17-0-2-1-1 ;17-2-0-1-1

by **JPF** » Mon May 08, 2006 3:58 pm

Ocean wrote:The first pseudo did not give any immediate results.
A slight modification of the second pseudo gives this minimal 21...

Thanks, Ocean.

JPF

by **JPF** » Mon May 08, 2006 4:36 pm

Here is the current list of the 20 & 21 clues puzzles with full symmetry :

M : Minimal ; Mx : Minimal, x clues.
SM (*) : Symmetric minimal, but not minimal.
x-y-z-t-u : pattern code (and equivalent symmetric patterns), as defined earlier in this thread.

Code: Select all: #01 Ocean [M20 0-5-2-0-0 ] . . . | . . . | . . . . . 1 | . 2 . | 3 . . . 4 . | 5 . 6 | . 7 . -------+-------+------- . . 4 | . . . | 1 . . . 7 . | . . . | . 8 . . . 2 | . . . | 6 . . -------+-------+------- . 8 . | 9 . 7 | . 5 . . . 3 | . 6 . | 2 . . . . . | . . . | . . . 0-5-2-0-0 0-6-1-0-0 5-0-2-0-0 6-0-1-0-0 9-2-0-0-0 10-1-0-0-0 #02 ab [M20 24-0-1-2-0 ] 3 8 . | . . . | . 7 1 9 . . | . . . | . . 4 . . . | . 2 . | . . . -------+-------+------- . . . | 8 . 9 | . . . . . 4 | . . . | 6 . . . . . | 1 . 2 | . . . -------+-------+------- . . . | . 5 . | . . . 8 . . | . . . | . . 7 7 3 . | . . . | . 9 8 1-4-4-2-0 1-12-0-2-0 4-1-4-2-0 8-8-1-2-0 20-1-0-2-0 24-0-1-2-0 #03 ab [M20 8-0-5-2-0 ] . 3 . | . . . | . 4 . 6 . . | . . . | . . 3 . . 7 | . 2 . | 9 . . -------+-------+------- . . . | 3 . 8 | . . . . . 9 | . . . | 7 . . . . . | 5 . 6 | . . . -------+-------+------- . . 2 | . 1 . | 4 . . 5 . . | . . . | . . 6 . 9 . | . . . | . 7 . 4-9-0-2-0 8-0-5-2-0 16-8-5-2-0 16-9-4-2-0 17-4-0-2-0 17-8-4-2-0 #04 ab [M20 16-2-5-0-0 ] 6 . . | . . . | . . 5 . . . | 4 . 3 | . . . . . 5 | . 7 . | 1 . . -------+-------+------- . 2 . | . . . | . 7 . . . 7 | . . . | 2 . . . 8 . | . . . | . 3 . -------+-------+------- . . 6 | . 2 . | 5 . . . . . | 7 . 8 | . . . 4 . . | . . . | . . 3 2-8-5-0-0 2-9-4-0-0 16-2-5-0-0 16-9-2-0-0 17-2-4-0-0 17-8-2-0-0 #05 ab [M20 2-5-0-0-0 ] . . . | 7 . 2 | . . . . . 2 | . 4 . | 6 . . . 6 . | . . . | . 5 . -------+-------+------- 4 . . | . . . | . . 9 . 1 . | . . . | . 3 . 3 . . | . . . | . . 7 -------+-------+------- . 8 . | . . . | . 9 . . . 4 | . 2 . | 1 . . . . . | 5 . 3 | . . . 2-4-1-0-0 2-5-0-0-0 4-2-1-0-0 5-2-0-0-0 8-1-2-0-0 9-0-2-0-0 #06 ab [M20 0-6-0-1-0 ] . . . | . . . | . . . . . 2 | 5 . 8 | 1 . . . 7 . | . . . | . 9 . -------+-------+------- . 5 . | . 6 . | . 4 . . . . | 3 . 2 | . . . . 6 . | . 9 . | . 3 . -------+-------+------- . 9 . | . . . | . 7 . . . 8 | 2 . 1 | 3 . . . . . | . . . | . . . 0-4-2-1-0 0-6-0-1-0 4-0-2-1-0 6-0-0-1-0 8-2-0-1-0 10-0-0-1-0 #07 ab [M20 2-4-0-1-0 ] . . . | 2 . 5 | . . . . . 7 | . . . | 4 . . . 9 . | . . . | . 3 . -------+-------+------- 2 . . | . 7 . | . . 1 . . . | 8 . 3 | . . . 1 . . | . 9 . | . . 5 -------+-------+------- . 4 . | . . . | . 8 . . . 8 | . . . | 5 . . . . . | 7 . 1 | . . . 2-4-0-1-0 2-8-4-1-0 4-2-0-1-0 8-0-2-1-0 16-2-4-1-0 16-8-2-1-0 #08* ab [SM20 0-10-5-0-0 ] . . . | . . . | . . . . 3 . | 9 . 8 | . 1 . . . 2 | . 7 . | 8 . . -------+-------+------- . 1 . | . . . | . 3 . . . 5 | . . . | 7 . . . 9 . | . . . | . 6 . -------+-------+------- . . 7 | . 5 . | 2 . . . 6 . | 1 . 7 | . 9 . . . . | . . . | . . . 0-9-6-0-0 0-10-5-0-0 17-0-6-0-0 17-10-0-0-0 18-0-5-0-0 18-9-0-0-0 #09 ab [M20 2-4-0-2-0 ] . . . | 4 . 5 | . . . . . 9 | . . . | 8 . . . 7 . | . . . | . 4 . -------+-------+------- 3 . . | 9 . 8 | . . 6 . . . | . . . | . . . 8 . . | 3 . 2 | . . 5 -------+-------+------- . 5 . | . . . | . 9 . . . 7 | . . . | 4 . . . . . | 5 . 1 | . . . 2-4-0-2-0 2-8-4-2-0 4-2-0-2-0 8-0-2-2-0 16-2-4-2-0 16-8-2-2-0 #10 ab [M20 1-6-0-0-0 ] . . . | . 6 . | . . . . . 6 | 1 . 3 | 5 . . . 4 . | . . . | . 2 . -------+-------+------- . 2 . | . . . | . 9 . 9 . . | . . . | . . 4 . 3 . | . . . | . 8 . -------+-------+------- . 9 . | . . . | . 1 . . . 5 | 6 . 7 | 3 . . . . . | . 5 . | . . . 1-4-2-0-0 1-6-0-0-0 4-1-2-0-0 6-1-0-0-0 8-2-1-0-0 10-0-1-0-0 #11 ab [M20 5-8-0-2-0 ] . . 7 | . 5 . | 3 . . . 6 . | . . . | . 5 . 8 . . | . . . | . . 9 -------+-------+------- . . . | 8 . 5 | . . . 9 . . | . . . | . . 2 . . . | 4 . 3 | . . . -------+-------+------- 4 . . | . . . | . . 8 . 2 . | . . . | . 4 . . . 5 | . 3 . | 7 . . 4-8-1-2-0 5-8-0-2-0 8-1-4-2-0 9-0-4-2-0 16-4-1-2-0 16-5-0-2-0 #12 ab [M20 0-8-6-1-0 ] . . . | . . . | . . . . 4 . | . . . | . 1 . . . 8 | 2 . 6 | 9 . . -------+-------+------- . . 6 | . 1 . | 7 . . . . . | 4 . 5 | . . . . . 7 | . 3 . | 2 . . -------+-------+------- . . 2 | 7 . 9 | 6 . . . 3 . | . . . | . 5 . . . . | . . . | . . . 0-8-6-1-0 0-10-4-1-0 16-0-6-1-0 16-10-0-1-0 18-0-4-1-0 18-8-0-1-0 #13 ab [M20 1-3-4-0-0 ] . . . | . 6 . | . . . . . . | 7 1 4 | . . . . . 2 | . . . | 9 . . -------+-------+------- . 4 . | . . . | . 8 . 3 7 . | . . . | . 4 1 . 1 . | . . . | . 5 . -------+-------+------- . . 8 | . . . | 2 . . . . . | 9 7 1 | . . . . . . | . 4 . | . . . 1-3-4-0-0 1-8-3-0-0 3-1-4-0-0 3-8-1-0-0 16-1-3-0-0 16-3-1-0-0 #14 ab [M20 1-8-6-0-0 ] . . . | . 3 . | . . . . 9 . | . . . | . 5 . . . 1 | 7 . 2 | 3 . . -------+-------+------- . . 3 | . . . | 2 . . 6 . . | . . . | . . 9 . . 4 | . . . | 7 . . -------+-------+------- . . 7 | 8 . 4 | 1 . . . 2 . | . . . | . 3 . . . . | . 5 . | . . . 1-8-6-0-0 1-10-4-0-0 16-1-6-0-0 16-10-1-0-0 18-1-4-0-0 18-8-1-0-0 #15 Ocean [M21 0-4-2-1-1 ] . . . | . . . | . . . . . 1 | . . . | 6 . . . 8 . | 3 . 9 | . 5 . -------+-------+------- . . 6 | . 7 . | 8 . . . . . | 2 8 5 | . . . . . 4 | . 1 . | 7 . . -------+-------+------- . 4 . | 5 . 2 | . 3 . . . 8 | . . . | 4 . . . . . | . . . | . . . 0-4-2-1-1 0-6-0-1-1 4-0-2-1-1 6-0-0-1-1 8-2-0-1-1 10-0-0-1-1 #16 ab [M21 0-3-5-0-1 ] . . . | . . . | . . . . . . | 7 1 9 | . . . . . 6 | . 5 . | 8 . . -------+-------+------- . 1 . | . . . | . 2 . . 3 8 | . 6 . | 9 1 . . 2 . | . . . | . 7 . -------+-------+------- . . 5 | . 9 . | 6 . . . . . | 2 4 1 | . . . . . . | . . . | . . . 0-3-5-0-1 0-9-3-0-1 3-0-5-0-1 3-9-0-0-1 17-0-3-0-1 17-3-0-0-1 #17 JPF [M21 17-2-4-0-1 ] 6 . . | . 7 . | . . 9 . . . | 4 . 9 | . . . . . 4 | . . . | 1 . . -------+-------+------- . 6 . | . . . | . 4 . 2 . . | . 8 . | . . 7 . 1 . | . . . | . 5 . -------+-------+------- . . 5 | . . . | 3 . . . . . | 1 . 6 | . . . 9 . . | . 2 . | . . 8 2-8-5-0-1 2-9-4-0-1 16-2-5-0-1 16-9-2-0-1 17-2-4-0-1 17-8-2-0-1 #18 ab [M21 1-8-6-0-1 ] . . . | . 8 . | . . . . 1 . | . . . | . 2 . . . 4 | 6 . 3 | 7 . . -------+-------+------- . . 9 | . . . | 4 . . 6 . . | . 5 . | . . 1 . . 7 | . . . | 5 . . -------+-------+------- . . 6 | 5 . 4 | 3 . . . 3 . | . . . | . 9 . . . . | . 7 . | . . . 1-8-6-0-1 1-10-4-0-1 16-1-6-0-1 16-10-1-0-1 18-1-4-0-1 18-8-1-0-1 #19 JPF [M21 16-9-4-2-1 ] 6 . . | . . . | . . 3 . 5 . | . 1 . | . 4 . . . 8 | . . . | 9 . . -------+-------+------- . . . | 3 . 6 | . . . . 4 . | . 2 . | . 5 . . . . | 9 . 4 | . . . -------+-------+------- . . 9 | . . . | 3 . . . 1 . | . 7 . | . 2 . 8 . . | . . . | . . 6 4-9-0-2-1 8-0-5-2-1 16-8-5-2-1 16-9-4-2-1 17-4-0-2-1 17-8-4-2-1 #20 JPF [M21 0-5-2-0-1 ] . . . | . . . | . . . . . 1 | . 4 . | 5 . . . 6 . | 1 . 7 | . 2 . -------+-------+------- . . 6 | . . . | 7 . . . 8 . | . 5 . | . 6 . . . 3 | . . . | 4 . . -------+-------+------- . 2 . | 7 . 6 | . 8 . . . 4 | . 9 . | 1 . . . . . | . . . | . . . 0-5-2-0-1 0-6-1-0-1 5-0-2-0-1 6-0-1-0-1 9-2-0-0-1 10-1-0-0-1 #21 JPF [M21 1-9-2-0-1 ] . . . | . 1 . | . . . . 9 . | . 5 . | . 3 . . . . | 4 . 7 | . . . -------+-------+------- . . 8 | . . . | 4 . . 5 6 . | . 4 . | . 1 9 . . 7 | . . . | 8 . . -------+-------+------- . . . | 2 . 8 | . . . . 1 . | . 9 . | . 6 . . . . | . 7 . | . . . 1-2-5-0-1 1-9-2-0-1 2-1-5-0-1 2-9-1-0-1 17-1-2-0-1 17-2-1-0-1 #22 JPF [M21 4-0-2-2-1 ] . . 1 | . . . | 7 . . . . . | . . . | . . . 8 . . | 6 . 3 | . . 9 -------+-------+------- . . 6 | 7 . 9 | 4 . . . . . | . 3 . | . . . . . 2 | 5 . 8 | 1 . . -------+-------+------- 3 . . | 9 . 5 | . . 7 . . . | . . . | . . . . . 4 | . . . | 2 . . 0-4-2-2-1 0-6-0-2-1 4-0-2-2-1 6-0-0-2-1 8-2-0-2-1 10-0-0-2-1 #23 JPF [M21 0-10-5-0-1 ] . . . | . . . | . . . . 5 . | 7 . 8 | . 6 . . . 2 | . 3 . | 9 . . -------+-------+------- . 6 . | . . . | . 7 . . . 9 | . 1 . | 5 . . . 7 . | . . . | . 1 . -------+-------+------- . . 3 | . 2 . | 4 . . . 2 . | 6 . 5 | . 8 . . . . | . . . | . . . 0-9-6-0-1 0-10-5-0-1 17-0-6-0-1 17-10-0-0-1 18-0-5-0-1 18-9-0-0-1 #24 JPF [M21 1-8-3-0-1 ] . . . | . 5 . | . . . . 8 . | . . . | . 2 . . . . | 1 3 4 | . . . -------+-------+------- . . 6 | . . . | 7 . . 2 . 1 | . 9 . | 4 . 3 . . 3 | . . . | 1 . . -------+-------+------- . . . | 6 1 3 | . . . . 7 . | . . . | . 5 . . . . | . 4 . | . . . 1-3-4-0-1 1-8-3-0-1 3-1-4-0-1 3-8-1-0-1 16-1-3-0-1 16-3-1-0-1 #25 JPF [M21 1-6-0-0-1 ] . . . | . 4 . | . . . . . 7 | 3 . 2 | 4 . . . 8 . | . . . | . 6 . -------+-------+------- . 5 . | . . . | . 7 . 8 . . | . 5 . | . . 6 . 1 . | . . . | . 8 . -------+-------+------- . 2 . | . . . | . 1 . . . 4 | 9 . 7 | 2 . . . . . | . 6 . | . . . 1-4-2-0-1 1-6-0-0-1 4-1-2-0-1 6-1-0-0-1 8-2-1-0-1 10-0-1-0-1 #26 JPF [M21 2-8-4-1-1 ] . . . | 4 . 3 | . . . . 8 . | . . . | . 6 . . . 3 | . . . | 1 . . -------+-------+------- 7 . . | . 9 . | . . 3 . . . | 8 2 5 | . . . 4 . . | . 7 . | . . 8 -------+-------+------- . . 4 | . . . | 5 . . . 5 . | . . . | . 8 . . . . | 1 . 7 | . . . 2-4-0-1-1 2-8-4-1-1 4-2-0-1-1 8-0-2-1-1 16-2-4-1-1 16-8-2-1-1 #27 JPF [M21 2-8-4-2-1 ] . . . | 3 . 7 | . . . . 1 . | . . . | . 5 . . . 2 | . . . | 1 . . -------+-------+------- 3 . . | 6 . 5 | . . 7 . . . | . 2 . | . . . 7 . . | 4 . 9 | . . 6 -------+-------+------- . . 3 | . . . | 2 . . . 9 . | . . . | . 4 . . . . | 5 . 6 | . . . 2-4-0-2-1 2-8-4-2-1 4-2-0-2-1 8-0-2-2-1 16-2-4-2-1 16-8-2-2-1 #28 JPF [M21 2-5-0-0-1 ] . . . | 4 . 9 | . . . . . 5 | . 1 . | 3 . . . 7 . | . . . | . 9 . -------+-------+------- 7 . . | . . . | . . 1 . 4 . | . 6 . | . 7 . 3 . . | . . . | . . 2 -------+-------+------- . 9 . | . . . | . 2 . . . 1 | . 4 . | 5 . . . . . | 3 . 7 | . . . 2-4-1-0-1 2-5-0-0-1 4-2-1-0-1 5-2-0-0-1 8-1-2-0-1 9-0-2-0-1 #29 JPF [M21 5-8-0-2-1 ] . . 2 | . 9 . | 7 . . . 5 . | . . . | . 8 . 1 . . | . . . | . . 3 -------+-------+------- . . . | 7 . 6 | . . . 5 . . | . 8 . | . . 1 . . . | 5 . 9 | . . . -------+-------+------- 4 . . | . . . | . . 5 . 7 . | . . . | . 4 . . . 9 | . 7 . | 6 . . 4-8-1-2-1 5-8-0-2-1 8-1-4-2-1 9-0-4-2-1 16-4-1-2-1 16-5-0-2-1 #30* ab [SM21 0-9-2-2-1 ] . . . | . . . | . . . . 4 . | . 6 . | . 9 . . . . | 5 . 1 | . . . -------+-------+------- . . 5 | 9 . 3 | 8 . . . 9 . | . 4 . | . 2 . . . 1 | 8 . 7 | 5 . . -------+-------+------- . . . | 7 . 8 | . . . . 6 . | . 9 . | . 3 . . . . | . . . | . . . 0-2-5-2-1 0-9-2-2-1 2-0-5-2-1 2-9-0-2-1 17-0-2-2-1 17-2-0-2-1 #31* ab [SM21 1-4-4-2-1 ] . . . | . 7 . | . . . . . 9 | . . . | 5 . . . 5 8 | . . . | 3 9 . -------+-------+------- . . . | 3 . 9 | . . . 7 . . | . 8 . | . . 2 . . . | 6 . 7 | . . . -------+-------+------- . 3 5 | . . . | 9 6 . . . 6 | . . . | 8 . . . . . | . 4 . | . . . 1-4-4-2-1 1-12-0-2-1 4-1-4-2-1 8-8-1-2-1 20-1-0-2-1 24-0-1-2-1 #32* ab [SM21 0-8-6-1-1 ] . . . | . . . | . . . . 4 . | . . . | . 6 . . . 2 | 9 . 7 | 5 . . -------+-------+------- . . 7 | . 6 . | 2 . . . . . | 5 3 8 | . . . . . 8 | . 4 . | 9 . . -------+-------+------- . . 9 | 2 . 6 | 8 . . . 6 . | . . . | . 5 . . . . | . . . | . . . 0-8-6-1-1 0-10-4-1-1 16-0-6-1-1 16-10-0-1-1 18-0-4-1-1 18-8-0-1-1 #33 Ocean [M20 0-9-6-0-0 ] . . . | . . . | . . . . 1 . | . 2 . | . 3 . . . 4 | 5 . 6 | 7 . . -------+-------+------- . . 6 | . . . | 5 . . . 2 . | . . . | . 8 . . . 8 | . . . | 9 . . -------+-------+------- . . 5 | 4 . 7 | 6 . . . 8 . | . 9 . | . 1 . . . . | . . . | . . . 0-9-6-0-0 0-10-5-0-0 17-0-6-0-0 17-10-0-0-0 18-0-5-0-0 18-9-0-0-0 #34 ab/Ocean [M20 0-2-5-1-0 ] . . . | . . . | . . . . . . | 6 . 5 | . . . . . 1 | . 3 . | 2 . . -------+-------+------- . 5 . | . 8 . | . 9 . . . 8 | 3 . 2 | 7 . . . 9 . | . 7 . | . 4 . -------+-------+------- . . 2 | . 1 . | 8 . . . . . | 4 . 9 | . . . . . . | . . . | . . . 0-2-5-1-0 0-9-2-1-0 2-0-5-1-0 2-9-0-1-0 17-0-2-1-0 17-2-0-1-0 #35 JPF/Ocean [M21 2-0-5-1-1 ] . . . | 4 . 2 | . . . . . . | . . . | . . . . . 1 | . 5 . | 8 . . -------+-------+------- 1 . . | . 3 . | . . 4 . . 3 | 9 1 8 | 5 . . 6 . . | . 2 . | . . 7 -------+-------+------- . . 5 | . 8 . | 2 . . . . . | . . . | . . . . . . | 6 . 7 | . . . 0-2-5-1-1 0-9-2-1-1 2-0-5-1-1 2-9-0-1-1 17-0-2-1-1 17-2-0-1-1 #36* JPF [SM21 16-0-6-2-1 ] 3 . . | . . . | . . 4 . . . | . . . | . . . . . 1 | 5 . 9 | 7 . . -------+-------+------- . . 5 | 3 . 1 | 9 . . . . . | . 6 . | . . . . . 7 | 9 . 2 | 1 . . -------+-------+------- . . 9 | 1 . 5 | 8 . . . . . | . . . | . . . 8 . . | . . . | . . 3 0-8-6-2-1 0-10-4-2-1 16-0-6-2-1 16-10-0-2-1 18-0-4-2-1 18-8-0-2-1 #37 JPF [M20 1-2-4-1-0 ] . . . | . 1 . | . . . . . . | 6 . 7 | . . . . . 3 | . . . | 4 . . -------+-------+------- . 6 . | . 9 . | . 8 . 7 . . | 8 . 2 | . . 1 . 1 . | . 5 . | . 3 . -------+-------+------- . . 5 | . . . | 7 . . . . . | 1 . 6 | . . . . . . | . 2 . | . . . 1-2-4-1-0 1-8-2-1-0 2-1-4-1-0 2-8-1-1-0 16-1-2-1-0 16-2-1-1-0 #38 ab [M21 0-2-5-2-1 ] . . . | . . . | . . . . . . | 8 . 6 | . . . . . 3 | . 2 . | 5 . . -------+-------+------- . 8 . | 2 . 9 | . 1 . . . 7 | . 4 . | 3 . . . 9 . | 1 . 3 | . 6 . -------+-------+------- . . 4 | . 5 . | 2 . . . . . | 9 . 8 | . . . . . . | . . . | . . . 0-2-5-2-1 0-9-2-2-1 2-0-5-2-1 2-9-0-2-1 17-0-2-2-1 17-2-0-2-1 #39 JPF . . . | . . . | . . . . 1 . | . . . | . 2 . . . 3 | 4 . 5 | 6 . . -------+-------+------- . . 5 | . 6 . | 3 . . . . . | 7 8 9 | . . . . . 9 | . 1 . | 4 . . -------+-------+------- . . 4 | 6 . 2 | 9 . . . 2 . | . . . | . 7 . . . . | . . . | . . . 0-8-6-1-1 0-10-4-1-1 16-0-6-1-1 16-10-0-1-1 18-0-4-1-1 18-8-0-1-1 #40 JPF . . . | . 1 . | . . . . . 2 | . . . | 3 . . . 3 4 | . . . | 2 5 . -------+-------+------- . . . | 2 . 4 | . . . 6 . . | . 7 . | . . 8 . . . | 6 . 1 | . . . -------+-------+------- . 2 5 | . . . | 4 6 . . . 6 | . . . | 7 . . . . . | . 9 . | . . . 1-4-4-2-1 1-12-0-2-1 4-1-4-2-1 8-8-1-2-1 20-1-0-2-1 24-0-1-2-1 #41 JPF [M21 1-2-4-1-1 ] . . . | . 1 . | . . . . . . | 2 . 3 | . . . . . 4 | . . . | 5 . . -------+-------+------- . 6 . | . 3 . | . 7 . 2 . . | 7 6 8 | . . 1 . 1 . | . 9 . | . 4 . -------+-------+------- . . 9 | . . . | 2 . . . . . | 1 . 6 | . . . . . . | . 4 . | . . . 1-2-4-1-1 1-8-2-1-1 2-1-4-1-1 2-8-1-1-1 16-1-2-1-1 16-2-1-1-1

Here is the list of all the different patterns of F.S. puzzles with 20 and 21 clues.

Code: Select all: LIST of the F.S. patterns (20 & 21 clues) (x are the non valid patterns, NM the non minimal patterns) Add -0 or -1 for the full code of the pattern. * for a non minimal solution. Clues |Clues 20 |21 FS Code | X |X 0-0-3-3 0-3-0-3 3-0-0-3 X |X 0-0-6-3 0-10-0-3 18-0-0-3 X |X 0-0-7-1 0-11-0-1 19-0-0-1 X |X 0-0-7-2 0-11-0-2 19-0-0-2 X |X 0-1-2-3 0-2-1-3 1-0-2-3 1-2-0-3 2-0-1-3 2-1-0-3 X |X 0-1-3-1 0-3-1-1 1-0-3-1 1-3-0-1 3-0-1-1 3-1-0-1 X |X 0-1-3-2 0-3-1-2 1-0-3-2 1-3-0-2 3-0-1-2 3-1-0-2 |NM 0-1-5-3 0-9-1-3 1-0-5-3 1-9-0-3 17-0-1-3 17-1-0-3 | 0-1-6-1 0-10-1-1 1-0-6-1 1-10-0-1 18-0-1-1 18-1-0-1 | 0-1-6-2 0-10-1-2 1-0-6-2 1-10-0-2 18-0-1-2 18-1-0-2 | 0-1-7-0 0-11-1-0 1-0-7-0 1-11-0-0 19-0-1-0 19-1-0-0 X |X 0-2-2-1 2-0-2-1 2-2-0-1 X |X 0-2-2-2 2-0-2-2 2-2-0-2 X |X 0-2-3-0 0-3-2-0 2-0-3-0 2-3-0-0 3-0-2-0 3-2-0-0 |NM 0-2-4-3 0-8-2-3 2-0-4-3 2-8-0-3 16-0-2-3 16-2-0-3 #34 ab/Ocean|#35 JPF/Ocean 0-2-5-1 0-9-2-1 2-0-5-1 2-9-0-1 17-0-2-1 17-2-0-1 |#38 ab 0-2-5-2 0-9-2-2 2-0-5-2 2-9-0-2 17-0-2-2 17-2-0-2 | 0-2-6-0 0-10-2-0 2-0-6-0 2-10-0-0 18-0-2-0 18-2-0-0 | 0-3-4-1 0-8-3-1 3-0-4-1 3-8-0-1 16-0-3-1 16-3-0-1 | 0-3-4-2 0-8-3-2 3-0-4-2 3-8-0-2 16-0-3-2 16-3-0-2 |#16 ab 0-3-5-0 0-9-3-0 3-0-5-0 3-9-0-0 17-0-3-0 17-3-0-0 |NM 0-4-1-3 0-5-0-3 4-0-1-3 5-0-0-3 8-1-0-3 9-0-0-3 #06 ab |#15 Ocean 0-4-2-1 0-6-0-1 4-0-2-1 6-0-0-1 8-2-0-1 10-0-0-1 |#22 JPF 0-4-2-2 0-6-0-2 4-0-2-2 6-0-0-2 8-2-0-2 10-0-0-2 | 0-4-3-0 0-7-0-0 4-0-3-0 7-0-0-0 8-3-0-0 11-0-0-0 |NM 0-4-4-3 0-12-0-3 4-0-4-3 8-8-0-3 20-0-0-3 24-0-0-3 | 0-4-5-1 0-13-0-1 4-0-5-1 8-9-0-1 21-0-0-1 25-0-0-1 | 0-4-5-2 0-13-0-2 4-0-5-2 8-9-0-2 21-0-0-2 25-0-0-2 | 0-4-6-0 0-14-0-0 4-0-6-0 8-10-0-0 22-0-0-0 26-0-0-0 | 0-5-1-1 0-9-5-1 5-0-1-1 9-1-0-1 17-0-5-1 17-9-0-1 | 0-5-1-2 0-9-5-2 5-0-1-2 9-1-0-2 17-0-5-2 17-9-0-2 #01 Ocean |#20 JPF 0-5-2-0 0-6-1-0 5-0-2-0 6-0-1-0 9-2-0-0 10-1-0-0 | 0-5-4-1 0-12-1-1 5-0-4-1 9-8-0-1 20-0-1-1 24-1-0-1 | 0-5-4-2 0-12-1-2 5-0-4-2 9-8-0-2 20-0-1-2 24-1-0-2 X |X 0-5-5-0 0-13-1-0 5-0-5-0 9-9-0-0 21-0-1-0 25-1-0-0 | 0-6-4-0 0-12-2-0 6-0-4-0 10-8-0-0 20-0-2-0 24-2-0-0 |NM 0-8-5-3 0-9-4-3 16-0-5-3 16-9-0-3 17-0-4-3 17-8-0-3 #12 ab |#39 JPF 0-8-6-1 0-10-4-1 16-0-6-1 16-10-0-1 18-0-4-1 18-8-0-1 |#36* JPF 0-8-6-2 0-10-4-2 16-0-6-2 16-10-0-2 18-0-4-2 18-8-0-2 | 0-8-7-0 0-11-4-0 16-0-7-0 16-11-0-0 19-0-4-0 19-8-0-0 #33 Ocean |#23 JPF 0-9-6-0 0-10-5-0 17-0-6-0 17-10-0-0 18-0-5-0 18-9-0-0 | 0-12-4-1 20-0-4-1 24-8-0-1 | 0-12-4-2 20-0-4-2 24-8-0-2 X |X 0-12-5-0 0-13-4-0 20-0-5-0 21-0-4-0 24-9-0-0 25-8-0-0 X |X 1-1-1-3 X |X 1-1-2-1 1-2-1-1 2-1-1-1 X |X 1-1-2-2 1-2-1-2 2-1-1-2 X |X 1-1-3-0 1-3-1-0 3-1-1-0 |NM 1-1-4-3 1-8-1-3 16-1-1-3 |NM 1-1-5-1 1-9-1-1 17-1-1-1 | 1-1-5-2 1-9-1-2 17-1-1-2 | 1-1-6-0 1-10-1-0 18-1-1-0 X |X 1-2-2-0 2-1-2-0 2-2-1-0 #37 JPF |#41 JPF 1-2-4-1 1-8-2-1 2-1-4-1 2-8-1-1 16-1-2-1 16-2-1-1 | 1-2-4-2 1-8-2-2 2-1-4-2 2-8-1-2 16-1-2-2 16-2-1-2 |#21 JPF 1-2-5-0 1-9-2-0 2-1-5-0 2-9-1-0 17-1-2-0 17-2-1-0 #13 ab |#24 JPF 1-3-4-0 1-8-3-0 3-1-4-0 3-8-1-0 16-1-3-0 16-3-1-0 |NM 1-4-0-3 1-8-4-3 4-1-0-3 8-0-1-3 16-1-4-3 16-8-1-3 | 1-4-1-1 1-5-0-1 4-1-1-1 5-1-0-1 8-1-1-1 9-0-1-1 | 1-4-1-2 1-5-0-2 4-1-1-2 5-1-0-2 8-1-1-2 9-0-1-2 #10 ab |#25 JPF 1-4-2-0 1-6-0-0 4-1-2-0 6-1-0-0 8-2-1-0 10-0-1-0 | 1-4-4-1 1-12-0-1 4-1-4-1 8-8-1-1 20-1-0-1 24-0-1-1 #02 ab |#40 JPF 1-4-4-2 1-12-0-2 4-1-4-2 8-8-1-2 20-1-0-2 24-0-1-2 X |X 1-4-5-0 1-13-0-0 4-1-5-0 8-9-1-0 21-1-0-0 25-0-1-0 X |X 1-5-1-0 1-9-5-0 5-1-1-0 9-1-1-0 17-1-5-0 17-9-1-0 X |X 1-5-4-0 1-12-1-0 5-1-4-0 9-8-1-0 20-1-1-0 24-1-1-0 | 1-8-5-1 1-9-4-1 16-1-5-1 16-9-1-1 17-1-4-1 17-8-1-1 | 1-8-5-2 1-9-4-2 16-1-5-2 16-9-1-2 17-1-4-2 17-8-1-2 #14 ab |#18 ab 1-8-6-0 1-10-4-0 16-1-6-0 16-10-1-0 18-1-4-0 18-8-1-0 X |X 1-12-4-0 20-1-4-0 24-8-1-0 | 2-2-4-0 2-8-2-0 16-2-2-0 #07 ab |#26 JPF 2-4-0-1 2-8-4-1 4-2-0-1 8-0-2-1 16-2-4-1 16-8-2-1 #09 ab |#27 JPF 2-4-0-2 2-8-4-2 4-2-0-2 8-0-2-2 16-2-4-2 16-8-2-2 #05 ab |#28 JPF 2-4-1-0 2-5-0-0 4-2-1-0 5-2-0-0 8-1-2-0 9-0-2-0 | 2-4-4-0 2-12-0-0 4-2-4-0 8-8-2-0 20-2-0-0 24-0-2-0 #04 ab |#17 JPF 2-8-5-0 2-9-4-0 16-2-5-0 16-9-2-0 17-2-4-0 17-8-2-0 | 3-4-0-0 3-8-4-0 4-3-0-0 8-0-3-0 16-3-4-0 16-8-3-0 | 4-4-0-1 8-4-0-1 12-0-0-1 | 4-4-0-2 8-4-0-2 12-0-0-2 X |X 4-4-1-0 8-5-0-0 13-0-0-0 X |X 4-4-4-0 8-12-0-0 28-0-0-0 X |X 4-5-0-0 5-4-0-0 8-4-1-0 9-4-0-0 12-0-1-0 12-1-0-0 |NM 4-8-0-3 8-0-4-3 16-4-0-3 16-8-4-3 | 4-8-1-1 5-8-0-1 8-1-4-1 9-0-4-1 16-4-1-1 16-5-0-1 #11 ab |#29 JPF 4-8-1-2 5-8-0-2 8-1-4-2 9-0-4-2 16-4-1-2 16-5-0-2 | 4-8-2-0 6-8-0-0 8-2-4-0 10-0-4-0 16-4-2-0 16-6-0-0 | 4-8-4-1 8-8-4-1 16-4-4-1 16-12-0-1 20-8-0-1 24-0-4-1 | 4-8-4-2 8-8-4-2 16-4-4-2 16-12-0-2 20-8-0-2 24-0-4-2 X |X 4-8-5-0 8-9-4-0 16-4-5-0 16-13-0-0 21-8-0-0 25-0-4-0 | 4-9-0-1 8-0-5-1 16-8-5-1 16-9-4-1 17-4-0-1 17-8-4-1 #03 ab |#19 JPF 4-9-0-2 8-0-5-2 16-8-5-2 16-9-4-2 17-4-0-2 17-8-4-2 X |X 4-9-1-0 5-9-0-0 8-1-5-0 9-0-5-0 17-4-1-0 17-5-0-0 X |X 4-9-4-0 8-8-5-0 17-4-4-0 17-12-0-0 20-9-0-0 24-0-5-0 | 4-10-0-0 8-0-6-0 16-8-6-0 16-10-4-0 18-4-0-0 18-8-4-0 X |X 4-12-0-0 8-4-4-0 12-0-4-0 12-8-0-0 20-4-0-0 24-4-0-0 X |X 5-8-1-0 9-1-4-0 16-5-1-0 16-9-5-0 17-8-5-0 17-9-4-0 X |X 5-8-4-0 9-8-4-0 16-5-4-0 16-12-1-0 20-8-1-0 24-1-4-0 X |X 16-12-4-0 20-8-4-0 24-8-4-0

JPF

by **JPF** » Mon May 08, 2006 8:47 pm

One more 21 clues, but not abs. minimal.
Unfortunately we need to keep r5c5.

Code: Select all: SM 21 16-0-6-2-1 3 . . | . . . | . . 4 . . . | . . . | . . . . . 1 | 5 . 9 | 7 . . -------+-------+------- . . 5 | 3 . 1 | 9 . . . . . | . 6 . | . . . . . 7 | 9 . 2 | 1 . . -------+-------+------- . . 9 | 1 . 5 | 8 . . . . . | . . . | . . . 8 . . | . . . | . . 3 0-8-6-2-1 0-10-4-2-1 16-0-6-2-1 16-10-0-2-1 18-0-4-2-1 18-8-0-2-1

JPF

by **JPF** » Mon May 08, 2006 10:51 pm

A new minimal 20 clues :

Code: Select all: M20 1-2-4-1-0 . . . | . 1 . | . . . . . . | 6 . 7 | . . . . . 3 | . . . | 4 . . -------+-------+------- . 6 . | . 9 . | . 8 . 7 . . | 8 . 2 | . . 1 . 1 . | . 5 . | . 3 . -------+-------+------- . . 5 | . . . | 7 . . . . . | 1 . 6 | . . . . . . | . 2 . | . . . 1-2-4-1-0 1-8-2-1-0 2-1-4-1-0 2-8-1-1-0 16-1-2-1-0 16-2-1-1-0

JPF

by **Ocean** » Tue May 09, 2006 11:35 am

I started to build a collection of minimal 20s with full symmetry. A few tousand so far. Here is a taste:

Code: Select all: # #M20. 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[Edit: some isomorphic puzzles taken out]

by **Ocean** » Tue May 09, 2006 11:44 am

Continued: Collection of minimal 20s with full symmetry.

Code: Select all: # #M20. 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[Edit: Puzzles replaced with a non-isomorphic set]

by **Havard** » Tue May 09, 2006 12:37 pm

Ocean wrote:I started to build a collection of minimal 20s with full symmetry. A few tousand so far. Here is a taste:

Great work! Why don't you compile them all into a file, and make it available as "Ocean's 1100" or something... (sorry, could not resist...)

Havard

by **JPF** » Tue May 09, 2006 12:43 pm

Ocean wrote:I started to build a collection of minimal 20s with full symmetry. A few tousand so far. Here is a taste:

Huge work !
Congratulations.

I’ve a few questions :
a) Any new patterns ?
b) I assume that all your puzzles are non-equivalent. Right ?
I would be interested to know how you test that.
c) Would it be possible for some patterns to make an exhaustive search (notably to know the number of possible puzzles) ?

JPF

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Fully symmetrical puzzles