17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Programs which generate, solve, and analyze Sudoku puzzles

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

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

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

Postby 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.

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

Postby 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..|
+---+---+---+

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

Postby 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.|
+---+---+---+

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

Postby 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
Last edited by coloin on Fri May 14, 2021 3:40 pm, edited 1 time in total.
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Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

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

Postby 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
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Posts: 2083
Joined: 05 May 2005

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

Postby 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!
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Posts: 28
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Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Postby 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
coloin
 
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Joined: 05 May 2005

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

Postby 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.)
Last edited by swb01 on Sat May 08, 2021 12:52 pm, edited 2 times in total.
swb01
 
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Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Postby 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
swb01
 
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Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Postby 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 ! :D
coloin
 
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Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Postby 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.
swb01
 
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Re: 17 Clue Puzzles Apparently Not in Row-Based Minlex Form

Postby 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
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