The New Sudoku Players' Forum

by **gsf** » Fri May 19, 2006 5:44 am

{ 69 70 } are marked SM but clues can be removed with symmetry retained
maybe PM for pretty minimal or pictorally minimal

here are the SM versions

Code: Select all: # 21 C26.M/S4.hv/F17.35/N21.20 . . . . . . . . . 1 . . 4 . 2 . . 5 5 . . 7 . 3 . . 2 . 1 8 . . . 9 7 . . 6 . . . . . 2 . . 2 7 . . . 4 5 . 7 . . 9 . 6 . . 1 2 . . 3 . 1 . . 9 . . . . . . . . . # 25 C26.M/S2.v/F16.39/N25.16 . . 4 . . . 5 . . 2 . . 5 . 1 . . 7 . . . 4 . 2 . . . . . . 3 . 8 . . . . 3 7 . . . 1 8 . 5 . . . . . . . 6 4 . . . . . . . 2 1 . . 6 . 5 . . 8 . 5 6 . . . 3 7 .

by **Red Ed** » Fri May 19, 2006 6:57 am

gsf wrote:{ 69 70 } are marked SM but clues can be removed with symmetry retained

Oooh, don't know how I missed that. Will debug later today and edit my previous post. Thanks.

EDIT: schoolboy error corrected. My original post has now been revised.

by **Ocean** » Fri May 19, 2006 11:30 am

A 22-stepper with double diagonal symmetry. Minimal, 20 clues.

Code: Select all: # # M20. 22 steps. # . . 1|. . 2|. . 3 . . .|. 4 .|. 5 . 6 . .|. . .|7 . . -----+-----+----- . . .|. . 1|. . 8 . 4 .|. . .|. 2 . 7 . .|9 . .|. . . -----+-----+----- . . 2|. . .|. . 6 . 5 .|. 8 .|. . . 1 . .|3 . .|4 . .

by ab » Fri May 19, 2006 1:56 pm

Nice puzzle Ocean, but by the new standards it doesn't make the list! You've already posted a type IV puzzle and the current record for type IV puzzles is 22 steps as posted by Red Ed!

I'd just like to point out a slight problem with Red Ed's proposal. Puzzle Ocean/ab 51 can easily be turned into a type III puzzle by swapping two pairs of rows (or columns) or into a type VI puzzle by swapping one pair of rows (or columns). So to qualify as a type III puzzle the puzzle must be one that can't be transformed into a type I puzzle and similarly for type VI puzzles it must be a puzzle that can't be transformed into a type III puzzle. There are probably other relationships out there between for instance type II and type V and also type IV and type VII.

by **Ocean** » Fri May 19, 2006 2:06 pm

ab wrote:Nice puzzle Ocean, but by the new standards it doesn't make the list! You've already posted a type IV puzzle and the current record for type IV puzzles is 22 steps as posted by Red Ed!

I'd just like to point out a slight problem with Red Ed's proposal. Puzzle Ocean/ab 51 can easily be turned into a type III puzzle by swapping two pairs of rows (or columns) or into a type VI puzzle by swapping one pair of rows (or columns). So to qualify as a type III puzzle the puzzle must be one that can't be transformed into a type I puzzle and similarly for type VI puzzles it must be a puzzle that can't be transformed into a type III puzzle. There are probably other relationships out there between for instance type II and type V and also type IV and type VII.

OK, sorry. One step up then. Or should it also be above 27, the record for full symmetry - since full symmetry implies all other symmetries?

A 23-stepper with double diagonal symmetry. 22 clues. Minimal.

Code: Select all: # # M22. 23 steps. # . . .|. . .|. . 1 . 2 3|. . 4|. . . . 5 .|. 6 1|. . . -----+-----+----- . . .|7 . .|8 3 . . . 5|. . .|6 . . . 9 4|. . 2|. . . -----+-----+----- . . .|2 5 .|. 4 . . . .|8 . .|7 2 . 3 . .|. . .|. . .

by ab » Fri May 19, 2006 3:36 pm

Ocean wrote:A 23-stepper with double diagonal symmetry. 22 clues. Minimal.

Yep that qualifies

Ocean also wrote:Or should it also be above 27, the record for full symmetry - since full symmetry implies all other symmetries?

I think you misunderstood me. By swapping certain rows (or columns) in a fully symmetric puzzle, you can get a puzzle which is no longer fully symmetric, but does have other symmetries.

Or maybe you were just being flippant

by ab » Fri May 19, 2006 5:06 pm

I found a 32 clue 2 step puzzle. It has full rotational symmetry, but is not symmetric minimal:

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

by **Red Ed** » Fri May 19, 2006 5:53 pm

ab wrote:I'd just like to point out a slight problem with Red Ed's proposal. Puzzle Ocean/ab 51 can easily be turned into a type III puzzle by swapping two pairs of rows (or columns) or into a type VI puzzle by swapping one pair of rows (or columns). So to qualify as a type III puzzle the puzzle must be one that can't be transformed into a type I puzzle and similarly for type VI puzzles it must be a puzzle that can't be transformed into a type III puzzle. There are probably other relationships out there between for instance type II and type V and also type IV and type VII.

Good point, I hadn't thought of that. Isn't it weird how well we're doing on the super-restrictive Type I symmetry?

I've fixed the bug reported by gsf and corrected/updated my list.

by **Ocean** » Fri May 19, 2006 7:05 pm

ab wrote:I found a 32 clue 2 step puzzle. It has full rotational symmetry, but is not symmetric minimal:

Good. Nice to have smallsteppers with few clues. Since we have one with 'symmetry' before, it won't go to the current "improvements list", but it will go into an expanded list which differentiates on symmetry type...

by ab » Fri May 19, 2006 7:18 pm

What are the latest records for low steppers? There are plenty of 39 clue one steppers in that grid, for example:

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

PS Red Ed you should credit Vidarino for his type V 28 stepper on your public service announcement list!

by **Red Ed** » Fri May 19, 2006 7:26 pm

ab wrote:PS Red Ed you should credit Vidarino for his type V 28 stepper on your public service announcement list!

Do you just mean that I should highlight it in red? If so, I disagree: vidarino's type V 28 stepper is only symmetric-minimal, which isn't quite as good as the two fully-minimal puzzles of the same type. How harsh!

by **Ocean** » Fri May 19, 2006 7:45 pm

ab wrote:What are the latest records for low steppers? There are plenty of 39 clue one steppers in that grid, for example:
Code: Select all
1 . . | . 9 7 | . 2 3 9 . . | . . 6 | . 5 . . . 2 | 3 . . | 7 4 . ------+-------+------ . 7 . | 5 . 8 | . . 1 3 5 . | . . . | . 8 6 2 . 8 | 4 . . | . 3 . ------+-------+------ . . 4 | . 8 3 | 9 1 . . 1 9 | 7 5 . | . . 2 5 6 . | . 2 9 | . . 4

This one will go to the 'record list'. The lowest one-stepper up to now has been JPF's symmetrical one with 40 clues, as far as I am aware.

by **Red Ed** » Fri May 19, 2006 7:54 pm

Here's a new one: 24 steps, symmetrically-minimal, type III symmetry.

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

by **Ocean** » Fri May 19, 2006 8:08 pm

Found a 7-stepper with 18 clues, minimal, rotational symmetry:

Code: Select all: # # M18. 7 steps. # . . .|. . .|. 1 . . . .|. 2 1|. . . . . 3|. . .|. 4 5 -----+-----+----- . . .|. . 6|2 . . . 7 .|. . .|. 8 . . . 4|5 . .|. . . -----+-----+----- 6 2 .|. . .|9 . . . . .|4 8 .|. . . . 9 .|. . .|. . .

A slight modification gives this 8-stepper (18 clues, minimal, rotational symmetry):

Code: Select all: # # M18. 8 steps: # .......1.....12.....3....45.....62...7.....8...45.....62....3.....84.....9.......

by ab » Fri May 19, 2006 9:36 pm

there's even a 38 clue 1 stepper there:

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

*edit* posted the wrong grid first time *edit*
any advances?

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