The New Sudoku Players' Forum

by **coloin** » Thu Sep 06, 2007 10:20 pm

mauricio wrote:

Code: Select all: +-------+-------+-------+ | . . . | . 1 . | . . . | | . . 1 | 2 3 4 | 5 . . | | . 2 6 | 5 . 7 | 4 1 . | +-------+-------+-------+ | . 3 4 | . . . | 6 2 . | | 2 1 . | . . . | . 5 4 | | . 6 8 | . . . | 1 3 . | +-------+-------+-------+ | . 8 2 | 7 . . | 3 4 . | | . . 3 | 1 2 8 | 7 . . | | . . . | . 4 . | . . . | +-------+-------+-------+ 35 clue minimal

Well done, Ive played around and cant get near this....its not far at all to get a 36 now...... [

I jest]

However you might want the solution grid of your eventual puzzle to have the 9 clues arranged similarly to this - so as they dont feature in your puzzle !

Code: Select all: +---+---+---+ |...|9..|...| |.9.|...|...| |...|...|..9| +---+---+---+ |9..|...|...| |...|...|9..| |...|..9|...| +---+---+---+ |...|.9.|...| |...|...|.9.| |..9|...|...| +---+---+---+

Code: Select all: ....8......53.76...782.4.3..86...57.53.....26.47...81..524.136...4835............ ....8......57..6...784.312..86...5..53.....46.47...31..523.7.6...48152......4....

two 32 clue puzzles with the 9s sited advantageously.

Code: Select all: ....4......56.83...863.154..64...83.2......64.37...12..781.425...27.64......5.... ....4......56.83...862..54..34...82.2......64.67...13..781.425...28674......5....

Im improving :!:

two 33 clue minimal puzzles

C

by **Mauricio** » Sat Sep 08, 2007 1:34 am

I tried a different pattern:

Code: Select all: +-------+-------+-------+ | . . . | . x . | . . . | | . x x | x . x | x x . | | . x x | x . x | x x . | +-------+-------+-------+ | . x x | . . . | x x . | | x . . | . . . | . . x | | . x x | . . . | x x . | +-------+-------+-------+ | . x x | x . x | x x . | | . x x | x . x | x x . | | . . . | . x . | . . . | +-------+-------+-------+

A 36 with 35 matching clues:

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

A 35 with diagonal symmetry

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

A 34 with double diagonal symmetry

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

But unfortunately no 36.

by **coloin** » Sat Sep 08, 2007 8:51 pm

Very respectable effort, I think you will get it one day......just may take a little longer.

The pattern changes look interesting, although with my method I dont think I will get furthur than this 34 without expanding into other grid solutions, which is indeed what we will have to do. Anyhow it is again without the "9" clues [in the template] which I believe is where you have hit solid rock.

Code: Select all: +---+---+---+ |...|.1.|...| |..1|284|7..| |.27|5.6|41.| +---+---+---+ |.74|...|32.| |21.|...|..4| |.63|...|1..| +---+---+---+ |.82|3.5|64.| |..5|168|2..| |...|.4.|...| +---+---+---+ 34 clues

Perhaps you can expand on this one ?

C

by **ravel** » Sun Sep 09, 2007 2:36 pm

Nice work, Mauricio.

I start to believe in a fully symmetric 36

by **Mauricio** » Tue Sep 11, 2007 12:40 am

The nature of the patterns of those high clues sudokus is strange, sometimes I can't find a 32, for some patterns I can randomly find a 31, but not a 34 (even with specialized algorithms).
Recently I have expanded my search space not just to valid minimal puzzles, but to invalid (multisolutional) "minimal" puzzles too, that has helped greatly.

Many patterns don't look like snow flakes:

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

by **Mauricio** » Mon Sep 17, 2007 5:22 am

My morale goes down with every pattern "failed". But I have to admit, generating a minimal puzzle with high number of clues and fixed pattern is not the easiest of things, and I am very proud of my improvement in that matter.

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

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

by **TTHsieh** » Thu Sep 27, 2007 5:06 am

Code: Select all: x . . | . . . | . . x . x . | x x x | . x . . . . | . . . | . . . - - - + - - - + - - - . x . | x x x | . x . . x . | x . x | . x . . x . | x x x | . x . - - - + - - - + - - - . . . | . . . | . . . . x . | x x x | . x . x . . | . . . | . . x

100000001010111010000000000010111010010101010010111010000000000010111010100000001TTHsieh

by **gsf** » Thu Sep 27, 2007 7:20 am

TTHsieh wrote:
28 clues, Hard Pattern ?
Is there any minimal puzzle ?
Code: Select all
x . . | . . . | . . x . x . | x x x | . x . . . . | . . . | . . . - - - + - - - + - - - . x . | x x x | . x . . x . | x . x | . x . . x . | x x x | . x . - - - + - - - + - - - . . . | . . . | . . . . x . | x x x | . x . x . . | . . . | . . x

here's one, not minimal

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

by **TTHsieh** » Thu Sep 27, 2007 8:04 am

Up to now, I can't find any minimal puzzle of this pattern.
The minimal rate of this pattern maybe is less than 1/1000000, 1/2000000, ..., or no minimal puzzle.

who knows...

TTHsieh

by **JPF** » Thu Sep 27, 2007 3:13 pm

TTHsieh wrote:
28 clues, Hard Pattern ?
Is there any minimal puzzle ?
Code: Select all
x . . | . . . | . . x . x . | x x x | . x . . . . | . . . | . . . - - - + - - - + - - - . x . | x x x | . x . . x . | x . x | . x . . x . | x x x | . x . - - - + - - - + - - - . . . | . . . | . . . . x . | x x x | . x . x . . | . . . | . . x

Here are 2 fully symmetric sub-patterns :

20 clues, minimal

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

24 clues, not minimal

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

Any minimal for this last one ?

JPF

by **TTHsieh** » Thu Sep 27, 2007 3:59 pm

JPF wrote:Any minimal for this last one ?

Here are some minimal puzzles.

Code: Select all: 1 . . | . . . | . . 2 . 3 . | 4 5 6 | . 1 . . . . | . . . | . . . - - - + - - - + - - - . 6 . | 7 . 2 | . 8 . . 2 . | . . . | . 4 . . 5 . | 8 . 9 | . 3 . - - - + - - - + - - - . . . | . . . | . . . . 4 . | 2 1 8 | . 5 . 3 . . | . . . | . . 6 ER=2.0

minimal puzzles wrote:
100000002030456010000000000060702080020000040050809030000000000040218050300000006 # 2.0
100000002030456010000000000070803060020000040050901080000000000010382050600000008 # 2.3
100000002020345060000000000010602050070000030040508090000000000030291040500000009 # 2.5
100000002030245060000000000010702050060000080040506030000000000020193040500000003 # 2.6
100000002030145060000000000070403050060000010040708020000000000010327040500000006 # 2.8
100000002020345010000000000010602050070000030040501080000000000030827040500000008 # 6.6
...

TTHsieh

by **m_b_metcalf** » Thu Sep 27, 2007 6:15 pm

JPF wrote:Any minimal for this last one ?

JPF

I came up with these:

Code: Select all: 800000001060491030000000000010207080050000040070608090000000000040836050600000009 1 SE 2.0 800000005060491030000000000010205080050000040070608090000000000040836050600000009 2 SE 2.8 800000005060194030000000000010205080050000040070608090000000000040836050600000009 3 SE 2.8 800000001030561080000000000010902060020000040050704030000000000040387050600000003 4 SE 7.1 400000001070259060000000000020705030010000040050802010000000000040371020500000007 5 SE 2.8 400000001070258060000000000020705030010000040050806010000000000040371020500000007 6 SE 2.8 400000001070258060000000000020805030010000040050906010000000000040371020500000007 7 SE 2.8

I haven't checked for isomorphs.

Regards,

Mike Metcalf

by **Mauricio** » Thu Sep 27, 2007 8:21 pm

TTHsieh wrote:
28 clues, Hard Pattern ?
Is there any minimal puzzle ?
Code: Select all
x . . | . . . | . . x . x . | x x x | . x . . . . | . . . | . . . - - - + - - - + - - - . x . | x x x | . x . . x . | x . x | . x . . x . | x x x | . x . - - - + - - - + - - - . . . | . . . | . . . . x . | x x x | . x . x . . | . . . | . . x

The best I could do is this minimal 27:

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

All minimal puzzles that I found with 27 clues, have the same pattern, and I was not looking for that.

by **JPF** » Thu Sep 27, 2007 9:48 pm

Thanks TTHsieh, m_b_metcalf

Here is a fully symmetric and minimal puzzle

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

... with 3 solutions

JPF

by **m_b_metcalf** » Thu Sep 27, 2007 10:11 pm

JPF wrote:Here is a fully symmetric and minimal puzzle
Code: Select all
1 . . | . . . | . . 2 . 3 . | 1 . 4 | . 5 . . . . | . . . | . . . -------+-------+------- . 5 . | 6 . 3 | . 4 . . . . | . . . | . . . . 6 . | 4 . 7 | . 3 . -------+-------+------- . . . | . . . | . . . . 4 . | 3 . 5 | . 6 . 8 . . | . . . | . . 9

... with 3 solutions

JPF

Can a 'puzzle' really be described as both minimal and as having several solutions? One with multiple solutions is surely sub-minimal.

Regards,

Mike Metcalf

The New Sudoku Players' Forum

Fully symmetrical puzzles