The New Sudoku Players' Forum

by **JPF** » Mon May 03, 2021 7:16 pm

I don't know if it's the "largest", but it"s certainly a MinLex puzzle.

JPF

by **swb01** » Mon May 03, 2021 7:35 pm

Yes. My program gives the same results.
I randomly scrambled bands/rows, stacks/columns, digits and row/column transposition resulting in:
.5...92....7.1..6.3..8....4.2.3...1..76..5..84...7.9....82..7...1..4...59....6.3.
then minlexed it to get:
..1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7.1.5
Mappings: Transposition = No, Digits 123456789 => 924875136, Rows 123456789 => 798123645, Columns 123456789 => 987564213
Thanks for the test.

by **JPF** » Tue May 04, 2021 10:38 am

Just to confuse every one: here is the MaxLex representation of the "largest" found minlex [minimal] puzzle

Code: Select all: +---+---+---+ |9..|8..|7..| |.6.|.5.|.4.| |..3|..2|..1| +---+---+---+ |7..|.6.|..2| |.4.|..3|8..| |..1|9..|.5.| +---+---+---+ |2..|..4|.9.| |1.5|.7.|3..| |.8.|1..|..6| +---+---+---+

I hope I did it right.

JPF

by **swb01** » Tue May 04, 2021 2:54 pm

Jpf Wrote:
Just to confuse every one: here is the MaxLex representation of the "largest" found minlex [minimal] puzzle

I was suspicious because the block with 4 digits is not in top/left position and minlexing
9..8..7...6..5..4...3..2..17...6...2.4...38....19...5.2....4.9.1.5.7.3...8.1....6 to
..1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7.1.5
requires no relabeling of digits: Transposition = No, Digits 123456789 => 123456789, Rows 123456789 => 321465978, Columns 123456789 => 789456123

So, by hand: 9..8..7..6.5.4..3..2...6..17....2.4..1..5.8....39....64...1...9.8.3...2...6..75.. is larger. I can't say it's "MaxLex" but it is larger. It maps to the minlex by the following:
Transposition = No, Digits 123456789 => 683751942, Rows 123456789 => 654798312, Columns 123456789 => 879654123

Code: Select all: +---+---+---+ |9..|8..|7..| |6.5|.4.|.3.| |.2.|..6|..1| +---+---+---+ |7..|..2|.4.| |.1.|.5.|8..| |..3|9..|..6| +---+---+---+ |4..|.1.|..9| |.8.|3..|.2.| |..6|..7|5..| +---+---+---+

by **JPF** » Tue May 04, 2021 3:52 pm

You are right, I had (at least) one bug in my program.
1 line = 1 bug !

I think, your puzzle is not maxlex either.
The box with 4 clues allows the following begining 98:
Starting from your puzzle: main diagonal symmetry + relabeling 6->8)

Code: Select all: +---+---+---+ |98.| | | | | | | | | | | +---+---+---+

My last proposal:

Code: Select all: +---+---+---+ |98.|7..|6..| |5..|.9.|.4.| |..3|..2|..1| +---+---+---+ |7..|1..|..5| |.2.|..4|.8.| |..9|.6.|3..| +---+---+---+ |4..|..3|7..| |.6.|.5.|..2| |..1|8..|.9.| +---+---+---+

JPF

by **coloin** » Tue May 04, 2021 5:32 pm

Just to confuse you all again ... its a strange puzzle

Code: Select all: +---+---+---+ |..1|..2|..3| |.4.|.5.|.6.| |7..|8..|9..| +---+---+---+ |..2|.6.|7..| |.5.|9..|..1| |8..|..3|.4.| +---+---+---+ |..6|1..|.8.| |.9.|..4|2..| |3..|.7.|..5| +---+---+---+ minus the clue in box 9

Adding a single clue - it seem there are 6x9=54 ways to make the same isomorphic puzzle ....
Edit - It seems there are 18 ways for each of the 3 isomorphs of the solution grid ... so it is at least 18

by **swb01** » Wed May 05, 2021 4:33 am

coloin wrote:
... its a strange puzzle ... Adding a single clue - it seem there are 6x9=54 ways to make the same isomorphic puzzle

Here's what I found:
Only 36 of the 54 cells, when added, result in a single solution.
After removing the 1 at r8xc7, the clues produce 3 solutions. The three solutions are the result of two unavoidable sets not being hit (or pinned down) by the missing 1. Each of the two unavoidable sets contain 45 cells with 36 cells being common to both. Nine cells in each unavoidable set only pin down one of the sets. The 36 cells common to both are:
6..7..45...9..18.7.3..4..1291...5.3.4.3.8.6...672....95...29..4..853..7..2.6.81.. Any one of these added the the 27 clues results in a single solution producing the same grid, since they pin down both of the unavoidable sets.

Code: Select all: Unavoidable Set #1 Set: 68.7..45.2.9..18.7.35.4..1291.4.5.3.4.3.876...6721...95...293.4..853..76.2.6.819. Not Set: ..1.92..3.4.35..6.7..8.69....2.6.7.8.5.9...218....354..761...8.19...42..3.4.7...5 ------------------------------- |*6*'8'(1)|*7* 9 (2)|*4**5*(3)| |'2'(4)*9*| 3 (5)*1*|*8*(6)*7*| |(7)*3*'5'|(8)*4* 6 |(9)*1**2*| ------------------------------- |*9**1*(2)|'4'(6)*5*|(7)*3* 8 | |*4*(5)*3*|(9)*8*'7'|*6* 2 (1)| |(8)*6**7*|*2*'1'(3)| 5 (4)*9*| ------------------------------- |*5* 7 (6)|(1)*2**9*|'3'(8)*4*| | 1 (9)*8*|*5**3*(4)|(2)*7*'6'| |(3)*2* 4 |*6*(7)*8*|*1*'9'(5)| Key: (x) = clues, *x* = in both sets, 'x' = only member of this set. ------------------------------- Set: 6..79.45...93.18.7.3..46.1291...5.384.3.8.62..672..5.957..29..41.853..7..246.81.. Not set: .81..2..324..5..6.7.58..9....246.7...5.9.7..18...13.4...61..38..9...42.63...7..95 Unavoidable Set #2 ------------------------------- |*6* 8 (1)|*7*'9'(2)|*4**5*(3)| | 2 (4)*9*|'3'(5)*1*|*8*(6)*7*| |(7)*3* 5 |(8)*4*'6'|(9)*1**2*| ------------------------------- |*9**1*(2)| 4 (6)*5*|(7)*3*'8'| |*4*(5)*3*|(9)*8* 7 |*6*'2'(1)| |(8)*6**7*|*2* 1 (3)|'5'(4)*9*| ------------------------------- |*5*'7'(6)|(1)*2**9*| 3 (8)*4*| |'1'(9)*8*|*5**3*(4)|(2)*7* 6 | |(3)*2*'4'|*6*(7)*8*|*1* 9 (5)| Key: (x) = clues, *x* = in both sets, 'x' = only member of this set. -------------------------------

If you solve the "Not set" in each case you will get two solutions. One the target grid and the unavoidable set alternate.

by **coloin** » Wed May 05, 2021 11:36 am

Yes .. as has been shown in the past these automorphic grid solutions stick together / share a lot of clues

There are three solution grids to the 27 clue sub-puzzle
Each box is essentially the same
For each box there are 12 options to add a clue to give one of the three solutions
6 options give the minimal puzzle - all isomorphic

Code: Select all: 6.1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7...5 9.1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7...5 ..1..2..3.43.5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7...5 ..1..2..3.49.5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7...5 ..1..2..3.4..5..6.73.8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7...5 ..1..2..3.4..5..6.76.8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7...5

The other 2 solution grids each are solved 3 per box = 27 ways by adding one clue

So these 2 solution grids have at least 27 automorphisms

Certainly every unavoidable set for each solution grid needs to be hit !

As the subpuzzle stands each of the unfilled cells options can give a valid puzzle - so that is 108 puzzles, 54 of one solution and 27 each of the 2 others...

27clue subpuzzle

by **swb01** » Thu May 06, 2021 4:40 pm

Try #2.

coloin wrote:
... its a strange puzzle ... Adding a single clue - it seem there are 6x9=54 ways to make the same isomorphic puzzle

As you noticed, I didn't quite understand your statement. I was focused on the single grid produced by the largest minlex puzzle. From your clarification I see you are counting ways any one of the three solutions can be made by adding a 28th clue to the reduced set. ... Now, I'll see if I can follow the rest.

In looking at this, I noticed that at least two different puzzles are produced (unless my minlex routine has another bug).

I haven't checked all cases, yet. But, the must popular minlex is the "largest minlex puzzle":
..1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7.1.5
However, sometimes another one pops up, e.g. when adding a 6 at r9xc7, or adding a 4 at r1Xc4.
..1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7.6.5
Which is larger than the largest!

by **coloin** » Thu May 06, 2021 7:33 pm

No your software is good - that is one of the other [non-minimal puzzles] - 2 clues can be removed in both - which reduces the minlex

Code: Select all: +---+---+---+ |..1|..2|..3| |.4.|.5.|...| |7..|8..|9..| +---+---+---+ |..2|.6.|7..| |.5.|9..|..1| |8..|..3|.4.| +---+---+---+ |...|1..|.8.| |.9.|..4|2..| |3..|.7.|6.5| +---+---+---+ #2 minimal

and the other

Code: Select all: +---+---+---+ |.61|...|..3| |.4.|.5.|.6.| |7..|8..|9..| +---+---+---+ |..2|.6.|7..| |...|9..|..1| |8..|..3|.4.| +---+---+---+ |..6|1..|.8.| |.9.|..4|2..| |3..|.7.|..5| +---+---+---+ #3 minimal

by **swb01** » Fri May 07, 2021 4:36 pm

Ahh. I didn't think about checking it for unnecessary clues.

So, I added a feature to my grid minlexer - Count how many times the minimal grid is hit in discovering the minimal grid.
I ran it against examples of the three grids and their common minlex grid.

In each case 36 different transformations hit the minimum. For the common minlex grid, one of the transformations was the identity. Since attachments are not currently available, here's the table (please excuse the shaky formatting):

Code: Select all: "Minimal Grid = Minlex grid common to MaxMin, Alt1 & Alt2 grids" Minimal Grid: 123456789457189236968372514291738465374265198685941327546813972732694851819527643 Max = with 6 at c0xr0 Max Grid: 681792453249351867735846912912465738453987621867213549576129384198534276324678195 Alt1 = with 5 at c0xr0 Alt1 Grid: 561492873948357162723816954432561798657948321819723546276135489195684237384279615 Alt2 = with 9 at c0xr0 Alt2 Grid: 981642573243759168765831924132468759654927831879513642426195387597384216318276495 Grid Seq Transposition Digits 123456789 ==> Rows 123456789 ==> Columns 123456789 ==> Minimal Grid 1 No 123456789 123456789 123456789 (identity) Minimal Grid 2 No 745891623 312645897 231645897 Minimal Grid 3 No 689237145 231564978 312564978 Minimal Grid 4 No 219654873 465132798 132897645 Minimal Grid 5 No 865732419 654321879 213978564 Minimal Grid 6 No 473198265 546213987 321789456 Minimal Grid 7 No 527819346 978546231 456123987 Minimal Grid 8 No 946273581 897654312 564312879 Minimal Grid 9 No 381465927 789465123 645231798 Minimal Grid 10 No 518723964 564987213 465879312 Minimal Grid 11 No 364189572 645879321 546798231 Minimal Grid 12 No 972645318 456798132 654987123 Minimal Grid 13 No 837564291 798123465 789321654 Minimal Grid 14 No 256918437 879312654 897132546 Minimal Grid 15 No 491372856 987231546 978213465 Minimal Grid 16 No 798546132 132789456 798546132 Minimal Grid 17 No 154327698 321897645 879465213 Minimal Grid 18 No 632981754 213978564 987654321 Minimal Grid 19 Yes 362785914 897312645 123546987 Minimal Grid 20 Yes 514629378 789231456 231654879 Minimal Grid 21 Yes 978143562 978123564 312465798 Minimal Grid 22 Yes 941875326 321879654 132879654 Minimal Grid 23 Yes 526413987 213798465 213798465 Minimal Grid 24 Yes 387269541 132987546 321987546 Minimal Grid 25 Yes 634587192 456213789 465312897 Minimal Grid 26 Yes 792341658 564132978 546123789 Minimal Grid 27 Yes 158926734 645321897 654231978 Minimal Grid 28 Yes 496578231 231465798 456978231 Minimal Grid 29 Yes 831962457 123546987 564897312 Minimal Grid 30 Yes 257314896 312654879 645789123 Minimal Grid 31 Yes 129857643 546978132 798213564 Minimal Grid 32 Yes 685431729 465789213 879132456 Minimal Grid 33 Yes 743296185 654897321 987321645 Minimal Grid 34 Yes 213758469 987564123 789645321 Minimal Grid 35 Yes 475692813 798456231 897564213 Minimal Grid 36 Yes 869134275 879645312 978456132 Max 1 No 469813275 789312465 123465897 Max 2 No 813275469 978231654 231546978 Max 3 No 275469813 897123546 312654789 Max 4 No 643729185 321798456 132978546 Max 5 No 729185643 213987645 213789654 Max 6 No 185643729 132879564 321897465 Max 7 No 896457231 546132897 465123798 Max 8 No 457231896 465321789 546231879 Max 9 No 231896457 654213978 654312987 Max 10 No 734658192 123564879 456987312 Max 11 No 658192734 312456798 564798123 Max 12 No 192734658 231645987 645879231 Max 13 No 326541987 564897132 789213456 Max 14 No 541987326 456789321 897321564 Max 15 No 987326541 645978213 978132645 Max 16 No 914562378 879546123 798564321 Max 17 No 562378914 798465312 879645132 Max 18 No 378914562 987654231 987456213 Max 19 Yes 927581346 123645798 123654978 Max 20 Yes 346927581 312564987 231465789 Max 21 Yes 581346927 231456879 312546897 Max 22 Yes 318572964 654132789 132789465 Max 23 Yes 964318572 546321978 213897546 Max 24 Yes 572964318 465213897 321978654 Max 25 Yes 789623145 798654123 465231987 Max 26 Yes 145789623 987546312 546312798 Max 27 Yes 623145789 879465231 654123879 Max 28 Yes 873419265 645789132 456879123 Max 29 Yes 265873419 564978321 564987231 Max 30 Yes 419265873 456897213 645798312 Max 31 Yes 754132698 978312546 789132564 Max 32 Yes 698754132 897231465 897213645 Max 33 Yes 132698754 789123654 978321456 Max 34 Yes 856291437 321987564 798645213 Max 35 Yes 437856291 213879456 879456321 Max 36 Yes 291437856 132798645 987564132 Alt1 1 No 632154798 456978132 123546789 Alt1 2 No 154798632 645897321 231654897 Alt1 3 No 798632154 564789213 312465978 Alt1 4 No 491256837 987465123 132897654 Alt1 5 No 256837491 879654312 213978465 Alt1 6 No 837491256 798546231 321789546 Alt1 7 No 364972518 321879645 465312879 Alt1 8 No 972518364 213798564 546123987 Alt1 9 No 518364972 132987456 654231798 Alt1 10 No 946381527 897312654 456798231 Alt1 11 No 381527946 789231546 564879312 Alt1 12 No 527946381 978123465 645987123 Alt1 13 No 473865219 123456987 789321645 Alt1 14 No 865219473 312645879 897132456 Alt1 15 No 219473865 231564798 978213564 Alt1 16 No 689745123 465132978 798456132 Alt1 17 No 745123689 654321897 879564213 Alt1 18 No 123689745 546213789 987645321 Alt1 19 Yes 792158634 456978132 123546789 Alt1 20 Yes 634792158 645897321 231654897 Alt1 21 Yes 158634792 564789213 312465978 Alt1 22 Yes 831257496 987465123 132897654 Alt1 23 Yes 496831257 879654312 213978465 Alt1 24 Yes 257496831 798546231 321789546 Alt1 25 Yes 514978362 321879645 465312879 Alt1 26 Yes 362514978 213798564 546123987 Alt1 27 Yes 978362514 132987456 654231798 Alt1 28 Yes 526387941 897312654 456798231 Alt1 29 Yes 941526387 789231546 564879312 Alt1 30 Yes 387941526 978123465 645987123 Alt1 31 Yes 213869475 123456987 789321645 Alt1 32 Yes 475213869 312645879 897132456 Alt1 33 Yes 869475213 231564798 978213564 Alt1 34 Yes 129743685 465132978 798456132 Alt1 35 Yes 685129743 654321897 879564213 Alt1 36 Yes 743685129 546213789 987645321 Alt2 1 No 347586921 123645798 123654978 Alt2 2 No 586921347 312564987 231465789 Alt2 3 No 921347586 231456879 312546897 Alt2 4 No 968574312 654132789 132789465 Alt2 5 No 574312968 546321978 213897546 Alt2 6 No 312968574 465213897 321978654 Alt2 7 No 149625783 798654123 465231987 Alt2 8 No 625783149 987546312 546312798 Alt2 9 No 783149625 879465231 654123879 Alt2 10 No 263415879 645789132 456879123 Alt2 11 No 415879263 564978321 564987231 Alt2 12 No 879263415 456897213 645798312 Alt2 13 No 694138752 978312546 789132564 Alt2 14 No 138752694 897231465 897213645 Alt2 15 No 752694138 789123654 978321456 Alt2 16 No 436297851 321987564 798645213 Alt2 17 No 297851436 213879456 879456321 Alt2 18 No 851436297 132798645 987564132 Alt2 19 Yes 279815463 789312465 123465897 Alt2 20 Yes 463279815 978231654 231546978 Alt2 21 Yes 815463279 897123546 312654789 Alt2 22 Yes 183725649 321798456 132978546 Alt2 23 Yes 649183725 213987645 213789654 Alt2 24 Yes 725649183 132879564 321897465 Alt2 25 Yes 236451897 546132897 465123798 Alt2 26 Yes 897236451 465321789 546231879 Alt2 27 Yes 451897236 654213978 654312987 Alt2 28 Yes 194652738 123564879 456987312 Alt2 29 Yes 738194652 312456798 564798123 Alt2 30 Yes 652738194 231645987 645879231 Alt2 31 Yes 986547321 564897132 789213456 Alt2 32 Yes 321986547 456789321 897321564 Alt2 33 Yes 547321986 645978213 978132645 Alt2 34 Yes 374568912 879546123 798564321 Alt2 35 Yes 912374568 798465312 879645132 Alt2 36 Yes 568912374 987654231 987456213

Does this demonstrate that the grid equivalence class is automorphic of order 35 (correct terminology)?
So, to demonstrate automorphism, is it sufficient to show that there exists more than one transformation from grid1 to grid2 in the equivalence class? That is, grid1 does not have to equal grid2. (I believe this must be true but also it must be elementary automorphism ... my apologies.)

by **swb01** » Sat May 08, 2021 2:50 am

coloin wrote:
As the subpuzzle stands each of the unfilled cells options can give a valid puzzle - so that is 108 puzzles, 54 of one solution and 27 each of the 2 others...

I find:
There are three solution grids to the 27 clue sub-puzzle. - check.
Each box is essentially the same. - check.
For each box there are 15 possibilities to add a clue - three of those options do not solve the puzzle, leaving 12 that do, distributed as shown below.

Code: Select all: For the MinMax grid, option counts in boxes 1 - 9 are: 3,3,6,6,3,3,3,6,3 - 36 For the Alt1 grid, option counts in boxes 1 - 9 are: 6,3,3,3,6,3,3,3,6 - 36 For the Alt2 grid, option counts in boxes 1 - 9 are: 3,6,3,3,3,6,6,3,3 - 36

by **coloin** » Sat May 08, 2021 3:55 pm

I thought you maybe could have been right - as I only checked box 1 ....
Box 1 = these six options give the minimal puzzle ... 6 x 9 = 54

Code: Select all: 6.1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7...5 9.1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7...5 ..1..2..3.43.5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7...5 ..1..2..3.49.5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7...5 ..1..2..3.4..5..6.73.8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7...5 ..1..2..3.4..5..6.76.8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7...5

So each box is the same ..... except your counts differ per each box !

by **swb01** » Mon May 10, 2021 4:52 pm

Yes. 54 options produce the MinMax puzzle as your original statement said, 6 per box.

I got off track looking at options that produce the three grids, not options that produce the three puzzles.

MinMax puzzle: ..1..2..3.4..5..6.7..8..9....2.6.7...5.9....18....3.4...61...8..9...42..3...7.1.5
Puzzle1: .....1..2..3.4..5..6.7..8....4..26...7..5...91..8...3..5...6.1..923....78.....4..
Puzzle2: .....1..2..3.4..5..6.7..8....4..26...7..5...91..8...3..5...6.1.4.2.....78...9.4..

MinMax grid: 681792453249351867735846912912465738453987621867213549576129384198534276324678195
Grid1: 561492873948357162723816954432561798657948321819723546276135489195684237384279615
Grid2: 981642573243759168765831924132468759654927831879513642426195387597384216318276495

Each box has 15 options. 12 solve the puzzle with: 6 solving to one grid, 3 to a second and 3 to the third according to this pattern:

For the MinMax grid, option counts in boxes 1 - 9 are: 3,3,6,6,3,3,3,6,3 - 36
For the Grid1, option counts in boxes 1 - 9 are: 6,3,3,3,6,3,3,3,6 - 36
For the Grid2, option counts in boxes 1 - 9 are: 3,6,3,3,3,6,6,3,3 - 36

For each box, the puzzles for 6 options are not minimal, after removing the two unnecessary clues, three minlex to the Puzzle1
and three minlex to the Puzzle2. The two sets of 3 puzzles minlex to MinMax puzzle.

by **coloin** » Mon May 10, 2021 6:54 pm

I get

Code: Select all: For the MinMax grid, option counts in boxes 1 - 9 are: 6,6,6,6,6,6,6,6,6 - 54 For the Grid1, option counts in boxes 1 - 9 are: 3,3,3,3,3,3,3,3,3 - 27 For the Grid2, option counts in boxes 1 - 9 are: 3,3,3,3,3,3,3,3,3 - 27

and I cannot see how you get the non minimal puzzles 36 x 2

swb01 wrote:For each box, the puzzles for 6 options are not minimal,

Correct - that means for each box 6 are minimal and that the 6 non minimal puzzles are 3 of one and 3 of the other

The New Sudoku Players' Forum

17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form