The New Sudoku Players' Forum

[urhegyi]

symm.png (18.46 KiB) Viewed 1523 times

I created this solution today. Are there rules to consider when starting to remove clues to create sudoku's with different hardness levels based on this. I think the first one is to hide the pattern which I used to create it. When someone discovers it to quick, it would spoil the solving pleasure.
First attempt with 26 clues:

Code: Select all

1..2...74.........9.3...8.......7.6...185.9.....3..2....29....1.....36.2.37..84.9

rated hard
Second attempt with 26 clues:

Code: Select all

1.62...74.........9.3...8.......7.6...18..9.....3..2....29....1.....36.2.37..84.9

rated unfair
Third attempt with 25 clues(removed one more clue from last example):

Code: Select all

1..2...74.........9.3...8.......7.6...18..9.....3..2....29....1.....36.2.37..84.9

rated extreme

[1to9only]

Your 3 puzzles:

Code: Select all

1..2...74.........9.3...8.......7.6...185.9.....3..2....29....1.....36.2.37..84.9 ED=6.6
1.62...74.........9.3...8.......7.6...18..9.....3..2....29....1.....36.2.37..84.9 ED=7.1
1..2...74.........9.3...8.......7.6...18..9.....3..2....29....1.....36.2.37..84.9 ED=7.1


I had a play with your solution grid, and generated these random puzzles:

Code: Select all

1.....37...473.19.9.3.......9.......3....2.4.74...6.18..2..........7.6.2...1.8... 25 ED=1.2
.5............5196.73..1.25....1.......8.2947......21..8..6.7....9.7....6..1..... 25 ED=1.5
........4...735.....3..182..9..1.5633..8.2..........1..829...3.4....36..........9 25 ED=1.5
.5...93.4.2....1....3..1.......1....3...52......3...1858.9.4....195..6..6......5. 25 ED=1.5
156....7.8..7.......364.8..2...1...3.6..529.7......2......6.....19....8....12.4.. 26 ED=1.5
1.62......2.....9...3...8...9...7...3......4.7....6..858....7.1.1.5....26...2.... 23 ED=2.0
...2.9.7.......1.69.3..1.2...84..5.3.........7.5.9...8...9........5.36.2.37.2.... 25 ED=2.0
.....9...82......6..3..1..52.....5..3618...4..4...6.....2.6..3..195....26..1.8... 26 ED=2.6
..6.....48..7.5.....3..1.2..9...75.....8.2.....5.....8..29.47....9...6...3.1...5. 24 ED=2.6
1.......482.7..19...3.....52.8.1........5..47..5....1.....6..3.4...7...2.3.1.8.5. 26 ED=3.2
..6.89......7.......3.4..25298..7......8..94........1.5......31....73....3....45. 24 ED=4.2
...2.....8.4..51..9..6..8.5.........36.....4.745.....8.....4.3.41..73.....7.28..9 26 ED=4.2
1......7......5..6973.......9..1.5.3.6.........53..2...8.9....1....7....637.2.4.. 24 ED=4.2
15...93....47..1...7.6...2..98......3..8.2.4.......2..5....4........368.........9 23 ED=5.6
..6.8..7...47..........18.52.....5.3.61.......4.3.6...5.2..........7..8...7.284.9 25 ED=5.6
...2....48..7...9...36.18......1..6.3.....9.7.45..........6..314..5.........2..5. 23 ED=6.6
1....93.4.....5.9..7..4..2.2...1.5...6......7.4.3.6....8......1....7.......12.4.. 23 ED=6.6
.5.28............69...41.2..98..7..3......94......6..8..2....31....7....6.712...9 25 ED=6.6
1..2...7......5.969.3...8....8...5.3.6.......7...9..1..8...........7.6...3..2..59 23 ED=7.1
1..2...7......5.969.3...8....8...5.3.6.......7...9..1..8...........7.6...3..2..59 23 ED=7.1
..6.893..8.4.3.1.........2..98.1....3..8...4......62..5.....7.1..9...6...3.....5. 24 ED=7.2
1....9.7..24.3............5..84.7.......5.9.7......21..8..6.....1....6.2.3...8..9 23 ED=7.2
15.....7.8.4........36....52....7....6.85.9...4..........96...1.1..7...2.....8459 25 ED=7.2
.56...3.......5....7.641...29.....63.....2.4.7.5....18....64..1...5.3...6..1....9 26 ED=8.3
..6....74.....51..9.3...........75...61...9...4...6.185829........5..6.......8..9 24 ED=8.3
.562.93...2..3....9.....8......17.6.3.1..2.4....39...85...6......9..36....7....59 27 ED=8.5
.5..8...4...7.5...9.36..8...9.4..5.......2...7....6.1..8.9..7...1...3...6......59 24 ED=8.5


[m_b_metcalf]

Here's some more:

Code: Select all

1..2.9.7..247..........1..5.9.4.7...3....29....5...2..5...6.....1..73...63.....59   ED=1.2/1.2/1.2   
...2.9..4..4...19....6..........7.....185..47.45....185.2....3.....7.6...371.....   ED=1.5/1.2/1.2   
15......4.....5..6....4.82...8...5....1.....77...9.2.8....64.3.4...7.....3.12....   ED=1.7/1.2/1.2   
1.6.89.....47.5.9....641..529.....6.3...5...7....9...85.....7....9.......3.1..4..   ED=2.0/1.2/1.2   
....8.3....47....697.6.....29..1.........2..7..5.......8.9.4......57..8.6......5.   ED=2.3/1.2/1.2   
1..2......2.735.96..3.4................85.9.7.4..9...8..2....3..19...6...37....59   ED=2.3/1.5/1.5   
1....9....2......6..3.4.8...9..1.....6...29.7...3...1...2...7...1.5.3..2......4.9   ED=2.5/1.2/1.2   
....8..7..247...9..7.6.1.2...8.1.5.......29..7.5.......8...4..1..9..36...3.....5.   ED=2.6/1.2/1.2   
15....3.48..........3....25.....7.6.3..85....74.3......82.6....4.95.........2...9   ED=3.0/1.2/1.2   
....893.4...7..1....3...82..........361.......453.62...82.........57....63.1..4..   ED=3.4/1.2/1.2   
.56......82...51..9.3..1.........5.3.6.8..94....3........96.73..1....6.2........9   ED=4.2/1.2/1.2   
.....9..4...73.19....6.......8...56.3.1..2.....5.9.....8.....31...5..68...7.....9   ED=4.4/1.2/1.2   
.5.2.9...8.......6....4....29......3.61.5...7.....6.18....6..3.4..57.....3.....59   ED=4.5/1.2/1.2   
......37.8.4......97.6....52.8....633..8...4...5.9......29.......95.368.......4..   ED=5.0/1.2/1.2   
1..2..3.48....5.......4..2.......563..1..2...7...9.....8...4.3....5..6..637..8..9   ED=6.6/1.2/1.2   
1...8..7.8....5..69..64.............36....9....539.2........7.1.1.5...82..7...4..   ED=6.8/1.2/1.2   
....8...4.2.7.5...9.36.....298.....3.6..5.9.7........8.8.9.47..4....36....7......   ED=7.1/1.2/1.2   
.....9...8.47...9....6....5....1......1..294.7.5....18...9..7..41.5....2.3.......   ED=7.2/1.2/1.2   
1....9..48.....1...73...8.52...17...3..8......45.........9..73.41.5.......7...4..   ED=7.3/1.2/1.2   
1.6....7.8...3..9......18..29.4...6.....5.....4......8...9..7.....5....263..2..5.   ED=7.4/1.2/1.2   
....8..7.8.4..51..9.3.....5...4..56.36..5...7.........5..96...1.1.....826....8...   ED=7.8/1.2/1.2   
1..2..3..8.4..5.....3..1....9..1.5...6..5...7...3..2....29...31......6..6......59   ED=7.9/1.2/1.2   
.5.2.93.....7....6.73.4....29........61...9.7.......18........1...5736..6......5.   ED=8.3/1.2/1.2   

Do you have a definition of hard? Producing very hard puzzles is hard.

[m_b_metcalf]

Here are few harder ones:

Code: Select all

....89..48......9.9.3....252....7.63...8.2.....5.9...8..2.6..3...95.3...6..1...5.   ED=8.4/1.2/1.2   
.5......4......1...73..1.2...8.1756....8.........9...........3.4.9.73.82.3..28..9   ED=8.5/1.5/1.5 
......3....4735..6.....1.2..98...5..3...5...77......1....96.7...1.........7..845.   ED=8.6/1.2/1.2     
.....93...2...5..6.736..8............618....7.4.....1.5....4....1...36....71....9   ED=8.8/1.2/1.2
.5...937...4...1...7......5.98..75..3...52........6..8........1..9.73.8.6...28...   ED=8.9/1.2/1.2   
..6..9.7..2..3....9....1.25..84..5.336.85............8.8.9......1..7...26.7...4..   ED=9.0/8.9/2.6     
.....9.7..2...51.6..36.........1.5...6......77.5.9.....8..6...141...3..2.3..2.4..   ED=9.1/1.5/1.5   

[Mauriès Robert]

Hi all,
By creating puzzles by removing candidates from the same solution, one exposes oneself to the risk of generating puzzles with multiple solutions. How do you proceed to guarantee uniqueness?
Robert

[m_b_metcalf]

By creating puzzles by removing candidates from the same solution, one exposes oneself to the risk of generating puzzles with multiple solutions. How do you proceed to guarantee uniqueness?

By testing for uniqueness at each step, and restoring any clue(s) whose removal causes the candidate puzzle not to have a unique solution.

Regards,

Mike

[Mauriès Robert]

By creating puzzles by removing candidates from the same solution, one exposes oneself to the risk of generating puzzles with multiple solutions. How do you proceed to guarantee uniqueness?

By testing for uniqueness at each step, and restoring any clue(s) whose removal causes the candidate puzzle not to have a unique solution.

Regards,

Mike

Thanks Mike. It's a tedious job. Do you do this with a solver or by hand?
Robert

[Hajime]

Hi all,
...by removing candidates from ...
Robert

I hope you mean: ... removing clues from the puzzle cells ...

There is no need for testing the uniqueness.
If the Solver only uses methods that are NOT T&E then the solution is guaranteed OR the puzzle is not solvable
In the latter case you have to restore the removed clue(s) back and try another cell(s).
If a solution is possible, this is the logical solution based on deterministic methods, than you can leave this cell empty and try next cell(s).
If the choice of next cell(s) is random selected, you do not even need a pattern (as urhegyi stated in the beginning of this posting).

Below is the loop of my Generator and Solver interaction, that is used in SeSiSuSo (both in excel and .exe).
SiSeSuSo is meant to solve puzzles with multiple overlapping grids, even scattered ones like "Clueless Explosion".
http://forum.enjoysudoku.com/sisesuso-simple-serial-sudoku-solver-t35062-15.html#p296783

Generator_Solver_Interaction.png (55.93 KiB) Viewed 1422 times

[m_b_metcalf]

There is no need for testing the uniqueness.
If the Solver only uses methods that are NOT T&E then the solution is guaranteed OR the puzzle is not solvable

But if you're trying to generate hard puzzles, then, if the candidate puzzle is not solvable using only methods that are NOT T&E, it will be rejected. How will you ever find a puzzle like this one? And how will you prove it's minimal?

Code: Select all

001050060600000002040000300030700000006010008000009000500020001070004900008000020 1to9only

[mith]

I generated 1k from the solution grid, curious what the distribution would be. Here's the result using skfr:

Code: Select all

9.1 (2)
9.0 (10)
8.9 (18)
8.8 (17)

8.7 (1)
8.6 (4)
8.5 (21)
8.4 (68)
8.3 (94)
8.2 (10)

7.8 (4)
7.7 (4)
7.6 (11)
7.4 (4)
7.3 (66)
7.2 (127)
7.1 (144)
7.0 (16)
6.9 (4)
6.8 (7)
6.7 (2)
6.6 (21)
6.5 (1)

5.6 (2)
4.5 (14)
4.4 (2)
4.2 (55)
3.8 (1)
3.6 (2)
3.4 (5)
3.2 (7)
3.0 (6)
2.8 (35)
2.6 (20)
2.5 (6)
2.3 (38)
2.0 (72)
1.7 (6)
1.5 (71)
1.2 (2)

Some of these (including the 9.1) are duplicates. The 9.1 is actually a 9.2 by SER 1.2.1; here's a list of the ones found with dynamic chains (removing duplicates):

Code: Select all

1..2..3....473..9...3..1..52..4..5...6.....4...5..6..8......7..41..7..8......8..9  ED=9.2/1.2/1.2(DCFC)
...2..3...24....9...36.1..52..4......6..5..4...5..6..85..9..7...1.57..8...7..84..  ED=9.1/1.2/1.2(DRFC)
1.....3...24.3..9...3..1..5..84.75...6..5..4.........85..9..7...1....6....7..8...  ED=9.1/1.2/1.2(DRFC)
1..2..3.4.2..35.9...3..1..52..4..5...6..5..4...5..6..8...9..7...1.....826....8..9  ED=9.1/1.2/1.2(DRFC)
1..2..3....4.3..9......1...2..4....3.6..5..4...5..6..85..9......1..7..8...7..84.9  ED=9.0/9.0/3.4(DCFC)
...2..3....4.3..9...3..1..52.....5...6..5..4....3.62..5..9..7...1....68...7.....9  ED=9.0/1.2/1.2(DLFC)
...2..3.4.2.7...9...3..1..52..4..5...6.....4...5..6..85..9..7...1....68...7..8...  ED=9.0/1.2/1.2(DRFC)
..62..3...2.....9...3..1..52..4......6..5..4.7.5..6..85..9..7...1..7..8.6.7..8...  ED=9.0/1.2/1.2(DLFC)
1..2......2..3..96..3.....52..4......6..5..4...5..6..85..9..7...1...36....7..8..9  ED=9.0/1.2/1.2(DLFC)
1..2......2..3..96..3.....52..4..5...6.....4...5..6..85.....7...1..7368...7..8..9  ED=9.0/1.2/1.2(DLFC)
1..2......24.3..9......1..5...4..5..36..5..4......6..85..9..73..1....6....7..8..9  ED=9.0/1.2/1.2(DLFC)
1..2....4.2.....9..73.....52..4..5...6..5..47.....6..85..9..7...1..7.68......8...  ED=9.0/1.2/1.2(DCFC)
1..2....4.2..3..9...3..1..52..4..5...6.....4.7.5..6..8...9..7..41.....8......8..9  ED=9.0/1.2/1.2(DLFC)
1..2....4.2..35.9......18.52..4.........5..4...5..6..85..9..7...1..7..8.6.7..8..9  ED=9.0/1.2/1.2(DLFC)
1..2..3....47...9...36....52..4..5...6..5..4......6..85..9..7...1..7.68...7..8...  ED=9.0/1.2/1.2(DLFC)
1..2..3...2..3..96.....1..52..4..5...6.....4...5..6..8...9..7...1.5..68...7..8..9  ED=9.0/1.2/1.2(DLFC)
1..2..3...2..3..96..3..1..52..4..5...6.....4...5..6..8...9......1.5..68...7..8..9  ED=9.0/1.2/1.2(DLFC)
1..2..3...24....9...3.....52.84..5...6.....4....3.6..8...9..7...1..7..8...7..84.9  ED=9.0/1.2/1.2(DLFC)
1..2..3.4....35.9..73.....52..4......6.....4...5..6..85..9......1..7..8.6....8..9  ED=9.0/1.2/1.2(DLFC)
1..2..3.4.2..3..9......1...2..4..5...6..5.......3.6..85..9..7..41.....8...7..8..9  ED=9.0/1.2/1.2(DLFC)
1..2..3.4.2..3..9...3.....52..4......6.........5..6..85.........1..73.8...7..84.9  ED=9.0/1.2/1.2(DRFC)
1..2..3.4.2..3..9...3..1...2..4..5...6..5..4..4...6..85..9..7...1.57..8.6....8..9  ED=9.0/1.2/1.2(DCFC)
1..2..3.4.2..35.9...3.....529.4......6..5..4...5..6..8...9..7...1..7.6.......8..9  ED=9.0/1.2/1.2(DRFC)
...2....4.2..3..9...3..1..529.4.75...6.....4...5.....85..9..7...1..7..8.6....8...  ED=8.9/1.2/1.2(DLFC)
...2....4.2..35.9...3..1...2..4..5...6.....4...5..6..85.....7...1..7..826....8..9  ED=8.9/1.2/1.2(DLFC)
...2..3...2.....96..3..1..52..4......6..5..4.7.5..6..85..9..7...1..7....6.7..8...  ED=8.9/1.2/1.2(DRFC)
...2..3...2.7...96..3..1..52..4..5...6.....4...5..6..85..9..7...1..7..8......84..  ED=8.9/1.2/1.2(DRFC)
..62..3...2..3..9...3..1...2..4..5.........4......62.85..9..7...1.57..8.6.7.....9  ED=8.9/1.2/1.2(DLFC)
..62..3...2..351....3..1..52..4......6.....4...5..6..8...9..7...1..7..8......84.9  ED=8.9/1.2/1.2(DRFC)
1..2......2..3..96..3.....52..4..5.3.6.....4...5..6..8...9..7...1..7..8.6.7..8..9  ED=8.9/1.2/1.2(DRFC)
1..2....4.2..3..9...3.....52..4..5...6..5.......3.6..85..9.47...1.....8...7..84..  ED=8.9/1.2/1.2(DCFC)
1..2....4.2..3..9..73.....52..4......6.........5..6..85..9..7...1.57..8......84.9  ED=8.9/1.2/1.2(DRFC)
1..2..3...2.....96..3..1...2..4....3.6..5..4...5..6..85..9..7...1..7..8.6....8..9  ED=8.9/1.2/1.2(DCFC)
1..2..3...2..3..96.........2..4......6.....4...5..6..85..9..7...1..736....7..8..9  ED=8.9/1.2/1.2(DLFC)
1..2..3...2..3..96........5.9.4..5..36.....4......6..85..9......1..7..8.6.7..8...  ED=8.9/1.2/1.2(DRFC)
1..2..3...24.3..9......1..52..4..5.3.......4...5..6..85..9..7...1.....8.6.7..8...  ED=8.9/1.2/1.2(DRFC)
1..2..3.4.2.....9...3..1..52..4......6..5..4...5..6..85.....7.1.1.57..8.6....8...  ED=8.9/1.2/1.2(DCFC)
1..2..3...24....9......1..52..4.7....6..5..4......6..8...9..7..41..7..8...7..8..9  ED=8.8/1.2/1.2(DRFC)
1..2..3.4.2..3..9.........52..4..5..3......4...5..6..85..9....1.1..7..8...7..84..  ED=8.8/1.2/1.2(DRFC)
1..2..3.4.2..3..9......1...2..4..5...6.....47..5..6.185.....7...1..7.68...7..8..9  ED=8.8/1.2/1.2(DCFC)
1..2..3.4.2..35.9...3..1..52..4..5...6.........5..6..8.8.9..7...1..7.6....7..8..9  ED=8.8/1.2/1.2(DRFC)
1.62......2..3..9.9....1..52..4.7....6..5..4......6..8...9..7...1..7..8...7..84.9  ED=8.8/1.2/1.2(DRFC)

This seems to be a pretty typical distribution for generating harder puzzles: about a third are in the 7.1-7.3 range (common forcing chains), about a fifth are 8.2-8.7 (cell/region forcing chains), and a few percent dynamic (47/1000 here, counting duplicates). Higher ratings become increasingly unlikely. (Getting things like jellyfish and quads is also extremely unlikely with this method. Even smaller fish and subsets are rare as the most difficult technique needed.)

[Hajime]

How will you ever find a puzzle like this one? And how will you prove it's minimal?

Code: Select all

001050060600000002040000300030700000006010008000009000500020001070004900008000020 1to9only

The original question was:
A. How to create a sudoku starting from a solution
I answered that.
Now there come up additional demands:
B. How to make difficult puzzles
C. Prove the puzzle is minimal

For B. the answer is simple but time consuming in executing...
It will be the same discussion you already had with Davy at
http://forum.enjoysudoku.com/generating-sudokus-t38093.html?hilit=generating#p292477
where you stated: " You could add a step 6.: if the first step in solving the candidate puzzle involves a single, repeat from 1."
I would suggest step 6: if the generated puzzle does not meet a certain difficulty, repeat from 1.
That is what I do for all of my published puzzles.

For C. This has little value for me. For bits & bytes solvers that may be a huge thing, but I am in for pencil & paper solvers.
Further I like symmetrical puzzle. They are always not minimal I presume.

[mith]

A few more, these from a batch of 100 after removing all givens on the diagonals.

Code: Select all

...2.93....4.3....9..6.1..52.....56..6.....47.4..9...858.9.........7.6....7..8...  ED=9.0/1.2/1.2 (DRFC)
..6..93......35..6.....1.252...1..63.6.8...4...5.....858.9.........7......7..84..  ED=9.0/1.2/1.2 (DLFC)
...2..3....4.3.....7..41..52.....5...61....4..4.....185..9.......957.6....7..8...  ED=8.8/1.2/1.2 (DRFC)

[m_b_metcalf]

Further I like symmetrical puzzle. They are always not minimal I presume.

May I remind you of

I loaded Mike's file in my site.

It can be down loaded from games_sample

I solved 26855 Sudoku's with an average solution time of 4.852 ms each (elapsed 2 minutes 10.29 seconds).

These puzzles from the Patterns Game are all symmetrical and all minimal, by definition.

Regards,

Mike

[m_b_metcalf]

As an exercise, I generated 1225 puzzles from this grid, with 'crossword symmetry'. Of these, 185 were minimal, 174 after removing 11 duplicates. These in turn yielded 33 different ratings:

Code: Select all

...2.937...47..1.6.........2...1....36.....47....9...8.........4.9..36...371.8...   ED=1.2/1.2/1.2   
.....9..4....3....9.36..82..9....5.3.6.8.2.4.7.5....1..82..47.1....7....6..1.....   ED=1.5/1.2/1.2   
...2.93...247..1...........2...1....36.....47....9...8...........9..368...71.8...   ED=1.5/1.5/1.5   
..........2..35..697.6..8..........3.618.294.7..........2..4.314..57..8..........   ED=2.0/1.2/1.2   
.5.2.93....4..5............29...7.6..61...94..4.3...18............5..6....71.8.5.   ED=2.0/1.5/1.5   
..............51.69736.....29......3.6.8.2.4.7......18.....47314.95..............   ED=2.0/2.0/2.0   
.........8.47.5....7...1....9..1.56.3.18.29.7.45.9..1....9...3....5.36.2.........   ED=2.3/1.5/1.5   
...289.748.47...9..........2..4......61.5.94......6..8..........1...36.263.128...   ED=2.3/2.3/2.3   
....8......4..5...97.6..8....8.1...3.61...94.7...9.2....2..4.31...5..6......2....   ED=2.5/1.2/1.2   
.........8.47.5.....3..1...29.4....3.6.8.2.4.7....6.18...9..7.....5.36.2.........   ED=2.5/1.5/1.5   
..........24..51..97.6.......8....633.18.29.774....2.......4.31..95..68..........   ED=2.6/1.2/1.2   
..6......8...35...97.6..8..........3.618.294.7..........2..4.31...57...2......4..   ED=2.6/1.5/1.5   
...........47..19.9.364..2..98.......6.8.2.4.......21..8..647.1.19..36...........   ED=2.8/1.2/1.2   
.....93...2.7351.6...6..8..........3.6.8.2.4.7..........2..4...4.9573.8...71.....   ED=3.0/1.2/1.2   
1.62..3.....7.........4.825.......6.3.1...9.7.4.......582.6.........3.....7..84.9   ED=3.2/1.2/1.2   
1...8..7..2..3...6...........8..756...18.29...453..2...........4...7..8..3..2...9   ED=3.4/1.2/1.2   
.........82.7...969.3.41...2........36.8.2.47........8...96.7.141...3.82.........   ED=4.2/1.2/1.2   
1.6.89.7...4..5.............98..7.6...........4.3..21.............5..6...3.12.4.9   ED=4.2/1.5/1.5   
.........8.4..5....7.6.18.529.....6.3..8.2..7.4.....185.29.4.3....5..6.2.........   ED=4.5/1.2/1.2   
1562..3......3...........2..98..7....6.....4....3..21..8...........7......7..8459   ED=4.5/1.5/1.5   
1..2..3.4.....5.....36......98..7.6...........4.3..21......47.....5.....6.7..8..9   ED=5.0/1.2/1.2   
.........8.47......7.6.1.25.9.....6.3..852..7.4.....1.58.9.4.3......36.2.........   ED=5.6/1.2/1.2   
...2.9.7.8.473..9.............4..5...6.8.2.4...5..6.............1..736.2.3.1.8...   ED=6.6/1.2/1.2   
1.62.........3.....7....8...9...7.63.6.8.2.4.74.3...1...2....3.....7.........84.9   ED=7.1/1.2/1.2   
.562..3......3....9..6....529.4.....3.......7.....6.185....4..1....7......7..845.   ED=7.1/2.3/2.3   
.........8.47...9...36418.........6.3.18.29.7.4.........29647...1...36.2.........   ED=7.2/1.5/1.5   
.56...3.....7.......3..1...29.4...6..6.8.2.4..4...6.18...9..7.......3.....7...45.   ED=7.3/1.2/1.2   
...........47..1...7...1.25..8.1...3.618.294.7...9.2..58.9...3...9..36...........   ED=7.3/1.5/1.5   
...........473......3.41.25.......6.3.18.29.7.4.......58.96.7......736...........   ED=7.5/1.2/1.2   
.........82.7...96.73.41...2........36.8.2.47........8...96.73.41...3.82.........   ED=7.6/1.2/1.2   
.5...93....47...............98....6.3.18.29.7.4....21...............36....71...5.   ED=8.3/1.2/1.2   
1.6.8..7..2.7.......36....5.9......3...8.2...7......1.5....47.......3.8..3..2.4.9   ED=8.4/1.5/1.5   
...........4.35...97.6..8...9....5...6.8.2.4...5....1...2..4.31...57.6...........   ED=9.0/1.2/1.2   


[Hajime]

Further I like symmetrical puzzle. They are always not minimal I presume.

May I remind you of

I loaded Mike's file in my site.

It can be down loaded from games_sample

I solved 26855 Sudoku's with an average solution time of 4.852 ms each (elapsed 2 minutes 10.29 seconds).

These puzzles from the Patterns Game are all symmetrical and all minimal, by definition.

Regards,

Mike

Oopsie daicy,
I did not know that those puzzles were minimal. Thanks Mike
I solved those puzzles with T&E brute force / back tracking. Because that is very fast.
When not using that method SiSeSuSo can solve puzzles up to a level what an XY chain is rated. About SE=7