inferior puzzles thread

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

Postby vidarino » Sun Apr 02, 2006 7:36 pm

Darned if I didn't find myself a 28-stepper, too.:)

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


Ruud's 28-stepper is still a tad better, though, as mine isn't fully minimal, only symmetrically so.
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Postby JPF » Sun Apr 02, 2006 10:52 pm

Ocean wrote:Then the current status for puzzles with some symmetry is (minimum known number of clues for each category):
Code: Select all
1-stepper: 48 clues
2-stepper: 36 clues
3-stepper: 28 clues
4-stepper: 24 clues
5-stepper: 22 clues
6-stepper: 22 clues


Sorry, a mix :

a 2-stepper (34 clues, not symmetric, not minimal)

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

JPF
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Postby Ruud » Sun Apr 02, 2006 11:33 pm

We could start here with the lowsteppers:

17-clues (minimal) non-symmetrical 8-steppers
Code: Select all
. . .|1 . .|. 6 .
3 . .|. . .|2 . .
5 . .|. . .|. . .
-----+-----+-----
. 1 7|. . .|. . .
. . .|. . 3|8 . .
. . .|. . .|. . .
-----+-----+-----
. 6 .|7 1 .|. 4 .
2 . .|. . .|3 . .
. . .|6 . .|5 . .

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

From Gordon Royle's collection.

And to close the new gap:

21 clues minimal symmetrical 7-stepper.

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

(from my own collection)

and a replacement: 21-clues minimal symmetrical 6-stepper.

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

also from my own microbrewery:D

Ruud.
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Postby JPF » Mon Apr 03, 2006 5:59 am

a 1-stepper (46 clues with some symmetry)

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



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Postby Ocean » Mon Apr 03, 2006 7:29 pm

Ruud wrote:We could start here with the lowsteppers: ...


Thanks for improvements and filling gaps.


A little more gap-filling:

Code: Select all
22 clues, minimal and symmetric (8 steps):
+-------+-------+-------+
| 5 . . | . . . | . . 8 |
| . . . | . . . | 3 . . |
| . 7 . | 4 . 1 | . 9 . |
+-------+-------+-------+
| . . 4 | . 6 . | 5 . . |
| . . . | 5 . 9 | . . . |
| . . 3 | . 7 . | 8 . . |
+-------+-------+-------+
| . 9 . | 1 . 6 | . 7 . |
| . . 8 | . . . | . . . |
| 3 . . | . . . | . . 1 |
+-------+-------+-------+

Code: Select all
18 clues, minimal (7 steps)
+-------+-------+-------+
| . 1 . | . 2 3 | . . . |
| . . . | . . . | . 4 5 |
| . . . | . . . | . . . |
+-------+-------+-------+
| 4 . 6 | . . . | . . . |
| . . . | . 6 . | 3 . . |
| 5 . . | . . . | . 7 . |
+-------+-------+-------+
| . . . | 4 1 . | . 6 . |
| . 3 . | . . . | 2 . . |
| 1 . . | . 8 . | . . . |
+-------+-------+-------+


Code: Select all
19 clues, minimal (6 steps):
+-------+-------+-------+
| . 1 . | 2 . . | . . . |
| . . . | . . . | 7 . 3 |
| . . 6 | . . . | 4 . . |
+-------+-------+-------+
| . . . | 5 . . | . 9 7 |
| 4 . . | . . . | 8 . . |
| . . . | 1 . . | . . . |
+-------+-------+-------+
| . 5 . | . . 6 | . 1 . |
| 7 . . | . 4 . | . . . |
| . . . | . 8 . | . . 9 |
+-------+-------+-------+


With updates from Ruud and JPF, and above, we have the table below. (Please correct me if I missed something, or misplaced numbers).

########################################################################

Code: Select all
Lowest known number of clues for Low-steppers:

#------------------------------+----+----+----+----+----+----+----+----+
Number of steps:               |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |
#------------------------------+----+----+----+----+----+----+----+----+
Symmetric + absolute minimal:  | -- | -- | -- | 24 | 20 | 20 | 18 | 18 |
Symmetric + minimal symmetric: | 44 | 32 | 24 | 24 | 20 | 20 | 18 | 18 |
Symmetric:                     | 40 | 32 | 24 | 24 | 20 | 20 | 18 | 18 |
Minimal:                       | -- | -- | -- | 24 | 20 | 19 | 18 | 17 |
Any sudoku:                    | 36 | 29 | 24 | 23 | 20 | 19 | 18 | 17 |
#------------------------------+----+----+----+----+----+----+----+----+
########################################################################


Code: Select all
A brief historic summary of puzzles that pushed 'the lowest known limits':

#(Ocean Mar 25, 2006) 3 steps - 28 clues:
94...37..5...6.3.......1..9.6...952....8.6....842...1.7..1.......3.2...7..57...42
#(vidarino Mar 25, 2006 )  A 4-stepper (28 clues):
.3.97.8....1......89.3..42.5628...................9546.16..7.95......7....9.46.1.
#(vidarino Mar 25, 2006) A 1-stepper, 48 givens, it *is* minimal. You can't remove a set of clues without breaking the (all-axis) symmetry or losing the unique solution:
3.52.89.4.879.416.96.3.1.25598...312.........123...74683.4.6.57.425.963.6.17.3|4.8
#(Ruud Mar 25, 2006) A 4-Stepper with only 24 clues. And yes, it is minimal symmetric:
...71..3.3......2.29.6.....1.23....9.........4....85.7.....9.68.7......1.3..45...
#(Ruud Mar 25, 2006) A 22-Clue 5-Stepper:
......68.2..37.......9...5...47....3.8.....1.6....54...7...2.......56..9.13......
#(Ocean; Apr 02, 2006) A two-stepper (36 clues, minimal with respect to its full symmetry):
7..935..6..5.7.9...9.8.1.2.9.3...5.242.....838.6...1.9.7.4.3.5...9.5.3..5..627..4
#(JPF; Apr 03, 2006) Sorry, a mix : a 2-stepper (34 clues, not symmetric, not minimal):
..2....6576.4...9...85.71......836...97...35..4.659...1.6...43237.21.....5..3...1
#(Ruud Apr 03, 2006) 17-clues (minimal) non-symmetrical 8-steppers. From Gordon Royle's collection:
...1..6.3.....2..5.........17...........38............ 6.71..4.2.....3.....6..5..
.1....7.......4.......6....5.4....6....12....6..3.....4....8.........3.5...7..1..
#(Ruud Apr 03, 2006) 21 clues minimal symmetrical 7-stepper (from my own collection):
.....6.58..92......5.....3.6...1......4.9.2......4...7.7.....1......54..32.9.....
#(Ruud Apr 03, 2006) A replacement: 21-clues minimal symmetrical 6-stepper:
....4.2..79........51..9...86..........782..........25...5..69........53..7.1....
#(JPF; Apr 03, 2006) A 1-stepper (46 clues with some symmetry) [replaced Apr 04 2006]:
4..8615..5..97.38.29.4..17..572..6.3.125.489.3.4..621..45..7.61.29.45..8..6189..2 
#(Ocean; Apr 03, 2006) 22 clues, minimal and symmetric (8 steps)[replaced Apr 04]:
5.......8......3...7.4.1.9...4.6.5.....5.9.....3.7.8...9.1.6.7...8......3.......1
#(Ocean; Apr 03, 2006) 18 clues, minimal, non-symmertric (7 steps):
.1..23..........45.........4.6..........6.3..5......7....41..6..3....2..1...8....
#(Ocean; Apr 03, 2006) 19 clues, minimal, non-symmetric (6 steps):
.1.2...........7.3..6...4.....5...974.....8.....1......5...6.1.7...4........8...9
#(JPF; Apr 04, 2006) A new 1-stepper (42 clues with some symmetry):
17856....94.783...3.....872..73.82.9.91...54.2.59.16..784.....1...176.38....94725
#(Ocean; Apr 04, 2006) A 32-clue 2-stepper, full symmetric (and 'symmetrically minimal'):
.4.....7.51..3..24...284.....16.39...34...51...24.78.....546...78..2..36.9.....5.
#(Ruud; Apr 04, 2006) A 20-clue minimal + symmetrical 8-stepper:
3......2..1.98.........68........978.........652........14.........72.5..9......1
#(Ocean; Apr 05, 2006) A 44-clue 1-stepper, full symmetry, symmetrically minimal:
.652.793.1..5.8..47.93.62.8513...682.........496...3179.86.14.53..7.2..6.214.987.
#(JPF; Apr 07, 2006) 1-stepper with 40 clues, some symmetry, but not symmetrically minimal.
326.874...7....89258..41....3.7.6..14.1...7.92..4.5.3....65..24952....8...812.573
#(Ocean; May 01, 2006) A minimal 24-clues 5-stepper, full symmetry.
..41.87.....2.6...7.......637.....12.........46.....595.......3...7.9.....28.49..
#(Ocean; May 16, 2006) 8-stepper, 19 clues. Minimal, rotational symmetry.
.......123....4........5..6......57...6.3.4...52......7..4........6....183.......
#(Ocean; May 18, 2006) 5-stepper, 20 clues. Minimal, rotational symmetry.
.......1...2....345...67.......31...7.......5...48.......24...938....6...1.......
#(Ocean; May 18, 2006) 6-stepper, 20 clues. Minimal, rotational symmetry.
.......1...2....344...56.......41...6.......7...38.......23...978....5...1.......
#(Ocean; May 18, 2006) 7-stepper, 20 clues. Minimal, rotational symmetry.
.......1...2....343...51.......36...7.......2...81.......49...716....5...2.......
#(ab; May 19, 2006) There are plenty of 39 clue one steppers in that grid, for example:
1...97.239....6.5...23..74..7.5.8..135.....862.84...3...4.8391..1975...256..29..4
#(Ocean; May 19, 2006) 7-stepper, 18 clues, minimal, rotational symmetry:
.......1.....21.....3....45.....62...7.....8...45.....62....9.....48.....9.......
#(Ocean; May 19, 2006) 8-stepper (18 clues, minimal, rotational symmetry):
.......1.....12.....3....45.....62...7.....8...45.....62....3.....84.....9.......
#(ab; May 19, 2006) there's even a 38 clue 1 stepper there:
1...97.239....6.5...23..74..7.5..2.135.9...862.84...3...4.8391..1975....56..2...4
#(gsf; May 27, 2006) VI,3,27,SM
000000000003409200980205067000000000000791000207000408010080020036000540050010030
#(gsf; Jun 05, 2006) Type VII, 3 steps, 25 clues, SM.
000085000006000700072090030000076005300004902150000000000000340900200600010950000
#(JPF; Jun 08, 2006) 2 steps ; 31 clues ; no symmetry.
002600009490070206503040010000000100021809004050007090700003058000501700300096000
#(JPF; Jun 08, 2006) 2 steps ; 30 clues ; no symmetry.
400000560003400080520073000100026000005000100000008975060907030008100000391004002
#(JPF; Jun 09, 2006) 1 step ; 37 clues ; no symmetry.
400900800900813002600000017007400680014020503530009070000041308052000706008762009
#(Ocean; Jun 09, 2006) Type II. 3 steps, 24 clues, SM.
000001230100004500670008000268000000000000000000000497000500081004700003093600000
#(Ocean; Jun 09, 2006) First absolute minimal four-stepper. 24 clues. Sym-type II.
000001020201003000004005670683000000000000000000000245068200900000800403090700000
#(JPF; Jun 10, 2006) 2 steps ; 29 clues ; no symmetry (Type 0).
040700200082001604000040003230400070090863040000000100001975000306000000008200050
#(JPF; Jun 12, 2006) 1 step ; 36 clues ; no symmetry (type 0)
300007190200806000459000060906001054000030200007204819040150003085020907600408000
#(Ocean; Jun 15, 2006) 4 steps. 23 clues. No symmetry. 
007100800062000930004207100000000000000010200030456000000538060009070000000000000
#
Last edited by Ocean on Thu Jun 15, 2006 8:17 am, edited 19 times in total.
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Postby JPF » Tue Apr 04, 2006 12:13 am

A new 1-stepper (42 clues with some symmetry) :


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


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Postby Ocean » Tue Apr 04, 2006 8:37 pm

JPF wrote:A new 1-stepper (42 clues with some symmetry) :
...
JPF

Fine. Have updated 'statistics' in the previous post.

Found a 32-clue 2-stepper, full symmetric (and 'symmetrically minimal'):
Code: Select all
+-------+-------+-------+
| . 4 . | . . . | . 7 . |
| 5 1 . | . 3 . | . 2 4 |
| . . . | 2 8 4 | . . . |
+-------+-------+-------+
| . . 1 | 6 . 3 | 9 . . |
| . 3 4 | . . . | 5 1 . |
| . . 2 | 4 . 7 | 8 . . |
+-------+-------+-------+
| . . . | 5 4 6 | . . . |
| 7 8 . | . 2 . | . 3 6 |
| . 9 . | . . . | . 5 . |
+-------+-------+-------+


And a 20-stepper with full symmetry (also symmetrically minimal):
Code: Select all
+-------+-------+-------+
| . 4 . | . . . | . 7 . |
| 2 . . | . 3 . | . . 4 |
| . . . | 9 . 1 | . . . |
+-------+-------+-------+
| . . 3 | . 6 . | 5 . . |
| . 5 . | 8 . 9 | . 6 . |
| . . 2 | . 7 . | 9 . . |
+-------+-------+-------+
| . . . | 2 . 6 | . . . |
| 4 . . | . 1 . | . . 8 |
| . 6 . | . . . | . 3 . |
+-------+-------+-------+
Last edited by Ocean on Tue Apr 04, 2006 5:10 pm, edited 1 time in total.
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Postby Ruud » Tue Apr 04, 2006 9:08 pm

I know we're hijacking ab's thread, but this is also a lot of fun (can't find any 29-steppers anyway, still looking)

Here is a 20-clue minimal + symmetrical 8-stepper for the list.

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


Ruud.
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Postby JPF » Wed Apr 05, 2006 11:30 am

a 1-stepper again , still with 42 clues and with some symmetry.

Code: Select all

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



JPF
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Postby Ocean » Wed Apr 05, 2006 12:03 pm

A 23-stepper with full symmetry:
Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . 2 | 1 . 3 | 7 . . |
| . 8 9 | . . . | 3 4 . |
+-------+-------+-------+
| . 1 . | . 8 . | . 6 . |
| . . . | 6 . 7 | . . . |
| . 3 . | . 4 . | . 2 . |
+-------+-------+-------+
| . 4 6 | . . . | 9 3 . |
| . . 5 | 7 . 6 | 4 . . |
| . . . | . . . | . . . |
+-------+-------+-------+

Ruud wrote:I know we're hijacking ab's thread, but this is also a lot of fun (can't find any 29-steppers anyway, still looking)

Here is a 20-clue minimal + symmetrical 8-stepper for the list.

List updated. Symmetrical puzzles with such low number of clues are hard to find!
The 'hijack' is probably a short episode, since we now are reaching limits that are difficult to push further.
JPF wrote:a 1-stepper again , still with 42 clues and with some symmetry.
Do you know if this one (or your previous) is also 'symmetrically minimal'? (it's a bit awkward to check...)
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Postby JPF » Wed Apr 05, 2006 12:46 pm

Ocean wrote:
JPF wrote:a 1-stepper again , still with 42 clues and with some symmetry.
Do you know if this one (or your previous) is also 'symmetrically minimal'? (it's a bit awkward to check...)


Sorry,

The two 1-steeper's (42 clues) are not symmetrically minimal.

JPF
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Postby ab » Wed Apr 05, 2006 1:59 pm

Ruud wrote:I know we're hijacking ab's thread, but this is also a lot of fun (can't find any 29-steppers anyway, still looking)

Ruud.


No problem. That's the nature of public forums. I think it's fair to say the puzzles you're looking for now do deserve the tag inferior puzzles:) I also agree they're fun.
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Re: inferior puzzles thread

Postby gsf » Wed Apr 05, 2006 2:05 pm

ab, non-symmetric 27 step puzzle#2 must have some typos
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Re: inferior puzzles thread

Postby ab » Wed Apr 05, 2006 2:31 pm

gsf wrote:ab, non-symmetric 27 step puzzle#2 must have some typos


Thanks for the heads up gsf. I've edited it now, hopefully it's right this time.
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Postby Ocean » Wed Apr 05, 2006 9:48 pm

JPF wrote:Sorry,

The two 1-steeper's (42 clues) are not symmetrically minimal.

JPF


Thanks. Both your 42-clues 1-steppers are 'best' so far, in this category! But here is a replacement for the 'symmetrically minimal':

Code: Select all
A 44-clue 1-stepper, full symmetry, symmetrically minimal.
+-------+-------+-------+
| . 6 5 | 2 . 7 | 9 3 . |
| 1 . . | 5 . 8 | . . 4 |
| 7 . 9 | 3 . 6 | 2 . 8 |
+-------+-------+-------+
| 5 1 3 | . . . | 6 8 2 |
| . . . | . . . | . . . |
| 4 9 6 | . . . | 3 1 7 |
+-------+-------+-------+
| 9 . 8 | 6 . 1 | 4 . 5 |
| 3 . . | 7 . 2 | . . 6 |
| . 2 1 | 4 . 9 | 8 7 . |
+-------+-------+-------+

Also 3 more 44-clues symmetrically minimal one-steppers. But the first one (above) is 'the most overdetermined':

608703902020408050503209406286000594000000000415000837704901308060305070109806205
004107300002893500590204087259000741010000050738000692380502016001386200005901400
046208530720403096800509007234000169000000000579000382400705003190304058058601270

These might suit as 'first puzzles' in 'beginner's books'. (I always wondered why they put such hard puzzles there...).

#
And for the sake of beauty:
Code: Select all
Another 20-stepper with full symmetry:
+-------+-------+-------+
| . 4 . | . 5 . | . 8 . |
| 7 . . | . 3 . | . . 4 |
| . . 3 | 7 . 4 | 2 . . |
+-------+-------+-------+
| . . 4 | . . . | 1 . . |
| 8 3 . | . . . | . 6 9 |
| . . 6 | . . . | 8 . . |
+-------+-------+-------+
| . . 8 | 5 . 6 | 7 . . |
| 6 . . | . 1 . | . . 8 |
| . 1 . | . 2 . | . 5 . |
+-------+-------+-------+
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