The New Sudoku Players' Forum

[Serg]

Hi, blue!
Since we're talking about patterns maximality ...
F1 pattern has no valid puzzles. It is, at least, symmetrically maximal (I checked this property). But is it maximal in the strict sense? My old result - "Man" pattern has no valid puzzles - proves, that F1 pattern is just symmetrically maximal. Unfortunately there is no independent crosscheck of my result. Could you check, does "Man" pattern really have no valid puzzles?

Code: Select all

  "Man" pattern

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

Serg

[Afmob]

I can confirm that "Man pattern" has no valid puzzles. I had to check about 1.571e9 ED puzzles which took ~3 hours.

[blue]

I should have mentioned in my earlier post, that I had verified the "Man" pattern too -- timing similar to Afmob's.

Cheers.

[Serg]

Hi, Afmob and blue!
Thank you for your help!

Serg

[Serg]

Hi, people!
This is yet another fully symmetrical pattern having no valid puzzles. (Exhaustive search was done in 36 hours.)

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        F6

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

This pattern is symmetrically maximal (checked), but looks like not maximal in the strict sense (fast random search found no valid puzzles for some 1-clue extentions).

Serg

[Afmob]

I can confirm that F6 has no valid puzzles. I had to check 5.34e9 ED puzzles which took 10 hours.

[Serg]

Hi, Afmob!

I can confirm that F6 has no valid puzzles. I had to check 5.34e9 ED puzzles which took 10 hours.

Thank you for confirmation! Your searching program generates and checks 150000 puzzles per second. Impressive result!

This is another fully symmetrical invalid pattern. Exhaustive search took 33 hours.

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        F7

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

Serg

[Edited. I changed exhaustive search duration, because previous reported duration (2.7 hours) was wrong (partial but not exhaustive search was done because of a bug in searching algoritm).]

[Afmob]

The pattern has 64 automorphisms and I would need to check about 2.95e9 ED puzzles, so I guess it would take me about 6 hours to check your result. I'll later edit this post once the computation is done.

Edit: I can confirm that F7 has no valid puzzles. I had to check 2.95e9 ED puzzles (estimate was spot on!) which took 5 hours.

[Serg]

Hi!
This is the last fully symmetrical invalid pattern with 9 clues in the central box. Exhaustive search took 2.4 hours.

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        F8

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

Serg

[Afmob]

F8 has also no valid puzzles. I had to check 1.49e8 ED puzzles which took about 25 minutes.

[Serg]

Hi, Afmob!

F8 has also no valid puzzles. I had to check 1.49e8 ED puzzles which took about 25 minutes.

Thank you for confirmation!

Here are new potentially invalid patterns.

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        F9                   F10

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

Serg

[Edited. I changed "1" by "x" in the patterns F9 and F10 definitions to get more common "human" view.]
[Edited2. Comment: both patterns - F9 and F10 are subsets of F11 invalid pattern. So, it was a waste of time checking both patterns... I should be more careful.]
[Edited3. My searching algorithm for F9 and F10 patterns was not exhaustive, so I withdraw my results for these patterns.]

[Serg]

Hi!
This is the next candidate invalid pattern with 5 clues in the central box.

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       F11

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

Serg

[Edited. I've done ehaustive search for this pattern - no valid puzzles.]

[Afmob]

That took longer than I thought: F9 and F10 have no valid puzzles. I had to check 1.41e10 ED puzzles for F9 and 1.42e10 ED puzzles for F10 which took about 10 hours for each pattern. Note that the computation was done using a different, slower CPU. 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.

[Serg]

Hi!
This is the next fully symmetrical invalid pattern with 5 clues in the central box. Exhaustive search took 13.8 hours.

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       F12

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

Serg

[Afmob]

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.

Serg, do you have an estimate on how many patterns you have to analyze for this study?