The New Sudoku Players' Forum

[Red Ed]

It may be too late, but here's a 25-step symmetrically minimal type II puzzle:

Code: Select all

. . .|4 5 .|8 . .
. 2 .|. . 3|. 7 .
5 . .|2 . 8|. . .
-----+-----+-----
. 8 9|. . .|7 . 1
1 . .|. . .|. . 9
7 . 3|. . .|5 8 .
-----+-----+-----
. . .|7 . 5|. . 6
. 5 .|6 . .|. 4 .
. . 6|. 1 4|. . .

And here's a 25-step symmetrically minimal type IV:

Code: Select all

. 5 .|3 . 2|. . .
6 . .|. 7 9|. . .
. . 2|. . .|8 . .
-----+-----+-----
2 . .|4 . .|. 9 8
. 8 .|. . .|. 5 .
3 1 .|. . 6|. . 7
-----+-----+-----
. . 1|. . .|7 . .
. . .|5 4 .|. . 6
. . .|9 . 7|. 8 .

The harder I look for puzzles with limited symmetry, the more impressed I am by the Ocean/ab 27-step type I (fully symmetric) example.

[ab]

It may be too late, but . . .

it's not too late. I've been a bit ruthless in adding puzzles of late, they have to beat personal records for the given symmetry. I'll keep this policy up for another week or so and if we haven't made 100 by then, maybe add in some of the puzzles I've ommitted. And possibly prune out some very similar puzzles.

The harder I look for puzzles with limited symmetry, the more impressed I am by the Ocean/ab 27-step type I (fully symmetric) example.

Ocean should take most of the credit for that puzzle. I just put his puzzle into a program I have that sees if there are other puzzles that differ from a puzzle by one clue.

[Red Ed]

Oh look, an asymmetric 30-stepper:

Code: Select all

...|..1|.7.
..6|...|4..
5..|...|...
---+---+---
81.|...|.3.
...|46.|...
...|.2.|...
---+---+---
..4|...|9.2
37.|8..|...
.9.|...|...

Credit entirely to gfroyle for that: I've just been testing his list of 18s.

[gsf]

here's a repost in both forms
I included some M's that weren't max because they seem harder to come by

also, can we make Red Ed's CSV post sticky
that page is out of the previous link range

Code: Select all

#II,23,28,SM,020009050800600004001037900509000010002000300010000605008760500900008001030200070,gsf,NEW

. 2 .  . . 9  . 5 .
8 . .  6 . .  . . 4
. . 1  . 3 7  9 . .

5 . 9  . . .  . 1 .
. . 2  . . .  3 . .
. 1 .  . . .  6 . 5

. . 8  7 6 .  5 . .
9 . .  . . 8  . . 1
. 3 .  2 . .  . 7 .

#II,24,28,SM,540030701000102008100000000080060030400207005020040090000000002200806000804020013,gsf,NEW

5 4 .  . 3 .  7 . 1
. . .  1 . 2  . . 8
1 . .  . . .  . . .

. 8 .  . 6 .  . 3 .
4 . .  2 . 7  . . 5
. 2 .  . 4 .  . 9 .

. . .  . . .  . . 2
2 . .  8 . 6  . . .
8 . 4  . 2 .  . 1 3

#III,22,24,M,000902000070000050008301400700000001030406090600000004005109300080000060000504000,gsf,NEW

. . .  9 . 2  . . .
. 7 .  . . .  . 5 .
. . 8  3 . 1  4 . .

7 . .  . . .  . . 1
. 3 .  4 . 6  . 9 .
6 . .  . . .  . . 4

. . 5  1 . 9  3 . .
. 8 .  . . .  . 6 .
. . .  5 . 4  . . .

#IV,24,28,SM,010405900209000000060012007500000603003000400802000009900370050000000704006804090,gsf,NEW

. 1 .  4 . 5  9 . .
2 . 9  . . .  . . .
. 6 .  . 1 2  . . 7

5 . .  . . .  6 . 3
. . 3  . . .  4 . .
8 . 2  . . .  . . 9

9 . .  3 7 .  . 5 .
. . .  . . .  7 . 4
. . 6  8 . 4  . 9 .

#VI,22,24,M,016800000000040000009006300000100026400600730000200058004005100000030000075900000,gsf,NEW

. 1 6  8 . .  . . .
. . .  . 4 .  . . .
. . 9  . . 6  3 . .

. . .  1 . .  . 2 6
4 . .  6 . .  7 3 .
. . .  2 . .  . 5 8

. . 4  . . 5  1 . .
. . .  . 3 .  . . .
. 7 5  9 . .  . . .

#VI,23,25,M,002400706000020004000005090019000800780500000054000900000001060000030008007600102,gsf,NEW

. . 2  4 . .  7 . 6
. . .  . 2 .  . . 4
. . .  . . 5  . 9 .

. 1 9  . . .  8 . .
7 8 .  5 . .  . . .
. 5 4  . . .  9 . .

. . .  . . 1  . 6 .
. . .  . 3 .  . . 8
. . 7  6 . .  1 . 2


[gsf]

Credit entirely to gfroyle for that: I've just been testing his list of 18s.

are the 18's posted anywhere?

[Ocean]

Type II symmetry: A 21-stepper. Minimal, 24 clues.

Code: Select all

# M24. 21 steps.
 *-----------*
 |1..|...|..2|
 |.34|5..|.6.|
 |...|..6|.5.|
 |---+---+---|
 |..6|.1.|.3.|
 |...|7.4|...|
 |.8.|.3.|2..|
 |---+---+---|
 |.7.|8..|...|
 |.5.|..7|89.|
 |8..|...|..4|
 *-----------*

Type III symmetry: A 24-stepper. 24 clues, symmetrically minimal.

Code: Select all

# SM24. 24 steps.
 *-----------*
 |12.|...|.34|
 |...|4.3|...|
 |..5|...|6..|
 |---+---+---|
 |4..|.3.|..1|
 |...|2.7|...|
 |8..|.6.|..9|
 |---+---+---|
 |..9|...|5..|
 |...|7.1|...|
 |63.|...|.87|
 *-----------*

Type VI symmetry: A 22-stepper. 24 clues, SM.

Code: Select all

# SM24. 22 steps.
 *-----------*
 |1.2|3.4|5.6|
 |...|6.7|...|
 |...|...|...|
 |---+---+---|
 |...|586|...|
 |...|...|...|
 |.58|...|19.|
 |---+---+---|
 |..5|...|9..|
 |.2.|.3.|.6.|
 |.3.|2.1|.8.|
 *-----------*

[Ruud]

It would be useful to start a new thread for the lowsteppers. I cannot find the highscores anymore

This is a lowstepper I found in my new batch:

Diagonal (type?) symmetry, SM, 28 clues, 3 stepper.

Code: Select all

. . 5|. . 9|1 . 2
. . .|. 4 2|. . .
4 . 9|. . 5|. . 6
-----+-----+-----
. . .|. . .|4 3 1
. 6 .|. . .|. 8 .
7 5 1|. . .|. . .
-----+-----+-----
6 . .|3 . .|7 . 4
. . .|1 9 .|. . .
9 . 3|2 . .|6 . .

Does it make it on the list? Where is that list anyway?

Ruud.

[Ocean]

It would be useful to start a new thread for the lowsteppers. I cannot find the highscores anymore

This is a lowstepper I found in my new batch:

Diagonal (type?) symmetry, SM, 28 clues, 3 stepper.

Code: Select all

. . 5|. . 9|1 . 2
. . .|. 4 2|. . .
4 . 9|. . 5|. . 6
-----+-----+-----
. . .|. . .|4 3 1
. 6 .|. . .|. 8 .
7 5 1|. . .|. . .
-----+-----+-----
6 . .|3 . .|7 . 4
. . .|1 9 .|. . .
9 . 3|2 . .|6 . .

Does it make it on the list? Where is that list anyway?

Ruud.

The original list of historic improvements for the lowsteppers, and the table of 'best so far' is here. A symmetric 3-stepper with 28 clues was the very first entry on that list, but that puzzle had rotational symmetry only (type V). I don't think anybody posted a 3-stepper with 28 clues and double diagonal symmetry, so your contribution will be currently 'best' on a new 'extended' list which differentiates on symmetry types. (not yet compiled.)

[Red Ed]

OK, I admit defeat on type I puzzles. Here's my best: 25 clues, symmetric minimal:

Code: Select all

. . 7|. . .|2 . .
. . .|4 . 5|. . .
4 . .|. 6 .|. . 8
-----+-----+-----
. 5 .|. 2 .|. 9 .
. . 1|5 . 3|7 . .
. 4 .|. 9 .|. 1 .
-----+-----+-----
8 . .|. 1 .|. . 9
. . .|7 . 6|. . .
. . 2|. . .|6 . .

Link to my sorted list: here.

[JPF]

It would be useful to start a new thread for the lowsteppers. I cannot find the highscores anymore

This is a lowstepper I found in my new batch:

Diagonal (type?) symmetry, SM, 28 clues, 3 stepper.

Code: Select all

. . 5|. . 9|1 . 2
. . .|. 4 2|. . .
4 . 9|. . 5|. . 6
-----+-----+-----
. . .|. . .|4 3 1
. 6 .|. . .|. 8 .
7 5 1|. . .|. . .
-----+-----+-----
6 . .|3 . .|7 . 4
. . .|1 9 .|. . .
9 . 3|2 . .|6 . .

Does it make it on the list? Where is that list anyway?

Ruud.

The original list of historic improvements for the lowsteppers, and the table of 'best so far' is here. A symmetric 3-stepper with 28 clues was the very first entry on that list, but that puzzle had rotational symmetry only (type V). I don't think anybody posted a 3-stepper with 28 clues and double diagonal symmetry, so your contribution will be currently 'best' on a new 'extended' list which differentiates on symmetry types. (not yet compiled.)

I think I did.

2 steps, SM, type IV symmetry, 38 clues

Code: Select all


 . 3 9 | . . 7 | . 6 .
 8 . 5 | 2 . 9 | . 4 1
 7 1 . | 4 . 8 | . . .
-------+-------+-------
 . 2 3 | . . . | 6 7 4
 . . . | . . . | . . .
 9 7 1 | . . . | 3 2 .
-------+-------+-------
 . . . | 9 . 4 | . 3 7
 1 8 . | 3 . 6 | 2 . 5
 . 9 . | 1 . . | 4 8 .
 

(assuming that the number of steps is the first criterion)

Actually, I am assuming that the low steppers are sorted by symmetry type, number of steps, number of clues.
Is that correct ?

JPF

[Ocean]

Type II symmetry: A 22-stepper. Minimal. 24 clues.

Code: Select all

# M24. 22 steps. Full rotational symmetry.
 *-----------*
 |...|.1.|...|
 |...|..2|1..|
 |.31|4..|5..|
 |---+---+---|
 |.4.|6.7|3..|
 |8..|...|..4|
 |..2|5.4|.6.|
 |---+---+---|
 |..4|..9|27.|
 |..8|3..|...|
 |...|.2.|...|
 *-----------*

Type VI symmetry: A 24-stepper. Minimal. 24 clues.

Code: Select all

# M24. 24 steps. Vertical symmetry.
 *-----------*
 |..1|2.3|4..|
 |...|...|...|
 |56.|...|.72|
 |---+---+---|
 |.8.|...|.2.|
 |...|1.4|...|
 |..7|...|6..|
 |---+---+---|
 |.4.|9.1|.8.|
 |8.3|4.5|9.7|
 |...|...|...|
 *-----------*

[ab]

I think Red Ed's 25 step fully symmetric puzzle should make the cut, which means if we restrict ourselves to 100 puzzles I can only accept one of Ocean's lates offerings. Given the nature of the thread, more steps should win over symmetry considerations, so the type VI puzzle is #100. I suppose the type II puzzle could replace Ocean's #58 ?:

[Ocean]

A new 28-stepper. Minimal, 23 clues.
Type VII symmetry.

Code: Select all

#
# M23.  28 steps. Diagonal symmetry.
#
. 1 .|2 3 .|. . 4
5 . .|6 . .|7 . .
. . .|. . .|8 3 .
-----+-----+-----
3 2 .|. . .|. 1 .
7 . .|. 2 .|. . 8
. . .|. . .|. 4 .
-----+-----+-----
. 8 9|. . .|. . .
. . 4|3 . 5|. . .
6 . .|. 4 .|. . .

[ab]

nice puzzle Ocean. I'll replace puzzle #59 with that.

In a sense this thread is different from the superior thread in that there's a record to be broken, so arguably it shouldn't close

[Ocean]

nice puzzle Ocean. I'll replace puzzle #59 with that.

Thanks. Found it quite accidentally, during analysis of about one million generated symmetric puzzles.

In a sense this thread is different from the superior thread in that there's a record to be broken, so arguably it shouldn't close

Agree. It will eventually slowly converge to the 'mathematically best possible'. And as it becomes harder to improve our personal records, submissions will be fewer from some of us.

If a selection criteria is needed (say, the day you should decide to publish a collection), then rather than the artificial "100 first submitted", maybe the "15 or 20 best from each symmetry type, at time of publication" would be more natural.

I think I did.(...) Actually, I am assuming that the low steppers are sorted by symmetry type, number of steps, number of clues.
Is that correct ?

I think the one-, two-, three-steppers, etc. belong to separate classes, and can not be compared directly. For low-steppers the number of clues is crucial: lower number of clues = better quality. For the sake of diversity, it's interesting to divide in symmetry types: what is the best we can achieve for each symmetry type.