The New Sudoku Players' Forum

by **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.

by **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

by **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

Ruud.

by **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

JPF

by **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 #

by **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

JPF

by **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 . | +-------+-------+-------+

by **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.

by **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

by **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...)

by **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

by 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.

by **gsf** » Wed Apr 05, 2006 2:05 pm

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

by 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.

by **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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