Low-stepper Puzzles.

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

Postby JPF » Sat Oct 14, 2006 11:26 pm

Impressive continuous work, Ocean !

JPF
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Postby JPF » Mon Oct 16, 2006 6:22 pm

New personnal records :

Code: Select all
Type II, 1 step, 40 clues

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


Code: Select all
Type II, 1 step, 40 clues

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


Code: Select all

Type I, 2 steps, 32 clues

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


Code: Select all
Type II, 2 steps, 32 clues

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


JPF
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Postby Ocean » Tue Oct 17, 2006 7:19 am

JPF wrote:Impressive continuous work, Ocean !

JPF
Thank you - and thanks for the new submissions. It seems that our methods are quite different: Your approach mainly from the low end, gsf's firm grip in the middle, and my efforts from the upper end.
Ocean
 
Posts: 442
Joined: 29 August 2005

minimal 3 stepper

Postby coloin » Mon Nov 06, 2006 2:18 pm

Here is a minimal 3-stepper with 34 clues.
A chameleon puzzle from the dukuso15 grid

Code: Select all
000000000004001052057043081018057034006480007000000000091025040070106008085900013


C
coloin
 
Posts: 1637
Joined: 05 May 2005

Re: minimal 3 stepper

Postby Ocean » Tue Nov 07, 2006 6:38 pm

coloin wrote:Here is a minimal 3-stepper with 34 clues.
A chameleon puzzle from the dukuso15 grid

Code: Select all
000000000004001052057043081018057034006480007000000000091025040070106008085900013


C

Great! First minimal 3-stepper!

Also, a new table is added: Lowest known number of steps for minimal 31+ puzzles.
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby coloin » Tue Nov 07, 2006 7:51 pm

Thanks for that
For optimistic analysis:
Here are the 35s in the dukuso15 grid
Code: Select all
Duk15
rating:     85 ,  ..........64..135..57.436.1.1..5793.5....9..7...31..65..1..57.6.7213.....8..742..
rating:     84 ,  ..........64..135..57.436.1.1..5793.5....9..7...31..6...1..57.6.7213.5...8..742..
rating:     83 ,  ..........64..135..57.436.1.1..5793......9..7...31..65..1..57.6.7213.....85.742..
rating:     87 ,  ..........64..135..57.436.1.1..5793......9..7...31..6...1..57.6.7213.5...85.742..
rating:     81 ,  ..........64..135..57.4.6.1.18.5793.5....9..7..931..65..1..57...7.13.....8..742.3
rating:     84 ,  ..........64..135..57.4.6.1.18.5793.5....9..7..931..6...1..57...7.13.5...8..742.3
rating:     84 ,  ..........64..135..57.4.6.1.18.5793......9..7..931..65..1..57...7.13.....85.742.3
rating:     85 ,  ..........64..135..57.4.6.1.18.5793......9..7..931..6...1..57...7.13.5...85.742.3
rating:     46 ,  ..........6...1352.57...6.1.18.5793....4.9..7..931..6...1..57...7.13.5...85.742.3
rating:     46 ,  ..........6...135..57..36.1.1..5793.5.64.9.....9.1..6...1.257...7213.5...8..742.3
rating:     66 ,  ..........6...135..57...6.1.1..5793....4.9..7..931..6...1.257.6.7213.5...85.742..
rating:     46 ,  ..........6...135..5..436.1.1..5793.5.64.9.....9.12....91.257...7213.5......742.3
rating:     46 ,  ..........6...135..5..436.1.1..5793.5.64.9.....9.12.....1.257...7213.5...8..742.3


As there are many many 33s [over 4500 34s] in the above grid, there may just be a lower stepper puzzle out there !

C
coloin
 
Posts: 1637
Joined: 05 May 2005

Postby Ocean » Tue Nov 07, 2006 8:30 pm

coloin wrote:Thanks for that
For optimistic analysis:
Here are the 35s in the dukuso15 grid
C

Four of the 35s were lowsteppers (all 6 steps). These are added to the list:

-,6,35,M,000000000060001352057000601018057930000409007009310060001005700070130500085074203,coloin,273
-,6,35,M,000000000060001350057003601010057930506409000009010060001025700072130500080074203,coloin,274
-,6,35,M,000000000060001350050043601010057930506409000009012000091025700072130500000074203,coloin,275
-,6,35,M,000000000060001350050043601010057930506409000009012000001025700072130500080074203,coloin,276
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby coloin » Mon Nov 13, 2006 1:51 pm

JPF has kindly filtered a few hundred thousand puzzles to get these 3 steppers - all from the MC grid.

Code: Select all
clues  steps
  31    3    ..3..678.7.....45..567..1..2.1...8...6...72.1.9..3.5..3126.5...6....8....7..12...
  32    3    ..3..678.7..1..45.4.678.1..23..648...6....2.1.........31264....6....8.....8.12..5
  33    3    .23..678.7..1..45.4.67..1..231.6.8...6...72...........31.6.5...6....8..2.78.12..5

And a 4 stepper from dukuso15 grid with 31 clues
Code: Select all
  31    4    ..............1352.57.4.6.1.18.5.93...6..9......312..5..1..57...7.13.....8..742.3

How likely is a minimal 2 stepper ?

C
coloin
 
Posts: 1637
Joined: 05 May 2005

Postby Ocean » Mon Nov 13, 2006 7:37 pm

coloin wrote:JPF has kindly filtered a few hundred thousand puzzles to get these 3 steppers - all from the MC grid.

Thanks. A good start for the minimal 31+ puzzles. Or is it the final word? We now have minimal 3-steppers with 31, 32, 33 and 34 clues. Tables updated.
coloin wrote:How likely is a minimal 2 stepper ?
Think it's most likely that minimal 2-steppers exist - but how to find one? Also, are there 2-steppers among the minimal 31+ puzzles?
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby Ocean » Wed May 02, 2007 10:29 pm

Two improvements for puzzles with type VI symmetry:

Code: Select all
# Type VI, 7-stepper, 21 clues, Minimal.
 *-----------*
 |1..|...|..2|
 |...|...|...|
 |3..|4.5|..6|
 |---+---+---|
 |2..|1.7|..4|
 |...|...|...|
 |..3|.2.|8..|
 |---+---+---|
 |..4|.6.|9..|
 |.9.|.1.|.8.|
 |..6|...|3..|
 *-----------*
#
# Type VI, 6-stepper, 21 clues, Minimal.
 *-----------*
 |...|...|...|
 |.1.|.2.|.3.|
 |2..|4.5|..6|
 |---+---+---|
 |4..|...|..2|
 |...|...|...|
 |1..|7.6|..8|
 |---+---+---|
 |.6.|.5.|.9.|
 |..7|.4.|3..|
 |.9.|...|.1.|
 *-----------*
#
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby JPF » Wed May 02, 2007 10:40 pm

Welcome back Ocean and low steppers!:)

JPF
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Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby Ocean » Fri May 04, 2007 5:50 pm

JPF wrote:Welcome back Ocean and low steppers!:)

Thanks! [And congratulations with breaking the "M2-conjecture"!]

Another improvement:
Code: Select all
# H22; S4
# Type VI, 4-stepper, 22 clues, Minimal.
 *-----------*
 |..1|...|2..|
 |2.3|...|4.5|
 |...|3.6|...|
 |---+---+---|
 |72.|...|.68|
 |...|...|...|
 |...|1.4|...|
 |---+---+---|
 |...|.1.|...|
 |..9|...|3..|
 |.4.|768|.2.|
 *-----------*
#
# And its companion:
# H22; S5
# Type VI, 5-stepper, 22 clues, Minimal.
 *-----------*
 |...|..1|.2.|
 |1..|..3|...|
 |..4|...|.56|
 |---+---+---|
 |5..|.6.|3..|
 |32.|...|...|
 |7..|.1.|4..|
 |---+---+---|
 |..8|...|.71|
 |9..|..2|...|
 |...|..9|.6.|
 *-----------*
#

Code: Select all
# Five steps.
# Minimal sudoku, 21 clues, no symmetry.
 *-----------*
 |..1|2..|...|
 |...|1..|.3.|
 |4..|...|.56|
 |---+---+---|
 |7..|...|.83|
 |...|5..|.2.|
 |..4|9..|...|
 |---+---+---|
 |.29|...|...|
 |..8|..4|9..|
 |...|..3|7..|
 *-----------*
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby Ocean » Tue May 08, 2007 2:05 pm

A further improvement:
Code: Select all
# Type VI, 5-stepper, 21 clues, Minimal.
 *-----------*
 |...|...|.12|
 |.3.|...|..4|
 |..5|.12|...|
 |---+---+---|
 |2..|6..|...|
 |...|37.|6..|
 |8..|1..|...|
 |---+---+---|
 |..6|.59|...|
 |.5.|...|..7|
 |...|...|.31|
 *-----------*
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby Ocean » Sun Sep 16, 2007 1:06 am

A few improvements.
Code: Select all
# Type V, 20 clues, minimal. Four-stepper.
 *-----------*
 |...|...|..1|
 |...|..2|...|
 |.3.|4..|5.6|
 |---+---+---|
 |...|..7|89.|
 |.6.|...|.2.|
 |.43|5..|...|
 |---+---+---|
 |2.7|..9|.8.|
 |...|6..|...|
 |1..|...|...|
 *-----------*
#
# Type V, 18 clues, minimal. Six-stepper.
 *-----------*
 |...|...|..1|
 |...|..2|...|
 |..1|...|.34|
 |---+---+---|
 |...|..5|67.|
 |..4|...|2..|
 |.18|9..|...|
 |---+---+---|
 |69.|...|7..|
 |...|4..|...|
 |2..|...|...|
 *-----------*
#
# Type IV, 18 clues, minimal. Six-stepper.
 *-----------*
 |..1|...|.23|
 |...|..4|..5|
 |6..|..7|...|
 |---+---+---|
 |...|...|78.|
 |...|...|...|
 |.52|...|...|
 |---+---+---|
 |...|2..|..9|
 |8..|3..|...|
 |47.|...|1..|
 *-----------*
#
# Trivially:
#
# Type IV, 18 clues, minimal. Seven steps.
001000023000004005200006000000000670000000000035000000000500004600200000740000800
#
# Type IV, 18 clues, minimal. Eight steps.
001000023000004005600007000000000480000000000032000000000200009800600000470000100
###
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby Mauricio » Sun Feb 10, 2008 4:55 am

Improvement, I'd think:
Code: Select all
Type 0, non minimal, 1 stepper, 33 clues each
........1..1.23.45.265.7..8...982...35..4..1.8.....762..4635...1.....93.78...4.2.
........1..1.23.45.265.7..8...982...35..4..1.8.....769..4635...1.....93.78...4.2.
........1..1.23.45.265.7..8...982...35..4..1.8...5.7.9..4635...1.....93.78...4.2.
........1..1.23.45.265.7..8...982...35..4.1..8.....762..46.5...1.....93.783..4.2.
........1..1.23.45.265.7..8...982...35..4.1..8.....762..4635...1.....93.78...4.2.
........1..1.23.45.265.7..8...982...35..4.1..8.....769..46.5...1.....93.783..4.2.
........1..1.23.45.265.7..8...982...35..4.1..8.....769..4635...1.....93.78...4.2.
........1..1.23.45.265.7..8...982...35..4.1..8...5.7.9..46.5...1.....93.783..4.2.
........1..1.23.45.265.7..8...982...35..4.1..8...5.7.9..4635...1.....93.78...4.2.
........1..2.34.56.376.2..8...983...46..5....8.....279..57.6.8.1.....94.284..5.3.
........1..2.34.56.376.2..8...983...46..5....8.....279..5746.8.1.....94.28...5.3.
........1..2.34.56.376.2..8...983...46..5..1.8.....279..5746...1.....94.28...5.3.
........1..2.34.56.376.2..8...983...46..5..1.8...6.2.9..5746...1.....94.28...5.3.
........1..2.34.56.376.2..8...983...46..5.1..8.....279..57.6...1.....94.284..5.3.
........1..2.34.56.376.2..8...983...46..5.1..8.....279..5746...1.....94.28...5.3.
........1..2.34.56.376.2..8...983...46..5.1..8...6.2.9..57.6...1.....94.284..5.3.
........1..2.34.56.376.2..8...983...46..5.1..8...6.2.9..5746...1.....94.28...5.3.
........1..2.34.56.376.2..8...983...46..5.8..8.....279..57.6...1.....94.284..5.3.
........1..2.34.56.376.2..8...983...46..5.8..8.....279..5746...1.....94.28...5.3.
........1..2.3456..375.2..8...983...45..6.1..8.....279..67.5...1.....94.284..6.3.
........1..2.3456..375.2..8...983...45..6.1..8...5.2.9..67.5...1.....94.284..6.3.
.......12..1.34.5.356..7.....76.3....142...388.....9.5.2..7....4..85..2696..1.8.4
......123...145....67..8..9..8.61...653.2..9.9.....47.3..8.....4.23..75.8..79..62
......123..1.245...56..7.......7..824..8.53.693..1...4..76.2...1.43....88.....695
......123..1.245...56..7.......7..824..8.53.693..1...4..76.2...1.43..6.88......95
......123..1.245...56..7.......7..824..8.53.693..1...4..76.2...1643....88......95
......123..1.245...56..7.......7..824..8.53.693..1...4..76.2...6143....88......95
......123..1.245...56..7.......7..824..85.3.693..1...4..76.2....143....88.....695
......123..1.245...56..7.......7..824..85.3.693..1...4..76.2...1.43....88.....695
......123..1.245...56..7.......7..824..85.3.693..1...4..76.2...1.43..6.88......95
......123..1.245...56..7.......7..824..85.3.693..1...4..76.2...1643....88......95
......123..1.245...56..7.......7..824..85.3.693..1...4..76.2...6143....88......95
......123..1.245...56..7.......7..827..85.3.693..1...4..76.2....143....88.....695
......123..1.245...56..7.......7..827..85.3.693..1...4..76.2...1.43....88.....695
......123..1.245...56..7.......7..827..85.3.693..1...4..76.2...1.43..6.88......95
......123..1.245...56..7.......7..827..85.3.693..1...4..76.2...1643....88......95
......123..1.245...56..7.......7..827..85.3.693..1...4..76.2...6143....88......95
......123..1.245...56..7.....76.2....143....88.....695.3..7.9..7..85.3.69...1..84
......123..1.245...56..7.....76.2....143..2.88......95.3..7....4..85.3.696..1..84
......123..1.245...56..7.....76.2....143..2.88......95.3..7....7..85.3.696..1..84
......123..1.245...56..7.....76.2...6143....88......95.3..7...27..85.3.69...1..84
......123..1.245...56..7.....76.2...6143....88......95.3..7.9..7..85.3.69...1..84
......123..1.245...56..7.....76.2...6143..2.88......95.3..7....7..85.3.69...1..84
......123..1.245...56..7..8..76.2...6143....99......85.3..7....7..95.3.68...1..94
......123..1.245...56..78....76.2...6143....88......95.3..7....7..85.3.69...1..84
......123..4..5.....6178..9..56...3..7.39..4892.8....73...2..7.51.9..26.8...41...
......123..4..5.....6178..9..56..3...7.39.4.891.8....73...1.7..52.9..61.8...42...
......123..4..5....16.78..9..56...3.29.8....77..39..48.3..2..7..8..41...15.9..26.
......123..4..5....16.78..9..56..3..19.8....77..39.4.8.3..1.7...8..42...25.9..61.
......123..4.15.....67.8..9..5.6..3..7.93..4892..8...73..2...7.51..9.26.8..4.1...
......123..4.15....67..8..9.1..3.6...52.7....9..24.81.39.6..5.77..19...68....43..
......123..4.15....67..8..9.2..3..6..51.7....9..14.28.39.6...577..29...68....4.3.
......123..4.56...781..9......7.1.89..6...4...1328.6...9.83...42679....14......57
......123..4.56...781..9......7.18.9..6...4...1328.5...9.837..426.9....14......57
......123..4.56...781..9......7.18.9..6...4...1328.5...9.837.6.26.9....14......57
......123..4.56...781..9......7.18.9..6...4...1328.6...9.83...426.9.7..14......57
......123..4.56...781..9......7.18.9..6...4...1328.6...9.83...42679....14......57
......123..4.56...781..9......7.18.9..6...4...1328.6...9.83...626.9.7..14......57
......123..4.56...781..9......7.18.9..6...4...1328.6...9.83...62679....14......57
......123..4.56...781..9......7.18.9..6...4...1328.6...9.83..4.26.9.7..14......57
......123..4.56...781..9......7.18.9..6...4...1328.6...9.83..4.2679....14......57
......123..4.56...781..9......7.18.9..6...4...1328.6...9.837..426.9....14......57
......123..4.56...781..9......7.18.9..6...4...1328.6...9.837..626.9....14......57
......123..4.56...781..9......7.18.9..6...4...1328.6...9.837.4.26.9....14......57
......123..4.56...781..9......7.18.9..6...4...1328.6...9.837.6.26.9....14......57
......123..4.56...781..9......7.18.9..6.8.4...132..5...9.837.6.26.9....14......57
......123..4.56...781..9..4...7.18.9..6...4...1328.6...9.837...26.9....14......57
......123..4.56...781..9..4...7.189...6...4...1238.6...9.82....36.9.7.1.4......75
......123..4.56...781..9..4...7.189...6...4...1238.6...9.82....3679...1.4......75
......123..4.56...781..9..4...7.189...6...4...1238.6...9.827...36.9...1.4......75
......123..4.56...781..9..6...7.18.9..6...4...1328.6...9.83....26.9.7..14......57
......123..4.56...781..9..6...7.18.9..6...4...1328.6...9.83....2679....14......57
......123..4.56...781..9..6...7.18.9..6...4...1328.6...9.837...26.9....14......57
......123..4.56...781..9..6...7.189...6...4...1238.6...9.82....36.9.7.1.4......75
......123..4.56...781..9..6...7.189...6...4...1238.6...9.82....3679...1.4......75
......123..4.56...781..9..6...7.189...6...4...1238.6...9.827...36.9...1.4......75

Mauricio
 
Posts: 1174
Joined: 22 March 2006

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