The New Sudoku Players' Forum

[coloin]

i'm stopped!

Youve done pretty well ... I think i am away for a few days too ...
However its still a challenging exercise... and I am wondering if the outlier MAX28 would have been found easily .... and its so long ago Mauricio must have forgot how he found it !
I will see what there is in the files for more usual 28 clues...

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MAX28#..1..2..3.2..4..5.6..7..8....2.5.6...4.6....17....3.9...51...3..84..92..3...6...4# MAX 28  -   coloin        [15th best]

Maybe next week I will run more cycles ...

[coloin]

I have further processed a search in the interesting area of the 27 clues.
Similar to the 18C/2 diagonal clues in a box, there is a Min and Max with 27C/3 all diagonal clues in a box.

As shown before there are only 18 ED patterns.
In general there are more puzzles in these patterns than random 27C patterns
Using gridchecker scanfor over 94 random solution grids

5.4e9/94 = 57.4e6
for random patterns
27 clue pattern 735 in 94 ~ 40 billion
26 clue 1845 puzzles in 94 ~ 105 billion
25 clue 2063 puzzles in 94 ~ 117 billion
24 1640/2008/819 ~ 100 billion
23 187 ~ 10 billion

for the 27C-alldiag
## pattern ## examplar # gsf code ## puzzles found in 94 grids ## ? symetries ## puzzles per pattern

Code: Select all

#01#..1..2..3.3..4..5.5..6..4....2..4..5.4..7..6.8..9..1....8..7..6.9..8..1.2..1..3..# C27.m/S4.da/M1.16.5##   36## 648##     2 billion puzzles per pattern
#02#..1..2..3.3..4..5.6..7..8....2..7..5.1..6..7.9..5..2....9..5..4.5..9.3..4..3...1.# C27.m/S4.da/M1.26.3## 1230##    ##                                   
#03#..1..2..3.3..4..5.2..5..6....3..7..5.8..1..4.9..4..2....8..6.2..2..5.1..1..7....4# C27.m/S2.d/M1.7.5  ## 1086##    ##                                   
#04#..1..2..3.2..3..4.4..5..6....7..5..1.1..4..6.3..8..5....6..3.5..3.6....92...8.3..# C27.m/S2.p/M1.1.56 ## 6463##    ##                                   
#05#..1..2..3.3..4..5.4..1..6....7..3..8.1..8..9.5..2..3....4.6.8...5.9....61....5.4.# C27.m/S2.p/M1.12.3 ##  779##    ##    40 billion puzzles per pattern
#06#..1..2..3.3..4..2.5..1..4....3..4..5.1..6.7..7..8...3...6..8..1.9.7...5.3...1.6..# C27.m/S4.da/M1.7.11##  937##    ##                                   
#07#..1..2..3.4..5..6.5..4..7....6..3..7.7..8.2..9..6...4...2..5.1..1.2....88...3.6..# C27.m/S2.d/M1.11.3 ## 7513##   4##                                   
#08#..1..2..3.2..4..5.6..3..7....6..3..7.3..1.6..1..2...3...7.5...8.1...7.9.5..6..1..# C27.m/S4.da/M1.5.32## 6856##   4##                                   
#09#..1..2..3.4..5..6.7..8..5....2..7..8.9..1.6..8..4...1...6.2...4.8.7...5.5....49..# C27.m/S2.d/M1.20.1 ##15085##   2##   840 billion puzzles per pattern
#10#..1..2..3.3..4..5.6..5..2....4..7..8.2..6.5..7..2...9...6.1..7..4...89..9..4....2# C27.m/S4.da/M1.24.1## 7340##    ##                                   
#11#..1..2..3.4..5..6.7..4..8....9..8..4.3..4.7..6..1...2...6.9..7..2.3....54....63..# No Symmetry        ##15782##   2##   870 billion puzzles per pattern
#12#..1..2..3.3..4..5.4..1..6....2..7.6..7..8.2..5..4....8..9.6...5.1.7...2.3....58..# C27.m/S2.d/M1.9.7  ## 2869##    ##                                   
#13#..1..2..3.3..4..5.6..7..2....2..4.6..4..6.1..8..5....2..6.8...7.2.4..5..1....7.8.# C27.m/S4.da/M1.28.3## 8187##   4##                                   
#14#..1..2..3.4..5..6.5..7..8....5..4.8..8..7.3..2..9....6..8.6..4..3.5..6..1....9..5# C27.m/S4.da/M1.2.31##  830##    ##                                   
#15#..1..2..3.4..1..5.6..3..7....8..6.7..6.9....44...8.2....9.3...8.2...54..1..2...9.# C27.m/S2.d/M1.9.17 ## 4159##    ##                                   
#16#..1..2..3.2..3..4.3..5..6....6..7.8..4.9....61...6.9....8.1...7.1.4..2..2....9.5.# C27.m/S4.da/M1.2.30## 8267##   4##                                   
#17#..1..2..3.3..4..5.4..6..7....8..9.7..2.1....53...2.9....9.1.3...1.8...4.6....3..8# C27.m/S4.da/M1.6.47## 2754##    ##                                   
#18#..1..2..3.4..5..1.5..6..7....3.8.9...2.1....77....4.3...83...6..7...53..9...6...2# C27.m/S2.d/M1.15.3 ##  151## 160##                                   


It shows that the canonical #01# has the least puzzles almost certainly related to the isomorphs - ? 9 x 6 x 6 = 432 or 9 x 9 x 6 = 648

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


But it appears to be the most efficient to search....
The MIN/MAX for pattern 01 shown above

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..1..2..3.2..1..4.3..4..1....2..1..4.3..4..1.1..2..5....6..7..5.8..9..6.5..3..9..
..1..2..3.2..4..5.6..7..8....4..8..9.3..6..7.9..1..2....7..5..2.8..9..1.4..3..6..

27clue diagonal minimum of all patterns

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..1..2..3.2..1..4.3..4..1....2..1..4.1..2..3.4..5..2....67....5.8..6..7.7....53..
..1..2..3.2..1..4.3..4..1....2..1..4.1..2..3.4..5..2....67...5..8...64..7...5...8
..1..2..3.2..1..4.3..4..1....2..1..4.1..2..3.4..5..6....37...6..5...84..7...6...8
..1..2..3.2..1..4.3..4..1....2..1..4.1..2..3.4..5..6....37...6..8...54..7...6...5
..1..2..3.2..1..4.3..4..1....2..1..4.1..2..3.4..5..6....37...6..8...54..7...6...8
..1..2..3.2..1..4.3..4..1....2..1..4.1..2..3.4..5..6....5..3..7.7.8..3..8...7..6.

Maximums found

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MAX27#..1..2..3.2..4..5.6..7..2....4.8.7...7...5.3.9..1....6..7..6.8..3..9.1..8..5....4# MAX 27  *   coloin [previous best]
Increasing at r4c3
MAX27#..1..2..3.2..4..5.6..7..8....2..1.6..8..9...79..4..3....7.3..9..4.6..1..5....8..4# MAX 27
MAX27#..1..2..3.2..4..5.6..7..8....3.6.2...8...4.1.4..5....9..5.8...7.7...9.3.2..1..4..# MAX 27
MAX27#..1..2..3.2..4..5.6..7..8....4..8..9.3..6..7.9..1..2....7..5..2.8..9..1.4..3..6..# MAX 27

It seems that 5@r4c3 is the maximum ... a 6 not found in minlex puzzle.

MAX27#..1..2..3.2..4..5.6..7..8....5..9..6.7..8..4.9..3..2....8..4..7.3.1...9.5...6.1..# MAX 27
MAX27#..1..2..3.2..4..5.6..7..8....5.3...8.7...8.6.9..1..4....68..2...8..9..1.4....5..7# MAX 27
MAX27#..1..2..3.2..4..5.6..7..8....56....9.8..7..1.9....32....7.8...2.3.1...6.4....57..# MAX 27

Pretty sure this wont be easily surpassed

Code: Select all

+---+---+---+
|..1|..2|..3|
|.2.|.4.|.5.|
|6..|7..|8..|
+---+---+---+
|..5|9..|2..|
|.8.|..5|..6|
|3..|.7.|.1.|
+---+---+---+
|..7|..6|4..|
|.1.|3..|..5|
|4..|.8.|.9.|
+---+---+---+  # MAX 27

MAX27#..1..2..3.2..4..5.6..7..8....59..2...8...5..63...7..1...7..64...1.3....54...8..9.# MAX 27

thanks to gridchecker and the minlexroutine software

[coloin]

And continuing to work on Max28 [apart from Mauicios] Max29 amd Max30 .....

[coloin]

Improvements in the MAX 28 [apart from Mauricio's puzzle]

Code: Select all

MAX 28#..1..2..3.2..4..5.6..7..8....2.5.6...4.6....17....3.9...51...3..84..92..3...6...4 # MAX 28  previous best
MAX 28#..1..2..3.2..4..5.6..7..8....2.5.7...6.3....93....4.1...48...6..1...93..83..6...2 # MAX 28               
MAX 28#..1..2..3.2..4..5.6..7..8....2.6.5...6.3....78....9.1...95...6..1...84..58..3...9 # MAX 28               
MAX 28#..1..2..3.2..4..5.6..7..8....2.7.6...9.1....53....8.1...43...9..7...53.85...6...1 # MAX 28               
MAX 28#..1..2..3.2..4..5.6..7..8....2.7.9...8.3....19....4.6...49...8..7..584..5...3...7 # MAX 28               
MAX 28#..1..2..3.2..4..5.6..7..8....2.8.7...7...4..69.46...1...6..9.8..1.3..9..4...5...2 # MAX 28               
MAX 28#..1..2..3.2..4..5.6..7..8....2.9.4...6.3....79....5.1..182...6..9...61..3...8...2 # MAX 28               
MAX 28#..1..2..3.2..4..5.6..7..8....21...9..1...84..37..5...2..7.9.5...8.4....64....3.1. # MAX 28               
MAX 28#..1..2..3.2..4..5.6..7..8....23...1..7...59..5.9.1...7..6.3.2...1.9....49....8.7. # MAX 28               
MAX 28#..1..2..3.2..4..5.6..7..8....23...9..7..8...631...95....7.3.2...9.5....45....6.1. # MAX 28               
MAX 28#..1..2..3.2..4..5.6..7..8....3.6.2...1.9....82....5.7..6...84...842...1.5...1...9 # MAX 28       


and an improvement on the MAX 29, more to follow Im sure

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MAX29#..1..2..3.2..4..5.5..6..7....7.6...4.6...8.9.1..3..6....893.2...1.8...7.9...17..8# MAX 29  *   m_b_metcalf
MAX29#..1..2..3.2..4..5.6..7..8....2..6..7.9.1..3..4.6.7..9...546.2...7.5....43....9.1.# MAX 29                 


and an improvement in MAX 30

Code: Select all

MAX30#..1..2..3.2..4..5.4..6..7....5.6.8.4.1...95..3..8...19..7.1.3.5.8.3..9..5....8.6.# MAX 30  *   1to9only
MAX30#..1..2..3.2..4..5.4673..8.2..54..2...9..8...51....5.3...69...7..1..6.3..8....4..6# MAX 30             
MAX30#..1..2..3.2..4..5.5..3..12...2..67...6..1...58..4...1...5..76.8.7..8..9.9.86..5..# MAX 30             


[JPF]

MIN21 to MIN29: three new minima, and proofs

In the thread What is the smallest minimal puzzle? I posted a computation indicating that Mauricio's MIN25 is the smallest valid puzzle in minlex form:

Code: Select all

.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..25.6..8..367.4.19

1) New records

Code: Select all

MIN21#.................1.....1..2..1..2..3..2....4...5.46..7.1...5.8.8...7..9.9..8..1..  previous (coloin)
MIN21#.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..287.....5...9..8.  new
                                                     ^ r6c3: 3 instead of 5

MIN22#.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..35.6....8..7...19  previous (1to9only)
MIN22#.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..25.64...7...5..8.  new
                                                                      ^ r8c2: 2 instead of 3

MIN29#.................1.....1..2..1..2..3..2....4...3.45..6.1.2.3.75.3576.1.872.1.83.4  previous (1to9only/coloin)
MIN29#.................1.....1..2..1..2..3..2....4...3.45..6.1..56.24.26.731.57.5.146.8  new
                                                               ^ r7c4: . instead of 2


2) Published records confirmed

Code: Select all

MIN23#.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..25.6..8.8...541..  Mauricio
MIN24#.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..25.6..8.8..754.1.  Mauricio
MIN25#.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..25.6..8..367.4.19  Mauricio
MIN26#.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..25.6.3...36754.28  Mauricio
MIN27#.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..2516.3.8.367.8.24  1to9only/coloin
MIN28#.................1.....1..2..1..2..3..2....4...3.45..6.1...3.7..27.543.8.397.8214  1to9only/coloin


3) Why these are the minima
Since no valid puzzle is smaller than Mauricio's puzzle M, an n-clue minimal puzzle smaller than the MIN-n above lies between M and it, so it agrees with M on every cell up to r8c1 for n = 21 to 28, and up to r7c3 for n = 29 (M and the MIN-n records all agree up to there).
All solution grids compatible with that beginning were enumerated (114648 and 2413904 grids, band 1 written with first row 123456789), and for each grid all puzzles made of the clues of M up to that cell plus any subset of the remaining cells: the smallest minimal puzzle in minlex form for each number of clues is the one given above.

4) Checks
All the puzzles above have a unique solution, are minimal and are in minlex form.
A second, independent program (different solver and enumeration, digits of M taken literally) finds exactly the same minimal puzzles.

If confirmed, MIN21 to MIN29 could get their "***".

Computations were done with the help of Claude (AI).

JPF

[JPF]

New MAX records, found by vicinity search (gridchecker as a fast pre-filter, minlex then verified by brute force on all 3359232 transformations):

Code: Select all

..1..2..3.2..13.4.3..4.52....3.6..7.16.5..8..7....14.6.1.7...2.2....6..78.7.2.6.4# MAX 33
..1..2..3.2..1..4.5..6..1....78..4...5...7.383...26.7..7298.31.1....4.8.83.26...4# MAX 34
.....1..2.12.3.45.674.2.1....18......4635.8.1.8..175.4.28.73.45.67...2..4..28....# MAX 37
.....1..2.12...34.56324.1.7..1.8.....8.1.64.36354..8.1.286.7.34.56...2..3..82....# MAX 38


Previous records:

Code: Select all

..1..2..3.2..1..4.5..6..7....2.8..9.18...9.379..15.2.8.1.9..3..2.3.7...989...1.7.# MAX 33   *      coloin
..1..2..3.2..1..4.5..6..1....24..6.7.7...6.848...7.3....8.274...3.16...82158.4.3.# MAX 34   *      1to9only
........1.....2.....3...245.16.7.8.2432.68.178.7..1.64.61.85...2.81.3..63.5.26..8# MAX 37   *      1to9only
.....1..2.....2341...34..5...6.....4.7..365188..714.36.6..5..2.5.8127.637...6318.# MAX 38   *      m_b_metcalf


JPF

[JPF]

New MIN20

Unless I’m mistaken, the last MIN20 posted in this thread is the one by 1to9only (Apr 27, 2026). Here it is with the new one below it:

Code: Select all

.................1.....1..2..1..2..3..2..3..4.5..6..7...3.8..1.6..7...5.7..5..... 1to9only
.................1.....1..2..1..2..3..2....4...3.45..6.5..7..8..6.8...9..7.1..... new
                                         ^


JPF

[coloin]

Recent posts from JPF added to page 1.

Well done JPF for extending the MIN29#
Also well done in also matching my best puzzles in MIN20,MIN21 and MIN22, thus probable **.

Great that you and AI are on the exercise, which especially in the MAX is not easy !

How are you using AI I wonder !! ??

I will post a few more from my records... [ n puzzle in my list]

Code: Select all

MAX33#..1..2..3.2..13.4.3..4.52....3.6..7.16.5..8..7....14.6.1.7...2.2....6..78.7.2.6.4# MAX 33  *   JPF                                                       
MAX34#..1..2..3.2..1..4.5..6..1....78..4...5...7.383...26.7..7298.31.1....4.8.83.26...4# MAX 34  *   JPF
MAX37#.....1..2.12.3.45.674.2.1....18......4635.8.1.8..175.4.28.73.45.67...2..4..28....# MAX 37  *   JPF                                                       
MAX38#.....1..2.12...34.56324.1.7..1.8.....8.1.64.36354..8.1.286.7.34.56...2..3..82....# MAX 38  *   JPF        [4]

MAX33#..1..2..3.2..13.4.3..45.2....2.3..6.6.32.5..778...63.2..6..4.7..7..6...49..5..6..# MAX 33  coloin      [16000]                                 
MAX34#..1..2..3.2..1..4.5..6..7....2.7...8.8.1.6.3.13...84...19.67.842.68...7.87...13..# MAX 34  coloin        [900]
MAX37#.....1..2.13.2456724.56..8...1..263..2..5..183..1.6..5..8..5.7..3....8.647.6...53# MAX 37  coloin        [230]
MAX38#.....1..2.12.3456.7.3.52.41...3.86.5..8.46....3......4.81....5.327.85.164..1.32.8# MAX 38  coloin          [3]   

[JPF]

New MIN19

Unless I’m mistaken, the last MIN19 posted in this thread is the one by coloin. Here it is with the new one below it:

Code: Select all

.................1.....1..2..1..3.....2.4..5...6.7.....4......3.5..26.8..9..5..4. coloin
.................1.....1..2..1..2..3..2....4...3.56....5..7.1...6.8......9.4...7. new
                                ^

JPF

[coloin]

Well done JPF ! You and AI are smashing it !

Here are the top 10 MIN19 in my list, confirming that you have matched my minimum !

Code: Select all

MIN19#.................1.....1..2..1..2..3..2....4...3.56....5..7.1...6.8......9.4...7.
MIN19#.................1.....1..2..1..2..3..2....4..56.7.....1...6...3...8.6..8..9..7..
MIN19#.................1.....1..2..1..2..3..2....4..56.7.....1...6...3..8..6..8..9..7..
MIN19#.................1.....1..2..1..2..3..2....4..56.7.....2...6...3..8..6..8..9..7..
MIN19#.................1.....1..2..1..2..3..2..3..4.5..6..7..6....8...7..9.5..4..3.....
MIN19#.................1.....1..2..1..2..3..2..3.4...3.4..5..6........7..5..8..9..8.7..
MIN19#.................1.....1..2..1..2..3..2..3.4...3.4..5..6........7..5..8..9..86...
MIN19#.................1.....1..2..1..2..3..2..3.4...3.4..5..6........7..5..86.9..8....
MIN19#.................1.....1..2..1..2..3..2..3.4...3.4..5..6........7..58.9..8..9....
MIN19#.................1.....1..2..1..2..3..2..3.4...3.4..5..6....7...7..8.....9..5..8.


.

[JPF]

Hi coloin,

Thanks for updating page 1. Two points about the status marks:

1) MIN21 to MIN29 are proven, not only matched (post of Nov 12): since Mauricio's MIN25 is the smallest valid minlex puzzle, any smaller n-clue minimal puzzle would agree with it up to r8c1 (r7c3 for n = 29), and all grids compatible with that beginning were enumerated, with two independent programs. So MIN21 to MIN29 could be ***, including the new MIN29, which is still marked * on page 1.

2) MIN19 and MIN20 are also exact, though I did not say so in my posts. They come from an ordered search: puzzles are built cell by cell in minlex order ('.' before digits), a beginning is discarded only when it is proven that it cannot lead to a unique solution, and the first valid minimal puzzle reached is the minimum. This was done with one program only, so it is up to you whether they get *** now or after an independent check.

MIN18 is not settled yet; the same search is running, and so far nothing smaller than Mike's puzzle has been found.

One question: what do the numbers in brackets mean, e.g. [16000] or [4th]?

JPF

[coloin]

Code: Select all

MIN18#.................1.....1.23.............4.5...12..6...54....7..6..3.2..87....9...# MIN 18  *   m_b_metcalf       [12th] 
MIN30#.................1.....1..2..1..2..3..2....4..35.46..7.53.68.1.1.6..387527..14.36# MIN 30  *   1to9only     not in my list ... [7th] 

The numbers in bracket represent the position the puzzle is on my list .. so for the MIN18 I have 11 smaller 18 clue puzzles.

Thanks for the explanation of your proof ... Very good have just read your link !!

Proving the MAX puzzles however might be more difficult and we dont know how Mauricio found his 28C as I was unable to find it de novo.

Simultaneous finding of a puzzle might be the best we can do...

I was unable to find another minlex puzzle with the first 9 clues 1-9 and didnt get near a 36 clue puzzle ...but I did find a MAX 30 which comes close.

[coloin]

so for the MIN18 I have 11 smaller 18 clue puzzles.

and I can see why AI is having trouble !!