The New Sudoku Players' Forum

[Mathimagics]

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 ...

[blue]

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 ?

[coloin]

Actually in your list of 49 puzzles there are only 6 ED puzzles

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.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 !

[Mathimagics]

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:

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......789456...............23......1..789...............5...........234.91.......

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

[tarek]

A few more rated puzzles

Hidden Text: Show

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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

[coloin]

Hi 1to9only
I know that you want to make it the same as SE, and its great that you have done this.
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

[coloin]

And an observational question
Do all latin square puzzles have ED=*.*/*.*/1.5 ?

[tarek]

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

[1to9only]

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


[1to9only]

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.

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!

[coloin]

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

[coloin]

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 !!!

[1to9only]

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.

[coloin]

Thanks !

[m_b_metcalf]

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:

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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:

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 . 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