## Fully symmetrical puzzles

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

Posts: 1738
Joined: 05 May 2005

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.
Mauricio

Posts: 1174
Joined: 22 March 2006

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
coloin

Posts: 1738
Joined: 05 May 2005

Nice work, Mauricio.

I start to believe in a fully symmetric 36
ravel

Posts: 998
Joined: 21 February 2006

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 . |+-------+-------+-------+`
Mauricio

Posts: 1174
Joined: 22 March 2006

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 . | . . . |+-------+-------+-------+`
Mauricio

Posts: 1174
Joined: 22 March 2006

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`
100000001010111010000000000010111010010101010010111010000000000010111010100000001
TTHsieh
TTHsieh

Posts: 1390
Joined: 13 July 2007

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`
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

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
TTHsieh

Posts: 1390
Joined: 13 July 2007

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
JPF
2017 Supporter

Posts: 3754
Joined: 06 December 2005
Location: Paris, France

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
TTHsieh

Posts: 1390
Joined: 13 July 2007

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 2.8800000005060194030000000000010205080050000040070608090000000000040836050600000009 3 SE 2.8800000001030561080000000000010902060020000040050704030000000000040387050600000003 4 SE 7.1 400000001070259060000000000020705030010000040050802010000000000040371020500000007 5 SE 2.8400000001070258060000000000020705030010000040050806010000000000040371020500000007 6 SE 2.8400000001070258060000000000020805030010000040050906010000000000040371020500000007 7 SE 2.8`

I haven't checked for isomorphs.

Regards,

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 9384
Joined: 15 May 2006
Location: Berlin

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.
Mauricio

Posts: 1174
Joined: 22 March 2006

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
JPF
2017 Supporter

Posts: 3754
Joined: 06 December 2005
Location: Paris, France

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

m_b_metcalf
2017 Supporter

Posts: 9384
Joined: 15 May 2006
Location: Berlin

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