## What is most solved cells with "n" clues?

Everything about Sudoku that doesn't fit in one of the other sections
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
2017 Supporter

Posts: 3903
Joined: 06 December 2005
Location: Paris, France

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
ChPicard

Posts: 16
Joined: 02 March 2008

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

JPF
JPF
2017 Supporter

Posts: 3903
Joined: 06 December 2005
Location: Paris, France

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 4468390743.....4.......5.7.....1....8..3............5.............6..3.2.574.......1...... # 15 31 8 8 14692089003..6...........5.1......4..9......2........3..5..4.......3..98..4.........1...... # 15 33 8 9 1499083065real    477h57m25.06suser    466h59m58.61ssys     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 8real    36h26m26.85suser    28h53m7.87ssys     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)
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

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.
eleven

Posts: 2280
Joined: 10 February 2008

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
JPF
2017 Supporter

Posts: 3903
Joined: 06 December 2005
Location: Paris, France

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

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)
olimpia

Posts: 35
Joined: 14 November 2008
Location: USA

### Improvement 13/19

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
JPSangin

Posts: 6
Joined: 10 July 2010

### Re: What is most solved cells with

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!
olimpia

Posts: 35
Joined: 14 November 2008
Location: USA

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