The New Sudoku Players' Forum

[Afmob]

I haven't checked them for minimality but I have them listed and therefore saved.

[coloin]

Here is a valid minimal puzzle for the each of sixteen 20 clue valid patterns

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Pattern F34 - ....5.....12...84..3.....6....1.3...3.......7...6.7....6.....8..45...61.....2....
Pattern F35 - .4..2..1.7.......5..5...7.....1.2...6.......8...3.4.....7...9..8.......6.1..3..4.
Pattern F36 - 5...9...8.7.....1...6...7.....1.2...6.......7...3.4.....8...9...1.....4.7...5...6
Pattern F37 - ...6.7....6.....2...3...4..9...1...7...2.3...5...4...6..8...3...2.....4....7.5...
Pattern F38 - .1.2.3.4.6.......3.........4...8...6...9.1...7...5...8.........8.......7.2.1.9.3.
Pattern F39 - 1..2.3..4.8.....3..........9...5...1...4.6...2...8...6..........6.....5.7..3.1..2
Pattern F40 - ...8.2....6.....5...4...6..1..2.3..4.........4..5.8..7..5...7...7.....2....9.4...
Pattern F41 - ...7.1.....1.2.3...5.....4.5.......6.4.....5.9.......2.1.....6...6.9.7.....5.8...
Pattern F42 - ...8.1....1..2..3...9...7..8.......5.3.....2.7.......8..3...9...9..4..6....5.7...
Pattern F43 - ..12.34......1....7.......63.......8.6.....5.1.......78.......9....5......27.41..
Pattern F44 - .1.2.3.4.7...8...5.........9.......6.2.....3.5.......7.........1...7...8.4.1.6.9.
Pattern F45 - 1..2.3..4....1......6...8..2.......1.7.....6.3.......5..3...7......5....4..1.9..2
Pattern F46 - 1..2.3..4.2..8..6..........3.......5.7.....8.5.......1..........6..2..9.7..5.1..3
Pattern F47 - ...1.5.......7......2...8..3...4...5.1.3.9.2.7...6...1..6...7......1.......4.2...
Pattern F48 - ...5.8....6..2..3..........5...1...8.1.2.3.4.7...4...9..........2..6..1....7.5...
Pattern F49 - ...753.......1......9...4..3.......812.....347.......6..6...7......3.......528...

Code: Select all

F17plus1:   57 ED valid puzzles - all minimal
F18plus1:    7 ED valid puzzles - only 1 minimal
F20plus1:    2 ED valid puzzles - both non-minimal
F21plus1:  212 ED valid puzzles - 63 minimal
F26plus1: 2222 ED valid puzzles - 1828 minimal
F27plus1: 1893 ED valid puzzles - 1793 minimal

Puzzles from the six 21-clue patterns, 4392 total, 3742 minimal.

Edited - F38 F40 replaced

[Serg]

Hi, coloin!
Thank you for 20-clue puzzles examples and for 21-clue puzzles! It turns out, pattern "F17plus1" aka pattern F50 is minimal, i.e. removal of any 1 clue makes this pattern invalid (because all its puzzles are minimal).

Serg

[Serg]

Hi, all!
I confirm that patterns F13, F17 and F18 have no valid puzzles.

Serg

[Serg]

Hi, people!
I've done hard work searching for old examples for valid fully symmetrical patterns published before ("49 patterns list").
5 examples were found in inferior puzzles thread.
3 examples were found in The SUPERIOR thread.
1 example was found in the thread experiment.
24 examples were found in the thread Fully symmetrical puzzles.
1 example (Fractal Pattern) was copied from the thread Valid puzzles for Fractal Pattern.

Totally 34 old examples were found. Old examples for all 20-clue patterns from "49 patterns list" were found (16 patterns in total), so I can say, that this project didn't find any new valid fully symmetrical 20-clue patterns (all possible such patterns were discovered before). Here are authors of found examples: ab, Afmob, blue, gsf, JPF, Ocean, tarek. I used those examples for search space reduction, so these authors contribute a lot to this project.

Found examples are published in my post with valid fully symmetrical patterns ("49 patterns list").

Soon I'll publish "new examples" for remaining 15 valid patterns - I mean valid puzzles found in this project.

Serg

[coloin]

Repeatedly relabeling the 16 20-clue puzzles over the w-e gave these ED totals, which probably reflects > 95%

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Pattern F34     2427
Pattern F35      343
Pattern F36     3115
Pattern F37     1607
Pattern F38     xxxx
Pattern F39      565
Pattern F40        6
Pattern F41     3280
Pattern F42      223
Pattern F43       50
Pattern F44     4984
Pattern F45       28
Pattern F46      300
Pattern F47        5
Pattern F48       18
Pattern F49     7626

[Serg]

Hi, coloin!

Repeatedly relabeling the 16 20-clue puzzles over the w-e gave these ED totals, which probably reflects > 95%

Code: Select all

Pattern F34     2427
Pattern F35      343
Pattern F36     3115
Pattern F37     1607
Pattern F38     1357
Pattern F39      565
Pattern F40        6
Pattern F41     3280
Pattern F42      223
Pattern F43       50
Pattern F44     4984
Pattern F45       28
Pattern F46      300
Pattern F47        5
Pattern F48       18
Pattern F49     7626

I don't understand - what do you mean? Did you publish number of valid puzzles for corresponding patterns? Are these numbers exact or estimate?

Serg

[coloin]

Code: Select all

Pattern F34   2436
Pattern F35    442
Pattern F36   3115
Pattern F37   1607
Pattern F38   xxxx
Pattern F39    565
Pattern F40      6
Pattern F41   3340
Pattern F42    883
Pattern F43     78
Pattern F44   4984
Pattern F45     28
Pattern F46    300
Pattern F47      5
Pattern F48     18
Pattern F49   7840
             27125


Yes, these are the lower bounds of the count of ED puzzles with the 16 patterns , some patterns have closed at {-3+3}, but there may well be a few more.
I can update a result of the {-4+4} but maybe Afmob will have the exact counts before then

[Afmob]

I've got the following counts:

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Pattern F34   2438
Pattern F35    453
Pattern F36   3119
Pattern F37   1642
Pattern F38   1222
Pattern F39    565
Pattern F40      6
Pattern F41   3466
Pattern F42    912
Pattern F43    138
Pattern F44   4984
Pattern F45     55
Pattern F46    303
Pattern F47      5
Pattern F48     18
Pattern F49   7916


coloin, can you please check your puzzles for F38 since I've got a smaller count of ED puzzles? I will update the table once the computation for F40 and F49 has finished.

Edit: Done!

[coloin]

Yes, my F38 pattern was incorrect ... well done

[Serg]

Hi, all!
I've published examples for all 49 fully symmetrical valid patterns in my post dated by March 15, 2017 2:19 am.
I tried to find oldest examples for each pattern at this Forum.
Here is a copy of that examples list in the line form.

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....1.....79...54..5.....7....1.2...8.......1...5.7....6.....3..24...79.....9....   #F34 ab
.7..5..3.8.......9..6...5.....8.5...9.......2...4.3.....2...4..4.......8.5..3..7.   #F35 ab
7...2...9.6.....3...3...4.....3.8...9.......7...5.6.....9...7...5.....6.2...1...4   #F36 ab
...2.5....7.....4...9...3..2...7...1...8.3...1...9...5..4...8...8.....5....7.1...   #F37 ab
.2.5.8.1.7.......9.........5...6...4...3.2...6...9...3.........9.......7.8.2.1.3.   #F38 ab
3..4.5..7.2.....6..........5...1...9...6.8...9...7...4..........3.....2.4..9.7..5   #F39 tarek
...4.5....9.....8...7...4..3..9.8..6.........8..3.2..5..5...9...7.....4....5.1...   #F40 ab
...7.2.....2.4.6...6.....5.4.......9.1.....3.3.......7.8.....9...4.2.1.....5.3...   #F41 ab
...4.3....5..7..1...6...5..2.......7.7.....2.8.......3..4...3...6..2..5....7.8...   #F42 ab
..61.35......6....4.......22.......9.9.....4.3.......89.......1....5......56.73..   #F43 ab
.4.1.5.6.1...2...3.........3.......7.8.....4.9.......2.........2...1...9.5.4.7.8.   #F44 Ocean
1..7.2..3....3......9...5..3.......2.6.....9.4.......7..2...3......5....7..8.4..1   #F45 ab
3..9.8..1.2..7..8..........1.......3.5.....7.9.......6..........7..5..2.6..1.7..9   #F46 ab
...6.7.......1......3...4..6...9...8.7.8.2.1.1...5...3..5...7......2.......1.6...   #F47 JPF
...1.2....3..4..5..........2...6...7.6.4.5.8.7...8...9..........5..3..6....9.7...   #F48 Ocean
...234.......1......1...5..2.......636.....424.......7..5...8......4.......967...   #F49 Ocean
.8.6.3.9.1.......7.........6..7.9..4....3....2..5.8..1.........4.......2.3.9.5.7.   #F50 JPF
1..5.9..7.3.....4..........5..3.1..9....6....7..9.2..1..........8.....3.9..1.5..8   #F51 JPF
...2.6.......1......7...8..6..1.2..9.2..3..1.1..4.5..7..4...2......8.......6.1...   #F14 Afmob
...5.1....4..6..9..........5..9.3..8.9..4..2.1..8.7..5..........6..9..3....7.8...   #F52 ab
...4.7....9..5..3.....1....8.......4.65.4.91.7.......8....7.....1..9..6....2.8...   #F53 JPF
...623....5..4..8..........7.......389..5..743.......2..........6..8..9....472...   #F54 ab
17.....535.......6..2...8.....123......4.6......789.....8...9..6.......531.....64   #F55 Serg
.3..6..7.4.2...3.1.8.....4....6.2...8.......9...7.4....4.....3.9.7...6.5.1..2..9.   #F56 gsf
.29.5.41.4.......56.......9...1.2...9.......4...3.4...3.......62.......7.87.6.29.   #F57 Serg
56..2..4142.....95............7.3...1.......3...1.8............97.....6228..5..19   #F58 Ocean
.2..1..5.71.....46............123...9..4.6..7...789............64.....18.3..9..2.   #F59 Serg
17..3..286.......4............123...3..4.6..9...789............9.......672..1..85   #F60 Serg
37..1..898...6...7............1.2...59.....32...3.4............7...2...861..7..93   #F61 Serg
..2.4.8......1....6.......4...123...79.4.6.21...789...4.......7....6......5.3.2..   #F62 Serg
6...1...3....9......8...7.....123...13.4.6.78...789.....9...2......6....4...3...1   #F63 Serg
.1.2.3.4.7.......8..5...6..1..5.8..6.........4..3.2..9..8...4..2.......7.3.1.6.9.   #F64 Ocean
.9.5.1.3.26.....81.........7..3.8..2.........6..4.7..5.........32.....68.5.7.4.9.   #F65 Ocean
15.3.4.269.......7.........3..1.9..5.........6..7.5..1.........7.......952.6.1.43   #F19 coloin
...2.3....1..4..2.....1....1..3.2..4.52...76.7..8.5..3....2.....4..5..9....6.7...   #F66 Afmob
..32.74.....9.3...7.......887.....43.........46.....151.......4...8.9.....73.69..   #F67 JPF
4..3.1..5...4.2.....2...9..93.....56.........67.....23..1...8.....5.3...7..9.6..1   #F68 gsf
5..9.6..7.9.8.5.6..........83.....91.........61.....84..........8.6.9.5.7..1.4..6   #F69 ab
...1.2......3.4.....1.5.6..64.....38..8...9..73.....54..2.9.8.....4.7......8.1...   #F70 Serg
1..5.9..7...3.8.......6....56.....41..9...2..27.....63....2.......8.1...4..7.5..9   #F71 ab
.3.189.7.5.......6.........7..4.1..52.......46..9.7..3.........3.......1.9.652.8.   #F72 Ocean
3..456..1.1.....2..........1..7.2..62.......45..6.8..9..........6.....1.4..327..5   #F73 JPF
...187....2..9..7..........6..4.8..147.....358..3.1..9..........9..3..4....862...   #F74 Serg
...457....2.9.6.4..........96.....123.......854.....79..........7.2.1.9....635...   #F75 Ocean
4..123..5...4.5............56.....297.......328.....41............8.7...3..219..4   #F76 Serg
63.....197.9...3.2.8.....6....9.7.......8.......6.5....2.....8.4.3...7.617.....25   #F77 Serg
15.....6363.....82..7...5.....1.2.......9.......4.5.....9...3..81.....2674.....91   #F78 blue
587...9649.......86.......1...634......9.5......872...8.......61.......2729...143   #F79 Serg
.746.915.1.......65.......86..9.3..1.........4..1.7..33.......79.......4.824.563.   #F80 Serg

Serg

[Serg]

Hi, people!
I've done exhaustive search for patterns F20, F21, F22, F23, F26, F27 and can confirm that these patterns have no valid patterns.

So, I hope I managed to present a proof - each fully symmetrical pattern having valid puzzles is superset of 49 valid patterns list, each fully symmetrical pattern having no valid puzzles is subset of 25 invalid patterns list.

If someone wants to know - has given fully symmetrical pattern valid puzzles, he should check - is given pattern a subset of any pattern from "25 invalid patterns list". If it is a subset, given pattern has no valid patterns. Otherwise it has valid puzzles. Alternatively, one can check - is given pattern a superset of any pattern from "49 valid patterns list". If it is a superset, given pattern has valid patterns. Otherwise it has no valid puzzles.

That's all I want to say.

Serg

[blue]

Hi Serg,

Part 1:

So, I hope I managed to present a proof - each fully symmetrical pattern having valid puzzles is superset of 49 valid patterns list, each fully symmetrical pattern having no valid puzzles is subset of 25 invalid patterns list.

If someone wants to know - has given fully symmetrical pattern valid puzzles, he should check - is given pattern a subset of any pattern from "25 invalid patterns list". If it is a subset, given pattern has no valid patterns. Otherwise it has valid puzzles. Alternatively, one can check - is given pattern a superset of any pattern from "49 valid patterns list". If it is a superset, given pattern has valid patterns. Otherwise it has no valid puzzles.

To avoid (possible) confusion in the future, it might be good to explain things in a little more depth.
Missing in the "proof" that you mention, is anything explaining how it is, that every fully symmetric pattern, must either be a "subset" of one of the 25 (maximal) "invalid" patterns, or a "superset" of one of the 49 (minimal) "valid" patterns.

A game for you ... a "fun challenge", if you like : Explain how these two (valid) puzzles, fit into your outline ...

Code: Select all

. . . | 8 1 5 | . . .
. . . | 3 . 6 | . . .
. . 3 | . . . | 4 . .
------+-------+------
8 2 . | . . . | . 9 6
5 . . | . . . | . . 1
1 3 . | . . . | . 8 2
------+-------+------
. . 7 | . . . | 9 . .
. . . | 2 . 4 | . . .
. . . | 5 8 9 | . . .


4 7 . | . . . | . 5 3
2 . 5 | . . . | 8 . 7
. 3 . | . . . | . 6 .
------+-------+------
. . . | 5 7 2 | . . .
. . . | 4 . 3 | . . .
. . . | 1 8 9 | . . .
------+-------+------
. 8 . | . . . | . 7 .
3 . 2 | . . . | 9 . 8
1 6 . | . . . | . 3 4

Part 2:

I can confirm that these patterns have no puzzles: F6-8,F11-13,F17,F18,F20-24,F26,F27.
For my part, that means I'm (now) a 2nd(3rd?) source of (complete) confirmation of your list of 25 invalid patterns.
I used testing similar to Afmob's ... checking all "ED" puzzles, having the given pattern, for being "valid".
With the exception of pattern "F11", my results were identical to Afmob's, and the timings were similar.

For "F11", Afmob wrote:

I think F11 will take at least 24 hours using my approach even though there are a lot of invalid puzzles (e.g. having no solution). Sadly, I don't have my estimation programm on this PC, so it's hard to guess how long it would actually take.

And later ...

I can confirm that F11 has no valid puzzles. I had to check 4.2e9 ED puzzles which took about 10 hours though I added some lines to my otherwise general code for this pattern to filter out invalid puzzles, otherwise it would have taken too long.

For that one, I only covered 2,950,603,794 "ED puzzles".
In theory, they were the "ED" puzzles, that could not be deemed to be "invalid, a priori", due to fewer than 4 digits still having candidates in the (4) empty cells in box 5.

That's the "short version" of the theory/story. The actual code, didn't function as might be imagined, given that description.
FWIW: I expected to match Afmob's "ED count", and when I didn't, I reviewed the code for bugs. It (still) seems to be correct.

Cheers,
Blue.

[Afmob]

Hi blue,

I will later (my CPU cores are currently busy with F78) repeat my checking of F11 using additional filtering. I don't have the added code anymore, so I can repeat this with a fresh mind. It could definitely be that I missed some a priori invalid configurations, so I doubt that your count is wrong. The general idea would be the following:

Check whether the clues of this subpattern

Code: Select all

F11 subpattern

. . . . x . . . .
. . . . x . . . .
. . . . x . . . .
. . . x . x . . .
x x x . x . x x x
. . . x . x . . .
. . . . x . . . .
. . . . x . . . .
. . . . x . . . .


allow for at least one solution. If yes, then add other 8 clues (in the corners), check automorphisms of pattern F11 and then check if the puzzle has a unique solution.

[Serg]

Hi, blue!
I am glad to see your "checking out" my results!

To avoid (possible) confusion in the future, it might be good to explain things in a little more depth.
Missing in the "proof" that you mention, is anything explaining how it is, that every fully symmetric pattern, must either be a "subset" of one of the 25 (maximal) "invalid" patterns, or a "superset" of one of the 49 (minimal) "valid" patterns.

I know the only way to check - is every fully symmetric pattern a subset of one of the 25 invalid patterns or a superset of one of the 49 valid patterns. I mean to do filtering 6016 ED fully symmetric patterns by those 2 sets. I've done filtering (by own filtering program) and found nothing after filtering. So, I can state that every fully symmetric pattern is "subset" or "superset".

A game for you ... a "fun challenge", if you like : Explain how these two (valid) puzzles, fit into your outline ...

Code: Select all

. . . | 8 1 5 | . . .
. . . | 3 . 6 | . . .
. . 3 | . . . | 4 . .
------+-------+------
8 2 . | . . . | . 9 6
5 . . | . . . | . . 1
1 3 . | . . . | . 8 2
------+-------+------
. . 7 | . . . | 9 . .
. . . | 2 . 4 | . . .
. . . | 5 8 9 | . . .


4 7 . | . . . | . 5 3
2 . 5 | . . . | 8 . 7
. 3 . | . . . | . 6 .
------+-------+------
. . . | 5 7 2 | . . .
. . . | 4 . 3 | . . .
. . . | 1 8 9 | . . .
------+-------+------
. 8 . | . . . | . 7 .
3 . 2 | . . . | 9 . 8
1 6 . | . . . | . 3 4

Your first pattern is superset of F49 pattern (one should swap rows r4/r5 and columns c4/c5 of F49 to get evident subset of your pattern).
I need some time to process your second pattern.

I can confirm that these patterns have no puzzles: F6-8,F11-13,F17,F18,F20-24,F26,F27.
For my part, that means I'm (now) a 2nd(3rd?) source of (complete) confirmation of your list of 25 invalid patterns.

Glad to see your confirmation, it's very important for me.

Serg

[Edited. I corrected a typo.]