What is most solved cells with "n" clues?

Everything about Sudoku that doesn't fit in one of the other sections

Postby JPF » Tue Mar 24, 2009 3:42 am

Back to this challenge

Edited :

7 digits - 16 clues
Code: Select all
 *-----------*
 |...|...|...|
 |...|..1|.23|
 |.45|.6.|...|
 |---+---+---|
 |...|...|..1|
 |..6|5..|...|
 |2..|...|..7|
 |---+---+---|
 |...|...|5..|
 |.2.|...|4..|
 |1..|..7|...|
 *-----------*

solved to
 *-----------*
 |312|.7.|645|
 |.6.|451|723|
 |745|362|1..|
 |---+---+---|
 |5.4|723|.61|
 |.76|51.|234|
 |231|6.4|.57|
 |---+---+---|
 |4.3|1.6|572|
 |627|.35|41.|
 |15.|247|3.6|
 *-----------*     2 solutions

6 digits - 16 clues
Code: Select all
 *-----------*
 |...|...|...|
 |...|...|.12|
 |..3|..4|..5|
 |---+---+---|
 |...|...|..1|
 |..4|..6|...|
 |..6|.43|...|
 |---+---+---|
 |...|...|6..|
 |.5.|...|...|
 |21.|.5.|...|
 *-----------*

solved to
 *-----------*
 |..1|5.2|346|
 |465|3..|.12|
 |.23|164|..5|
 |---+---+---|
 |.32|..5|461|
 |5.4|.16|2.3|
 |1.6|243|5..|
 |---+---+---|
 |34.|.21|65.|
 |65.|43.|12.|
 |21.|65.|.34|
 *-----------*    24 solutions

5 digits - 15 clues
Code: Select all
 *-----------*
 |...|...|...|
 |...|...|.12|
 |...|.34|...|
 |---+---+---|
 |...|...|..3|
 |...|..3|4.5|
 |..1|...|...|
 |---+---+---|
 |...|1..|.2.|
 |.3.|2..|...|
 |45.|...|...|
 *-----------*

solved to
 *-----------*
 |..5|.21|.34|
 |.43|5..|.12|
 |21.|.34|.5.|
 |---+---+---|
 |5.4|..2|1.3|
 |.2.|.13|4.5|
 |3.1|45.|2..|
 |---+---+---|
 |...|145|32.|
 |13.|2..|54.|
 |452|3..|..1|
 *-----------*     1368 solutions

4 digits - 14 clues
Code: Select all
 *-----------*
 |...|...|...|
 |...|...|.12|
 |...|.34|...|
 |---+---+---|
 |...|...|..3|
 |...|2..|4..|
 |.13|...|...|
 |---+---+---|
 |...|.2.|...|
 |..4|...|3..|
 |.2.|1..|...|
 *-----------*

solved to
 *-----------*
 |...|.12|.34|
 |43.|...|.12|
 |2.1|.34|...|
 |---+---+---|
 |.42|..1|..3|
 |...|2.3|4.1|
 |.13|4..|2..|
 |---+---+---|
 |...|32.|14.|
 |1.4|...|32.|
 |32.|14.|...|
 *-----------*     2406720 solutions

JPF
JPF
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Postby ChPicard » Thu Mar 26, 2009 9:19 am

JPF wrote:5 digits - 15 clues
[code] *-----------*
|...|...|...|
|...|...|.12|
|...|.34|...|
|---+---+---|
|...|...|..3|
|...|..3|4.5|
|..1|...|...|
|---+---+---|
|...|1..|.2.|
|.3.|2..|...|
|45.|...|...|
*-----------*

solved to
*-----------*
|..5|.21|.34|
|.43|5..|.12|
|21.|.34|.5.|
|---+---+---|
|5.4|..2|1.3|
|.2.|.13|4.5|
|3.1|45.|2..|
|---+---+---|
|...|145|32.|
|13.|2..|54.|
|452|3..|..1|
*-----------* 1368 solutions

JPF


HI JPF

Royle spoke about a 15 given sudoku with only 596 completions. But I never see it.

ChPicard
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Joined: 02 March 2008

Postby JPF » Thu Mar 26, 2009 10:50 am

It has been brought back page 1 of the thread...

JPF
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Postby gsf » Thu Mar 26, 2009 11:04 am

just finished a run through all of the 15s in the 17s catalog (as of the start of the run)
15/33 is the best, although there could be a better 15 that is not a subpuzzle of a 17
Code: Select all
time g -go-2 -q- -e 'max(determined()+9-(%#vX))' -f'%v # %G %2(determined())x %#vX %#rn %#sn' g.dat
...................2...........5.4.7..8...3....1.9....3..4..2...5.1........8.6... # 15  3 9 1 715
.........4.........2...........5.4....8...3....1.9....3..4..2...5.1........8.6... # 15  3 8 2 2228
.......1.......................5.4.7..8...3....1.9....3..4..2...5.1........8.6... # 15 22 9 3 6759
.......134..2.................46.5...1......72..5.........31.........42.......... # 15 24 7 4 1304490
.......16.......4..5.2.....4...6.3........2......41......9..78.1................. # 15 29 9 5 2782241
.......16.......4..5.2.....4...6.3........2......41......5..79.1................. # 15 29 8 6 2834011
...34..6..17...............5.....69.3..1.7......8..............6...9............1 # 15 30 8 7 446839074
3.....4.......5.7.....1....8..3............5.............6..3.2.574.......1...... # 15 31 8 8 1469208900
3..6...........5.1......4..9......2........3..5..4.......3..98..4.........1...... # 15 33 8 9 1499083065


real    477h57m25.06s
user    466h59m58.61s
sys     1m38.70s

for comparison, here's the output from a run trough all the 16s from the 17s
Code: Select all
time g -go-1 -q- -e 'max(determined()+9-(%#vX))' -f'%v # %G %2(determined())x %#vX' g.dat
.........4.........2...........5.4.7..8...3....1.9....3..4..2...5.1........8.6... # 16  3 9
.......1.4.....................5.4.7..8...3....1.9....3..4..2...5.1........8.6... # 16 30 9
.......1.4.....................5.6.4..8...3....1.9....3..4..2...5.1........8.7... # 16 31 9
.......16.......4..5.2.....4...6.3.......52......41......9..78.1................. # 16 40 9
.......21.5.................7....89....2.1......4......3..9.5..1...3....4.....6.. # 16 44 9
....1...47......2.3.........8....2.....7...3..1............48.16.23.............. # 16 47 7
....4.2...36............1.....6.....2.....4.....7...8........375...1.......8...6. # 16 49 8
...6..74.8...5..........1......3...5.7........1.......3.2.........7..4..5..1..... # 16 51 8

real    36h26m26.85s
user    28h53m7.87s
sys     0m7.31s

in the grand unix tradition I've aliased my solver to an easier to type name (g for graph as in vertex+edge)
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Postby eleven » Sat Mar 28, 2009 12:44 am

JPF, congratulations for finding a second 16 clue puzzle with 2 solutions - at least 3 years after the first one was found.

It also is a good sample, that multi solution puzzles can be nice to solve:)
Code: Select all
+----------------+----------------+----------------+
| 3    1    2    | 89   7    89   | 6    4    5    |
|@89   6   #89   | 4    5    1    | 7    2    3    |
| 7    4    5    | 3    6    2    | 1   #89  @89   |
+----------------+----------------+----------------+
| 5    389  4    | 7    2    389  | 389  6    1    |
|@89   7    6    | 5    1    389  | 2    3-89 4    |
| 2    389  1    | 6    89   4    | 389  5    7    |
+----------------+----------------+----------------+
| 4    89   37   | 189  389  6    | 5    17   2    |
| 6    2    37   | 189  389  5    | 4    17  @89   |
| 1    5   @89   | 2    4    7    |#389 #389  6    |
+----------------+----------------+----------------+

r3c8 and r5c1 are a remote naked pair, so 89 can be eliminated from r8c8.
With another remote pair 89 you then can get to the "final" grid with 2 solutions.
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Postby JPF » Sat Mar 28, 2009 1:53 am

eleven wrote:JPF, congratulations for finding a second 16 clue puzzle with 2 solutions - at least 3 years after the first one was found.

Sorry to disappoint you, but the 2 puzzles are isomorphic:(

JPF
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Re: 12 or 13 givens, which solve more than 14 and 17

Postby olimpia » Sat Mar 28, 2009 5:35 pm

ChPicard wrote:ChPicard , modest discoverer of # 47742, 47743, 47782 and 48014 in the Royle's database.


Good work. I like to hear the news about more 17s being discovered! Its way more interesting than the (endless) search for prime numbers. When someone finds a new prime number its so big you can't even look at it (I think it would take a book just to print it). And then you can't do anything with it.

But the new 17s are a great achievement for humanity:!: . (Or at least for programmers and math people):D
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Improvement 13/19

Postby JPSangin » Fri Jul 16, 2010 7:17 pm

Hi

I found this one:

000000000000000001000002000000003020001000300004000000000010004020000030030040000

000000000
000000001
000002000
000003020
001000300
004000000
000010004
020000030
030040000

Which gives:

003001002002030001010002003000103420201000300304020010000310204420000130130240000

003001002
002030001
010002003
000103420
201000300
304020010
000310204
420000130
130240000

Best regards

JPS
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Re: What is most solved cells with

Postby olimpia » Wed Jul 28, 2010 11:46 pm

Good work! that improves the 13 clue starting grid by 2 more positions solved! After being idle for so long, its great to see someone who tested the limits, and cracked it!
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