LatinExplainer - to solve and rate 9x9 latin squares

Programs which generate, solve, and analyze Sudoku puzzles

Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby Mathimagics » Sat Nov 23, 2019 5:48 pm

1to9only wrote:I had LE generate over 1m grids (some are in post #2), I've scanned these and found only 1 which is also a sudoku grid with a unique solution, but it's not minimal.

Are the grids restricted to valid Sudoku grids? If not, then the chances of a random Latin Square being a Sudoku solution grid are (roughly) only 1 in a million ...
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby blue » Sat Nov 23, 2019 6:00 pm

Mathimagics wrote:The fact that I having a great deal of trouble finding any other Sudoku grid with a low-clue minimal LS puzzle is perhaps evidence that these are very rare. For 20-clues in particular perhaps this is the only grid?

Have you scanned your LCT database for valid LS puzzles ... 19C in particular ?
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby coloin » Sat Nov 23, 2019 7:04 pm

Actually in your list of 49 puzzles there are only 6 ED puzzles
Code: Select all
.2.4.6............7.9....5........9.5.7.9..3....2.4....4.6.8..2.....2...9......7.
1......89.567..............2.....891.67......8.........4567.....7.......9.......8
.23..67..4...8.........3....3...7...5..89...48..................7...23..9...4...8
1....6....5........89...45.2...67..1.....1....9....5...45...9..6...12............
.....678945...............62345.....5...............67345.....................678
1.3.5.7........1...8......6..........6.8....4..1.3.5...4.6.8..2....1.3..........8


They are all valid LS puzzles with ED=1.5/1.5/1.5 [as we know 1.5 is a hidden single in a row/column]

indeed this automorphic [how many ?] grid should have a name - as it cant be the MC grid ?
Maybe there is a single 18C sudoku puzzle in the grid ... but cant see a 19 which is a LS and there are many 20C sudoku puzzles therfore, and maybe more LS puzzles to be found.
In the 3rd puzzle every clue can be mutable - so thats another find !
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby Mathimagics » Sun Nov 24, 2019 4:19 am

coloin wrote:indeed this automorphic [how many ?] grid should have a name - as it cant be the MC grid ?

The original LS, with c1 = {123456789}, from which this puzzle was obtained is known as the "Back Circulant" LS, so I suggest that we call the Sudoku version the BC grid.

It has 54 Sudoku automorphisms. I have looked at some other grids with high-automorphism counts but can't find a "magic" case.

It does have 18C Sudoku puzzles (189 of them, all minimal). Here is one:
Code: Select all
......789456...............23......1..789...............5...........234.91.......


blue wrote:Have you scanned your LCT database for valid LS puzzles ... 19C in particular ?

I have scanned band 6 only, the largest (96 million grids). No 19C puzzle in the LCT catalog is a valid LS puzzle - but my conjecture is that, among the Sudoku grids, there are no 19-clue LS puzzles. So I didn't search any other bands.

To test this conjecture we would need an Enum19C function. To find out whether any other grid has a 20-clue minimal LS/Sudoku puzzle we need an Enum20C. (Are these extensions to the BlueMagic suite feasible?)

Cheers
MM
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby tarek » Sun Nov 24, 2019 10:29 pm

A few more rated puzzles
Hidden Text: Show
Code: Select all
Rated with Sukaku Expliner v1.11.3 Q0 option
468.....15.142..6.27.64.....56..8.248..3.....14.....856....79.2.2..53......7..... ED=9.6/2.3/2.3
.856.324...21...3........21.5.....7.81.2..3....13.7562..643215...7..5613........6 ED=6.1/1.5/1.5
...8...3.2..5.467.8.4.13...3562.14..1...6....6.54.23..42318.5..5.23..7....7...... ED=5.4/1.5/1.5
......8.2.2..175.3.31.7.2.68...4.3..164..3..7....5.4..486.3...55.3..17.4.7.....9. ED=5.4/1.5/1.5
.47..6.83....6..156.3.4..52521..3.46.7..1........5..21.3......72..8.1.6..8.4..... ED=5.4/1.5/1.5
1..6.9...48..25..1.4.29....27..46.1.6...52.48..7461.23...7..5..8.5.13............ ED=5.4/1.5/1.5
3452.6.7.6.4.82...25.734....2716.....7..4..1.5624.....4......83.1.....3.......... ED=5.4/1.5/1.5
8..2...3..8.1.4....2...8346.52.....7.1......2341..6.75.368.152.56...2413......7.. ED=5.4/1.5/1.5
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby coloin » Wed Nov 27, 2019 2:32 pm

Hi 1to9only
I know that you want to make it the same as SE, and its great that you have done this. :D
Could you easily extend the "analyse" function for puzzles with multiple solutions to include the number of solutions [below what it takes to compute in say 5 sec?] ?
Also removing "impossible" pencil marks in incomplete puzzles would make puzzle construction easier [if maybe that was also an aim.] :?: Thanks
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby coloin » Wed Nov 27, 2019 2:48 pm

And an observational question
Do all latin square puzzles have ED=*.*/*.*/1.5 ?
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby tarek » Wed Nov 27, 2019 3:35 pm

coloin wrote:And an observational question
Do all latin square puzzles have ED=*.*/*.*/1.5 ?
Hi Colin,
Not really
Code: Select all
.5342.8..528.......6.137...4...8.5...7...8....4.7.3.1..1.....6...564.2.7..9.6.... ED=7.2/7.2/6.6
..79.8...51.2...3..2.5..34.7.......12.6..15...8.452..3.4.....9..3..276.51.......2 ED=8.3/7.3/3.0
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby 1to9only » Wed Nov 27, 2019 3:42 pm

coloin wrote:Do all latin square puzzles have ED=*.*/*.*/1.5 ?

In post #2 in this thread, there are examples of puzzle ratings of ER/EP/ED where the ED > 1.5. - Already answered.
In Sudoku, 1.2 is a Hidden Single in a 3x3 block - there are no block contraints in Latin Square so no 1.2 rating is possible.
In Latin Square, an x.x/1.0/1.0 is possible when there is a Full House in a column or row, e.g.
Code: Select all
1324.7689
324......
24.......
4........
.........
........5
.......57
......576
.....5768 ED=1.5/1.0/1.0
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby 1to9only » Wed Nov 27, 2019 3:52 pm

coloin wrote:Could you easily extend the "analyse" function for puzzles with multiple solutions to include the number of solutions [below what it takes to compute in say 5 sec?] ?

Existing SE code is used, there are no plans no add any new code.

coloin wrote:Also removing "impossible" pencil marks in incomplete puzzles would make puzzle construction easier [if maybe that was also an aim.] :?: Thanks

Does Ctlr-R (Tools->Reset potential values) do that? Else manual removal is by Right-click on potential value, it is red highlighted, Right-click again to remove potential value - this can quickly become dedious!
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby coloin » Wed Nov 27, 2019 4:13 pm

Thanks thats very helpful
The 1.0 would never happen in a minimal puzzle but furthur down the solving process.
So the 1.2 cant happen in LS puzzles
as well as , pointing 2.6, claiming 2.8, naked pair in a block 3.0 - these cant be used
but a hidden pair pair in a row 3.4 would be in order
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby coloin » Wed Nov 27, 2019 4:16 pm

tariq wrote:
Code: Select all
.5342.8..528.......6.137...4...8.5...7...8....4.7.3.1..1.....6...564.2.7..9.6.... ED=7.2/7.2/6.6

Well thats very impressive, and the record so far !!! :D
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby 1to9only » Wed Nov 27, 2019 4:56 pm

In here tarek posted a 9.6/2.3/2.3. In post #2 I've posted a few diamonds, the highest being 9.2/9.2/9.2.
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby coloin » Wed Nov 27, 2019 6:04 pm

Thanks !
:oops:
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Re: LatinExplainer - to solve and rate 9x9 latin squares

Postby m_b_metcalf » Thu Nov 28, 2019 4:27 pm

Mathimagics wrote:I assume that you really meant "start with a Sudoku grid", then find minimal LS puzzles, checking these for being minimal Sudoku puzzles. They will of course all be valid Sudoku puzzles, just not necessarily minimal.

So I decided to try that out myself. I have no dramatic results to add, but here's a small selection of non-trivial LS puzzles:
Hidden Text: Show
Code: Select all
12.3...4..54216.37.7....52...51.3....8..6.7..3.98.24......31.8.2...98..........56   ED=4.5/2.0/2.0   
123......4......566..4....2..6.42.7.834..6.2.5.2..86...9...38....5...1.7.4..6729.   ED=4.6/1.5/1.5   
.1.2..34.3...5.6..67....1.8..8..45.21.3.....4..751..3.....2..75...4962...91....6.   ED=6.6/2.3/2.3   
123.......451.6..7.865..9..3....94..4.......8....2.7.3.1.69......7..85..2.8.4536.   ED=6.7/1.5/1.5   
12..3..4.......15..6.57..23..4.18.....86.7.......423.5.76....18...769.3..9...3...   ED=6.8/1.5/1.5   
.12.....3...4.526.53..21.7.3....618.8....4..56.1....4...3.4871...4..2..6..7.9.8..   ED=6.9/1.5/1.5   
1.2...3...3.12.4....567..8......5.6..1.....2...739.....58.162..9....4.7864....5.9   ED=7.1/2.0/2.0   
..1.2.34..456......7..43.5.6.81......9..86.3.15.97.......79.2152.....4..5.9....8.   ED=7.2/7.2/3.2   
1.2.....3....3...4.4...5.6...7.2.6586...843.18..6.1.4..5.8..9...9...27...8.39.41.   ED=7.3/7.3/7.1   
123..4.56.7..1....45....73..3....6..7..5.8.4......2..95.7...1.361..83.2...295..6.   ED=7.4/7.3/3.0   
1..23....34..56.7..5..71.4856..4.9.1.93....86...569....8....493.........2.46.7.1.   ED=7.5/2.0/2.0   
..123.4...25..46.14.7.512......8.5...8.4....6.....6.385......67.1...7....329..1..   ED=8.3/8.3/3.2   
.....123....4.2..5.61........5...7.31...8..929862..4..8..6..3.4.1..45..8749.2....   ED=8.4/8.4/7.3   
.12...3.435..6..2.7..1.3.8.234..7.9.9..538.7.587.....1..84..........5.......9.21.   ED=8.5/8.5/7.2   
12..34..5......2635738.......86...7.95.4....1....59.4.21...8.......9.4...4756.9..   ED=8.6/8.5/3.2   
123......45.3...61..71.4..8...63..799..2.81..3...5..4......69....6.9.78.....82..5   ED=8.7/1.5/1.5   
1......23...2.3.4......5..6.74...8..2.854...9391........9.58612..6...49.81.9..7..   ED=8.8/8.8/3.0 
1..2.34......5.613..4....7..3..82.....93.5....7.64.1..7285....19..43..6.6...2..85   ED=8.9/8.9/8.4   
.1....23...452.67.8276...9....16978.6...72......8.5.4..6879...3.3......41...5.8..   ED=9.0/9.0/7.3   
1....2..32.4.5..6..6....7......85....9.2..63.81649.......54...1..9...47.5..8..296   ED=9.1/9.1/8.4   
1...2...3...4.51..5673.........7...837...46..458..2....3.2.9.1.7.5.8..9....53.2.6   ED=9.2/9.2/3.2   
..123.....2.1..43..5...67...4.7.81.........48.6349.2..6....9..7.7..5....5.23...9.   ED=9.3/9.3/3.2   


All the puzzles I generated were non-minimal when treated as sudoku puzzles, and almost all are trivially solved in that mode. An example of one that wasn't is:
Code: Select all
 . 8 . . 6 . 4 1 .
 . . 2 . . . . . .
 . . . 2 4 . 8 5 3
 . 7 9 . 2 3 . . .
 . . . 4 5 6 . 2 .
 . 6 . 7 . 9 . . .
 9 . 3 . . . . . 8   ED=5.5/1.2/1.2 SukakuExplainer
 . . . . . . . 4 1   ED=6.8/1.5/1.5 LatinExplainer
 8 . 6 . . . . . 9   ED=7.1/1.2/1.2 SudokuExplainer


Regards,

Mike
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