SF Grid Has Exactly 29 17s

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SF Grid Has Exactly 29 17s

Postby Moschopulus » Tue Aug 22, 2006 11:23 am

There is a new faster version of checker available now, and using it we have searched the SF grid completely for 17-clue puzzles. The total number found was 29. gfroyle found 29 so this means he found all of them (which everyone suspected).

The old checker estimated the search of SF for 17s would take several months. With the new checker it took 6 days.

I picked a random grid from gfroyle's list
286537941541982736379614258917358624452176893863429517625743189194865372738291465
and searched it for 17s and found exactly one:
000000041500900000070600000000350600402000000800000000000040080090000300030000000
The search took 3 hours 20 minutes.
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Postby ronk » Tue Aug 22, 2006 11:48 am

For those of us that don't know, what does SF stand for?
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Postby udosuk » Tue Aug 22, 2006 12:13 pm

ronk wrote:For those of us that don't know, what does SF stand for?

As the #1 poster of this forum, you should know this Strangely Familiar solution grid which produces 29 17-clue puzzles, a hot topic this time last year...

As the #2 poster (for now) I think I should be the one to tell you...:)
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Postby JPF » Tue Aug 22, 2006 6:13 pm

In the Gordon’s list, are there other “strange grids” (i.e. containing more than one 17s) ?
In which case one could make the same test on them.

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Postby coloin » Tue Aug 22, 2006 6:31 pm

I am sure Mosch's computor is whirring !

Was it RW's spot on the missing unavoidable that speeded it up - or have you tweaked it some more ?

I note the MCN stayed at 9.

C
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Postby Moschopulus » Wed Aug 23, 2006 12:43 am

ronk wrote:For those of us that don't know, what does SF stand for?

Yes, Strangely Familiar. It appeared in the sudoku article in June 2006 Scientific American (in two different, but equivalent, forms).


JPF wrote:
In the Gordon’s list, are there other “strange grids” (i.e. containing more than one 17s) ? In which case one could make the same test on them.


I ran numbers 2 and 3 of the top 5. Number 2 is
873692451649517328521348976132976845498125637765483192954761283386254719217839564
gfroyle found: 20 17-clue puzzles
checker found: 20

Number 3 is:
438926751796451382251738469123687945647593218589214673362175894914862537875349126
gfroyle found: 14
checker found: 14

coloin wrote:Was it RW's spot on the missing unavoidable that speeded it up - or have you tweaked it some more ?

No, it was tweaked some more. The improvement for small MCN grids is huge.
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Postby coloin » Wed Aug 23, 2006 1:42 am

Excellent - mind you we need it !

Remember this post ?
dukuso wrote:well, what I called the "most canonical" sudoku-grid 3 posts ago,
isn't really most canonical, I think now.
It's used in the NP-complete proof and it's so cyclical,
but it uses gangsters : 1,1,1 - 42,42,42 , while this one:

123456789
456789123
789123456
231564897
564897231
897231564
312645978
645978312
978312645

uses gangsters 1,1,1 - 1,1,1 so I think it's the most canonical.
It could also be the one requiring the most clues, since gangster1
stands for 1728 bands, the most of all gangsters.

So now I tested whether there is a 18-clues sudoku whith that
grid as unique solution.
18 clues are required at least, as we have seen before
and these must be arranged such that 2 clues solve each of the
18 3*3 latin subsquares.
This gives only 1296 possible configurations of the 18 clues
and none of them give a sudoku with unique solution.
We have :
18 configurations with 413108 solutions
108 configurations with 141917 solutions
36 configurations with 47479 solutions
18 configurations with 44148 solutions
162 configurations with 41224 solutions
162 configurations with 22245 solutions
18 configurations with 16740 solutions
324 configurations with 15156 solutions
162 configurations with 9258 solutions
108 configurations with 4914 solutions
162 configurations with 411 solutions
18 configurations with 96 solutions

it seems that we have 18-fold symmetry here.

With 19 clues however there are uniquely solvable sudokus
over this grid.

.........
..6.8.1..
7....3.52
..1.6.8..
.....7.3.
...2.....
3....5.7.
.4.......
..8...6..


Well I checked it out as I couldnt find ANY 19s in the grid with checker - [I ran it for 2% there should be 648 morphs of the one puzzle "supposedly" found originally.

Code: Select all
+---+---+---+
|...|...|...|
|..6|.8.|1..|
|7..|..3|.5.|
+---+---+---+
|..1|.6.|8..|
|...|..7|.3.|
|...|2..|...|
+---+---+---+
|3..|..5|.7.|
|.4.|...|...|
|..8|...|6..|
+---+---+---+ this is one of the 411 solutions.....it.needs 3 clues to complete.


Im not sure this grid has a 19 now.......

C
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Postby Moschopulus » Thu Aug 24, 2006 8:48 am

I see what you mean. This puzzle
...........6.8.1..7....3.5...1.6.8.......7.3....2.....3....5.7..4.........8...6..
has 411 solutions. dukuso added one clue
...........6.8.1..7....3.52..1.6.8.......7.3....2.....3....5.7..4.........8...6..
to get a puzzle that does indeed have one solution, but the solution is not the canonical grid that he started with.

None of us must have checked that at the time (dukuso has very good credibility).

So the question is still open:

Does the canonical grid

123456789
456789123
789123456
231564897
564897231
897231564
312645978
645978312
978312645

have a puzzle with 19 clues?
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Postby Moschopulus » Thu Aug 24, 2006 8:53 am

Just for the record, I ran another grid chosen at random (well, not quite!):

937612458854937261126584397341758629672149583589263714213876945768495132495321876

Checker did a complete search for puzzles with 17 clues and found 6:

000010400800000060000500000041050000070000083000000000200806000060000100000300000
000010400800007060000500000041050000000000083000000000200806000060000100000300000
007010400800000060000500000041050000000000083000000000200806000060000100000300000
000010400800000060000500090041050000000000083000000000200806000060000100000300000
000010400800000060000500000041750000000000083000000000200806000060000100000300000
000010400800000060000500000041050000000000083000000700200806000060000100000300000

Gordon would have found all of these, particularly since they are close to each other.
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Postby coloin » Fri Aug 25, 2006 7:20 am

Excellent, so you have tweaked checker....you can search an MCN 9 grid for a 17 in 6 days !

Edit I see you have upgraded the download

Code: Select all
Gordon would have found all of these, particularly since they are close to each other.

yes, assuming that you used a puzzle/grid from "the list"

These two canon grids have been puzzling me
Code: Select all
+---+---+---+
|123|456|789|
|456|789|123|
|789|123|456|
+---+---+---+
|231|564|897|
|564|897|231|
|897|231|564|
+---+---+---+
|312|645|978|
|645|978|312|
|978|312|645|
+---+---+---+

+---+---+---+
|123|789|456|
|456|123|789|
|789|456|123|
+---+---+---+
|231|564|897|
|564|897|231|
|897|231|564|
+---+---+---+
|312|645|978|
|645|978|312|
|978|312|645|
+---+---+---+


One was said to have an 19 the other only a 20
But they have the same bands ! [using index416.exe]. But they are different grids......[?]

The first has a 648 symmetry property - so I should have found one with my search. I will try with new checker.

Edit - instead of 500 days - it is now an everdecreasing 4 days and 5 hours ! - sacra bleu encredable !

C
Last edited by coloin on Fri Aug 25, 2006 10:59 am, edited 2 times in total.
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Postby fermat » Fri Aug 25, 2006 7:41 am

udosuk wrote:
ronk wrote:For those of us that don't know, what does SF stand for?

As the #1 poster of this forum, you should know this Strangely Familiar solution grid which produces 29 17-clue puzzles, a hot topic this time last year...

As the #2 poster (for now) I think I should be the one to tell you...:)


For those of us really dumb, what is this thread about?
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Postby udosuk » Fri Aug 25, 2006 1:41 pm

fermat wrote:what is this thread about?

Minimum number of clues

Perhaps I shouldn't reply since I think nobody here is "really dumb"...:!:
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