The New Sudoku Players' Forum

by **gsf** » Sat Jun 10, 2006 5:10 am

still ~1/day

Code: Select all: #V,3,26,SM,080000024050009000014750000008040600000102000002060700000015360000300090590000040,gsf,2006-06-10 . 8 . . . . . 2 4 . 5 . . . 9 . . . . 1 4 7 5 . . . . . . 8 . 4 . 6 . . . . . 1 . 2 . . . . . 2 . 6 . 7 . . . . . . 1 5 3 6 . . . . 3 . . . 9 . 5 9 . . . . . 4 .

by **JPF** » Sat Jun 10, 2006 7:25 am

2 Improvements :

Type VI ; 1 step ; 41 clues

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

3 steps ; 26 clues ; no symmetry (Type 0)

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

JPF

by **JPF** » Sat Jun 10, 2006 9:28 am

Type IV ; 1 step ; 43 clues

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

2 steps ; 29 clues ; no symmetry (Type 0)

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

JPF

by **Ocean** » Sat Jun 10, 2006 8:16 pm

Lots of contributions lately. Great! The table now has 62 entries (only two holes left). There is still room for improvement for most of the numbers. But not all: Ten entries cannot possibly be beaten unless new 17s (or lower) are found.

Code: Select all: # 1. The current state: 1 2 3 4 5 6 7 8 I 44 32 28 28 24 24 24 20 II -- 32 24 24 24 20 20 20 III -- 34 28 25 22 22 22 22 IV 43 34 28 26 25 24 24 24 V 40 35 26 24 20 20 18 18 VI 41 35 27 25 24 24 22 22 VII 40 34 25 25 23 23 18 18 0 37 29 26 26 24 19 18 17 #

Entries that cannot possibly be beaten unless new 17s (or lower) are found:

Code: Select all: # 2. Almost lowest possible: 1 2 3 4 5 6 7 8 I -- -- -- -- -- -- -- 20 II -- -- -- -- -- 20 20 20 III -- -- -- -- -- -- -- -- IV -- -- -- -- -- -- -- -- V -- -- -- -- -- -- 18 18 VI -- -- -- -- -- -- -- -- VII -- -- -- -- -- -- 18 18 0 -- -- -- -- -- -- 18 17 #

Entries that match the 'accumulated list' in some way or another:

Code: Select all: # 3. Matching accumulated lowest: 1 2 3 4 5 6 7 8 I 44 32 -- -- -- -- -- -- II -- 32 24 24 -- 20 -- -- III -- -- -- -- -- -- -- -- IV -- -- -- -- -- -- -- -- V 40 -- -- 24 20 20 18 18 VI -- -- -- -- -- -- -- -- VII 40 -- -- -- -- -- 18 18 0 37 29 -- -- -- 19 18 17 #

by **gsf** » Sun Jun 11, 2006 5:39 am

another

Code: Select all: #IV,2,32,SM,002806030000004809600095070800000354006000700591000006010670008309100000040209600,gsf,2006-06-10:21:56 . . 2 8 . 6 . 3 . . . . . . 4 8 . 9 6 . . . 9 5 . 7 . 8 . . . . . 3 5 4 . . 6 . . . 7 . . 5 9 1 . . . . . 6 . 1 . 6 7 . . . 8 3 . 9 1 . . . . . . 4 . 2 . 9 6 . .

by **gsf** » Sun Jun 11, 2006 2:13 pm

an improvement

Code: Select all: #VI,6,23,SM,000008000000035810067000000002060503000040000005080907049000000000051280000009000,gsf,2006-06-11:02:09 . . . . . 8 . . . . . . . 3 5 8 1 . . 6 7 . . . . . . . . 2 . 6 . 5 . 3 . . . . 4 . . . . . . 5 . 8 . 9 . 7 . 4 9 . . . . . . . . . . 5 1 2 8 . . . . . . 9 . . .

and a type II 1 stepper

Code: Select all: #II,1,41,-,100900873806005000200781050098040207003526900604090310060278009000300601352009004,gsf,2006-06-11:02:0 1 . . 9 . . 8 7 3 8 . 6 . . 5 . . . 2 . . 7 8 1 . 5 . . 9 8 . 4 . 2 . 7 . . 3 5 2 6 9 . . 6 . 4 . 9 . 3 1 . . 6 . 2 7 8 . . 9 . . . 3 . . 6 . 1 3 5 2 . . 9 . . 4

by **Ocean** » Sun Jun 11, 2006 7:33 pm

Two puzzles with double diagonal symmetry.

Code: Select all: # Type IV. 8 steps. 20 clues. SM *-----------* |...|..1|.23| |..1|...|..4| |.5.|.2.|...| |---+---+---| |...|6..|..7| |..8|...|5..| |3..|..8|...| |---+---+---| |...|.5.|.8.| |5..|...|9..| |26.|7..|...| *-----------* # # Type IV. 7 steps. 20 clues. SM *-----------* |...|..1|.23| |..2|...|..4| |.5.|.6.|...| |---+---+---| |...|3..|..7| |..8|...|2..| |6..|..7|...| |---+---+---| |...|.2.|.5.| |1..|...|6..| |74.|8..|...| *-----------* #

by **JPF** » Sun Jun 11, 2006 11:36 pm

1 step ; 36 clues ; no symmetry (type 0)

this one :

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

or this one :

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

Some 1 steppers, 37 clues , type 0 :

Code: Select all: 702600019503007000000823060900031850054080670017040020201000007000309482090205000 860305009005074002009008300002000840638009070070600005904850763100230500700400100 054300007700100043610900502300820470001060809570000200809503000200090051100047600 020600000001080540300921780064700000900250003850006209400193820080000634500004010 410000052300420069000068000000907208047200003005310796060540000100003670859001300 740001300012000680000729050060500740308090005090102000480000030007630920620950401 367000910080090406005081000070562030003000647091003080800400071500900302026105000 002634000008001570490058302003900681007310020065000009320047010070000000506803900 286009400009510800000000670635900000090000732100084000002468050500273901470100008 681004090003080500004003128048710630050940080060000057890001000000539072700002004 600000450591080070824003900042090106000076090005408020073500002080140600100030709 032590007050080962080700050490063000021000800605004100009208074067050003203010008 390000065050190024060200080004003000020871009805640013087054600006000790109008400 640050091703008054800092000010000739000670002530210008020000687008705900409030100 000045006007830501830090002903100648060580000020000730076209010382006000001070064 080600000000002950040185270010728090829003600350000400102076000690530001004009803 090076000006380071000100240704900513200704009800035000040291705001040680523000000 060090704201040069009370051983000100006002030700005800430600000502814600010700902

JPF

by **JPF** » Mon Jun 12, 2006 12:21 am

4 steps ; 25 clues ; no symmetry (type 0)

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

Type IV ; 1 step ; 41 clues

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

JPF

by **JPF** » Mon Jun 12, 2006 12:30 am

Ocean, you wrote:Entries that match the 'accumulated list' in some way or another...

What does that mean ?
JPF

by **JPF** » Mon Jun 12, 2006 7:32 am

a new entry ; the last one ?

type III ; 1 step ; 44 clues

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

JPF

by **Ocean** » Tue Jun 13, 2006 10:01 am

JPF wrote:a new entry ; the last one ?

Nice to have all entries in the table! The table in is also updated with new improvements.

JPF wrote:
Ocean, you wrote:Entries that match the 'accumulated list' in some way or another...

What does that mean ?
JPF

With 'accumulated list' I meant this upper/summary part of the table:

Code: Select all: #------------------------------+----+----+----+----+----+----+----+----+ 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 | 24 | 20 | 19 | 18 | 17 | #------------------------------+----+----+----+----+----+----+----+----+

... and picked those entries for each symmetry type that match the current 'accumulated'. Which now is:

Code: Select all: # 3. Matching accumulated lowest: 1 2 3 4 5 6 7 8 I 44 32 -- -- -- -- -- -- II -- 32 24 24 -- 20 -- -- III -- -- -- -- -- -- -- -- IV -- 32 -- -- -- -- -- -- V 40 -- -- 24 20 20 18 18 VI -- -- -- -- -- -- -- -- VII 40 -- -- -- -- -- 18 18 0 36 29 -- -- -- 19 18 17 #

If we take the 1-steppers as an example: Lowest number of clues for any sudoku is 36 clues, which is found for puzzles with no symmetry. For a symmetric sudoku, the lowest number of clues found is 40. This is found for symmetry types V and VII, but not (yet) for the other symmetries. 44 clues is the lowest number for SM (found for type I symmetry), while no absolute minimal 1-stepper is found.

My assumption is that symmetry groups with 'lower symmetry' will (with high probability) contain puzzles with at least as few clues as puzzles with higher symmetry (for a given step count). (Any other opinions?) For instance: Since a 3-stepper with 24 clues is found with symmetry type II, it is expected that this (or lower) should exist also for symmetry types III-VII + 0.

by **gsf** » Tue Jun 13, 2006 12:52 pm

another improvement

Code: Select all: #VII,6,22,M,000000030000305809006001070700000240430900000000020060200000500000090000005014000,gsf,2006-06-12:18:16 . . . . . . . 3 . . . . 3 . 5 8 . 9 . . 6 . . 1 . 7 . 7 . . . . . 2 4 . 4 3 . 9 . . . . . . . . . 2 . . 6 . 2 . . . . . 5 . . . . . . 9 . . . . . . 5 . 1 4 . . .

by **Ocean** » Tue Jun 13, 2006 4:53 pm

An improvement (5-stepper, diagonal symmetry):

Code: Select all: # Type VII, 5 steps. 22 clues. Minimal. 1 2 .|. 3 4|. . . 5 . .|. . .|6 . . . . 3|. . .|7 . . -----+-----+----- . . .|. . 8|. 1 . 3 . .|. . .|. 2 8 2 . .|7 . .|. . . -----+-----+----- . 8 9|. . .|. . 3 . . .|4 5 .|. . . . . .|. 1 .|9 . . #

by **JPF** » Tue Jun 13, 2006 9:59 pm

Ocean wrote:My assumption is that symmetry groups with 'lower symmetry' will (with high probability) contain puzzles with at least as few clues as puzzles with higher symmetry (for a given step count). (Any other opinions?) For instance: Since a 3-stepper with 24 clues is found with symmetry type II, it is expected that this (or lower) should exist also for symmetry types III-VII + 0.

I agree.
There are actually 4 "classes" of symmetries :
Order 8 : Type I (F)
Order 4 : Type II,III,IV (L,P,X)
Order 2 : Type V,VI,VII (R,H,D)
Order 1 : Type 0 (A)

with the following notations :

st : symmetry type (A<D;H;R<X;P;L<F)
s : number of steps
m : minimality (NM<SM<M)
N(st,s,m) = Min of clues

we can assume that :
st<st’ => N>=N’ (other parameters being equal)
s<s’ => N>=N’
m<m’ => N>=N’

JPF

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