The 35 was found in the canonical grid, which has a 19 but no 18.
Would there be a higher chance of finding a 36 in a grid which has a 20 but no 19?
145726983837495261926381574293874156581269347674153892318547629459632718762918435
157|629|834
826|743|591
493|185|267
---+---+---
268|491|375
934|257|618
571|836|942
---+---+---
385|914|726
619|572|483
742|368|159
Ocean wrote:Here are two minimal sudokus with 35 clues:
#
100056780780120450400700103201064800060090001800200500302645000640070000000002000
103006780780120450400700103201064800060090001800200500302645000640070000000002000
#
100006780780120450000700103201064800060090001800000500302645000640070000000002000
103006780780100450000700103001064800060090001800000500302645000640070000000002000
Ocean wrote:Here are two minimal sudokus with 35 clues:
- Code: Select all
+---+---+---+
|1..|.56|78.|
|78.|12.|45.|
|4..|7..|1.3|
+---+---+---+
|2.1|.64|8..|
|.6.|.9.|..1|
|8..|2..|5..|
+---+---+---+
|3.2|645|...|
|64.|.7.|...|
|...|..2|...|
+---+---+---+
and
+---+---+---+
|1.3|..6|78.|
|78.|12.|45.|
|4..|7..|1.3|
+---+---+---+
|2.1|.64|8..|
|.6.|.9.|..1|
|8..|2..|5..|
+---+---+---+
|3.2|645|...|
|64.|.7.|...|
|...|..2|...|
+---+---+---+
Minimal as in: Not able to remove a clue without causing a puzzle with multiple solutions?
.......which they do, 15 and 55 respectively.Ruud wrote:That would make the following 2 non-existent?
- Code: Select all
100006780780120450000700103201064800060090001800000500302645000640070000000002000
103006780780100450000700103001064800060090001800000500302645000640070000000002000
Ruud wrote:Ocean wrote:Here are two minimal sudokus with 35 clues:
#
100056780780120450400700103201064800060090001800200500302645000640070000000002000
103006780780120450400700103201064800060090001800200500302645000640070000000002000
#
Minimal as in: Not able to remove a clue without causing a puzzle with multiple solutions?
That would make the following 2 non-existent?
- Code: Select all
100006780780120450000700103201064800060090001800000500302645000640070000000002000
103006780780100450000700103001064800060090001800000500302645000640070000000002000
Ruud.
Sure - that is straightforward if you have the right tool (which i do not have). But there is no point in distinguishing between common and non-common clues in that respect. Planned do write some tools which could give further insight, but haven't got time for it yet - it takes time to figure out how to do things in a proper way.coloin wrote:Is there a way of working out which are the non-common clues in one grid which map to the non-common clues in the other
Had a 'quick' look at it. Found two minimal 32s in this grid so far. Maybe you can do better...Moschopulus wrote:The 35 was found in the canonical grid, which has a 19 but no 18.
Would there be a higher chance of finding a 36 in a grid which has a 20 but no 19?
145726983837495261926381574293874156581269347674153892318547629459632718762918435
coloin wrote:I presume Ocean's computor is continuing to scan the canonical for a 36 !
coloin wrote:Interesting that you have shown the morphed puzzles....number 2 and number 3 in your list have 20 common clues.
- Code: Select all
.2.4.6.89.89.23.56.5..8.12.23.5.4.9...4..72...9..3..6.31.645....45..8......3.....
.23.5.7.9.89.23.5645..8..2..3.56.8.75....7..1.9..3..6....64.978....78..2......6..
.2......9.89.23.56.5..8..2..3.5..........7....9..3..6....64.........8............
Most have considerably less - was this deliberate ?
Maybe there are ones which are even better than this ?
Is there a way of working out which are the non-common clues in one grid which map to the non-common clues in the other ?
C
.2.4.6.89.89.23.56.5..8.12.23.5.4.9...4..72...9..3..6.31.645....45..8......3.....
.2.4.6.89.89.2..56.5..8.12.23.5.4.9...4..72...9..3..6.31.645....45..8......3.....
.2.4.6.89.89.23.56.5..8.12.23.5.4.9...4..72......3..6.31.645....45..8......3.....
--------------X-------------------------------Y----------------------------------
.23.5.7.9.89.23.5645..8..2..3.56.8.75....7..1.9..3..6....64.978....78..2......6..
.23.5.7.9.89.23.5.45..8..2..3.56.8.75....7..1.9..3..6....64.978....78..2......6..
.23.5.7.9.89.23.5645..8..2..3.56.8.75....7..1.9.....6....64.978....78..2......6..
-----------------X-------------------------------Y-------------------------------
(The 20 common clues:)
.2......9.89.23.56.5..8..2..3.5..........7....9..3..6....64.........8............
coloin wrote:Until we find [if we ever do] a better overlap of isomorphs, ...
C
123456789789123456456789123231548967564937218897612345312875694645391872978264531
123456789789123456456789123231548967564937218897612345312875694645391872978264531
+---+---+---+
|...|45.|7..|
|7.9|.23|4.6|
|4.6|7.9|.23|
+---+---+---+
|2..|54.|...|
|56.|.37|21.|
|..7|..2|3..|
+---+---+---+
|.12|...|6..|
|6.5|...|.7.|
|...|...|.3.|
+---+---+---+
...45.7..7.9.234.64.67.9.232..54..6.564.372.......23...12......6.5....7.9......3.
...45.7..7.9.234.64.67.9.232..54..6.56..3721...7..23...12......6.5....7........3.
...45.7..7.9.234.64.67.9.232..54..6.56..372....7..23...12......6.5....7.9......3.
...45.7..7.9.234.64.67.9.232..54....56..3721...7..23...12...6..6.5....7........3.
coloin wrote:This grid
- Code: Select all
123456789789123456456789123231548967564937218897612345312875694645391872978264531
is constructed from the 12347 Boxes of our canonical grid
I thought there would be a 33 but.......here is a minimal 34.
...45.7..7.9.234.64.67.9.232..54..6.564.372.......23...12......6.5....7.9......3.
...45.7..7.9.234.64.67.9.232..54..6.56..3721...7..23...12......6.5....7........3.
...45.7..7.9.234.64.67.9.232..54..6.56..372....7..23...12......6.5....7.9......3.
...45.7..7.9.234.64.67.9.232..54....56..3721...7..23...12...6..6.5....7........3.
...45.7....9.234.6..67.9.232..54..6.564.3721...7..23...12......6.5....7.9......3.
...45.7....9.234.6..67.9.232..54..6.56..3721...7..234..12......6.5....7.9......3.
....5.7..7.9.234.6..67.9.232..54..6.56..372....7..23...12...6.46.5....7........31
dukoso wrote:here is some statistics, starting from a full grid and generating 1e6
random locally minimal sudokus from it.
1) one grid from each G-class at random
2) Gordon's grid with 29 17s, the SF grid
3) our canonical grid,(1,1,1-1,1,1)
- Code: Select all
clues , 1) 2) 3)
----------------------------
17, 0 0 0
18, 0 0 0
19, 0 4.3 0
20, 59 182 0
21, 2428 6051 85
22, 33966 61826 1775
23,170727 227480 21648
24,342620 352289 116766
25,298349 248568 286836
26,122691 86061 329853
27, 25237 15908 185028
28, 2733 1547 50469
29, 205 74 7040
30, 7.6 8.6 486
31, 0 0 12
32, 0 0 2.4
-------------------------------
aver.24.38 24.10 25.72
+---+---+---+
|6.9|.4.|...|
|.8.|.65|..3|
|5.7|983|6..|
+---+---+---+
|...|...|..6|
|79.|.3.|85.|
|...|..9|23.|
+---+---+---+
|.4.|..8|...|
|8..|.94|37.|
|..5|326|4..|
+---+---+---+ 34 clue minimal
6.9.4.....8..65..35.79836..........679..3.85......923..4...8...8...9437...53264..
6.9.4.....8..65..35.79.36.....8....679..3285......923..4...8...8...9.37...53264..
6.9.4........65..35.79.36.....8....679..3285...8..923..4...8...8...9.37...53264..
clues % solved with these clues
78 100
40 28
35 10
30 2
16 0 sample size 1000 for 40,35,30
clue count total number of ways incidence of minimal puzzles
35 clues 81!/46! = 1.1*e^63 one grid has two
30 clues 81!/51! = 3.7*e^54 generated at the rate of 7.6 per million
24 clues 81!/57! = 1.4*e^44 all grids have a "very large" number. A guess would be 10^10
19 clues 81!/62! = 1.8*e^35 perhaps one per million generated - almost all grids have at least one
18 clues 81!/63! = 2.9*e^33 one in seven grids have at least one
17 clues 81!/64! = 48*10^30 one in ten thousand grids may have at least one
clue count total number of ways incidence of minimal puzzles
35 clues 81!/35!46! = 1.01*10^23 three grids have several
30 clues 81!/30!51! = 1.41*10^22 generated at the rate of 7.6 per million
24 clues 81!/24!57! = 2.30*10^20 all grids have a "very large" number. ? 10^11 [maybe more ?]
19 clues 81!/19!62! = 1.51*10^18 almost all grids have at least one
18 clues 81!/18!63! = 4.56*10^17 one in seven grids have at least one
17 clues 81!/17!64! = 7.14*10^15 one in ten thousand grids may have at least one