The New Sudoku Players' Forum

[mith]

Yes, the 375759 is for all singles-expanded forms. (This potentially includes forms which don't have any minimals expanding to them!)

My next project will be to write a script finding min-expands, and yes then publish an additional database with them (retaining IDs and such from the full expanded db). (The current set will already include all min-expands, since the minimizer script has been run on them - that is, the set contains all singles-expanded forms of all minimals of the set.)

In the meantime, here are the 375759 puzzles with IDs, for anyone who wants to work with them (; separated). I will eventually get this up in sqlite database form as well, along with the minimals (which I may organize first by expanded form ID).

unix format
dos format

The first 972 are the puzzles originally posted in the google sheets - this has obviously gotten a bit too big for that. The last column of these is for the shortened name of the SE technique for the ER step - this is missing from the first 972 because I hadn't retained it at that point, but I'll run those again at some point.

[denis_berthier]

Yes, the 375759 is for all singles-expanded forms. (This potentially includes forms which don't have any minimals expanding to them!)

How is that possible? Expanded forms are expanded from minimal puzzles. I must be getting it wrong.

My next project will be to write a script finding min-expands, and yes then publish an additional database with them (retaining IDs and such from the full expanded db). (The current set will already include all min-expands, since the minimizer script has been run on them - that is, the set contains all singles-expanded forms of all minimals of the set.)

As you know, I'm mainly interested in the min-expands, for two reasons:
- in order to avoid redundant analyses, especially as the db size grows so fast;
- I think min-expands are a fundamental concept, much more interesting than ordinary minimals, especially now that expansion is systematically used to grow the database.
.

[mith]

The expanded form database started from singles expansions of minimals - however, the correct way to read "singles-expanded form" in the current database is "singles expanded from a depth 3 puzzle, which may or may not be minimal".

This is due to the depth_adder script, which takes a given expanded form and tries every possible digit addition, checking for depth. If the depth is still 3, this new puzzle is (after singles expansion, if applicable) added to the database, but there is no guarantee that it is reachable from a minimal by singles.

If you'll recall Loki, its expanded form is 29c; however, when you applied T&E(2), you ended up with a pencilmark grid having 31 digits filled. This 31c is the "max-expand" of Loki - it is in depth 3, but no more digits can be added without reducing the depth. However, none of its four minimals single expand back up to the 31c.

Code: Select all

solution_minlex of expanded forms in the Loki family:
1.3.56....571.9...69.37......1.93..75.96.73.....51.......96..........4....5...86. (Loki and a 27c singles-expand to this 29c)
1.3.56....571.9.3.69.37......1.93..75.96.73.....51.......96..........4....5...86. (a 26c and a 27c singles-expand to this 30c)
1.3.56....571.9...69.37......1.93..75.96.73.....51.......96..........4..9.5...86. (no minimals singles-expand to this 30c)
1.3.56....571.9.3.69.37......1.93..75.96.73.....51.......96..........4..9.5...86. (max-expand 31, no minimals singles-expand to it)

The full "tree" (not really a tree in the graph theoretical sense) for this family would look like:

Code: Select all

    31c
  /     \
 30c   30c
  \     /
    29c

------

As progress on mapping out these trees and finding the min-expands, I have added the full solution grid in canonical form to the database. There are currently 14155 solution grids. 471 of these only have one expanded form associated with them (so these are necessarily both min-expand and max-expand). The most expanded forms for one solution grid is 905.

Obviously there will be a lot more min-expands than distinct solution grids, but there will also be more max-expands. Just taking that 905 as an example, there are two 37c puzzles associated with it:

Code: Select all

.234.678.4.6......78..2346..3..48..664.2.7..88..63.....7....65..6....912....628.7
.234.678.4.6......78..2346..3..48..664.2.7..88..63....37....65..6....91.....628.7

It is possible that there will be some max-expands like this where we can add one of two digits to an existing puzzle but not both without lowering the depth. However, this one is a case of two distinct trees, despite the huge overlap - the 36c intersection of these is not unique! (The 38c union solves with one x-wing and singles.)

[denis_berthier]

.
OK, thanks for the explanations. I was still with the idea that you expanded only minimals.

[mith]

Generating the min-expands now; expecting around 73k based on the current ratio of min-expands per solution grid. [edit]Had to restart because of a really dumb bug that was skipping some. Should run faster now though.[/edit]

The script I'm using should be easy to invert for the max-expands.

[mith]

63137 min-expands:

unix
dos

15606 max-expands:

unix
dos

Both files have three columns:
solution_minlex (if you want the gsf puzzle_minlex form, you'll need to cross-reference with the expanded_te3 files linked a few posts ago)
tree (this is just an ID of the solution grid, assigned in order of lowest expanded_form ID for a puzzle with that solution)
ID (ID of the expanded form)

[mith]

Running a check now for max-expands that are connected by sub-puzzles; here's the first such case:

Code: Select all

   862        864
    |         /\
    |        /  \
    73     904  83
    | \   / |  /
    |  \ /  | /
    \  929 177
     \  |  /
      \ | /
       228

...4.67.9..6....32.89.....5.9184......86.7.9167......4.649.8....1..74.....716....|32|862
...4.67....6....32.89.....5.9184......86.7.9167......4.649.8....1..74.....716....|31|73

...4.67.9..6....32.89.....5.9184..76..86.7.9167......4.6.9.8....1..74......16....|32|864
...4.67....6....32.89.....5.9184..76..86.7.9167......4.6.9.8....1..74......16....|31|83
...4.67.9..6....32.89.....5.9184..7...86.7.9167......4.6.9.8....1..74......16....|31|904
...4.67....6....32.89.....5.9184..7...86.7.9167......4.6.9.8....1..74......16....|30|177

...4.67.9..6....32.89.....5.9184......86.7.9167......4.6.9.8....1..74......16....|30|929
...4.67....6....32.89.....5.9184......86.7.9167......4.6.9.8....1..74......16....|29|228

[mith]

The largest case is four max-expands; there are four such families, here's the earliest:

Code: Select all

max-expands:
1.3...78..56789...78....5.....59.67..6..728...7.6.8.2...7...2.86.28.795....92..67|37|1229
1.3...78..56789...78....5.....59.67..6..728.5.7.6.8.2.......2..6.28.795....92..6.|35|203207
1.3....8..56789...78......6...59.67..6..728...7.6.8.2..........6.28.795....92..6.|32|10703
1.3....8..56789...78..........59.67..6..728...7.6.8.2.....6....6.28.795....92..6.|32|10706

min-expand:
1.3....8..56789...78..........59.67..6..728...7.6.8.2..........6.28.795....92..6.|31|16475

[hendrik_monard]

hendrik, to make sure I don't miss anything would you mind compiling a single list of your 11.6+ puzzles since my March 21 post (the-hardest-sudokus-new-thread-t6539-1230.html#p318907)?

The last time I consulted this thread was about a week ago, so I saw your post only just now.
After March 21st I posted lists of 11.6+s on April 5th and May 15th.
I did not check them against the expanded minlex list you posted on March 21 assuming that your list was a different presentation of previously posted puzzles.

I am ready to put them all together in a single list but the question is how to transfer this long list? Do you have a website where I can upload them, or can I send them by PM to you?

P.S. After reading your more recent posts I want to ask if you still need the list you requested on June 20th?

[mith]

hendrik, let's just do it this way: here's the list I put together: monh-202206

Can you check that I haven't missed any?

[mith]

This is not unexpected, but I ran a check anyway:

All known depth 3 puzzles have the properties that...

1. Exactly three digits appear at most once each. (Obviously at least two must appear. It's a pretty even split between ...110 and ...111 distributions, slightly more of the latter.)
2. Those digits (the ones that appear at all) appear in the same box.

This will make identifying TH patterns simple for the current set: they must occur in the four boxes not seeing that single box, and they much include all cells in those four boxes limited to the three digits with this property. This should allow for a quick script to get the count of guardian cells for all the min-expands. I'll work on that next (possibly two versions - one with the puzzle as is, one with the puzzle after basics, since hidden pairs in the TH boxes are fairly common from what I've seen).

[denis_berthier]

This will make identifying TH patterns simple for the current set: they must occur in the four boxes not seeing that single box, and they much include all cells in those four boxes limited to the three digits with this property. This should allow for a quick script to get the count of guardian cells for all the min-expands. I'll work on that next (possibly two versions - one with the puzzle as is, one with the puzzle after basics, since hidden pairs in the TH boxes are fairly common from what I've seen).

Not only Hidden Pairs but any Subset of size ≤ 3.
Moreover, in many cases, the pattern appears (or appears in simpler form, with much fewer additional candidates) only after applying many more rules than only Subsets.

[hendrik_monard]

hendrik, let's just do it this way: here's the list I put together: monh-202206

Can you check that I haven't missed any?

Hi mith,

One batch of 615 11.6s (my second post of April 5th) are not in the list you compiled. You can find them (a hidden list) here:
the-hardest-sudokus-new-thread-t6539-1230.html#p319648

[denis_berthier]

.
See my first analyses of the collection here: http://forum.enjoysudoku.com/the-tridagon-rule-t39859-60.html

[mith]

hendrik, let's just do it this way: here's the list I put together: monh-202206

Can you check that I haven't missed any?

Hi mith,

One batch of 615 11.6s (my second post of April 5th) are not in the list you compiled. You can find them (a hidden list) here:
the-hardest-sudokus-new-thread-t6539-1230.html#p319648

Thanks hendrik, I will process these before I start my scripts back up, and include the resulting expanded forms in the next batch.