Max number of clues 2

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

Postby Havard » Sun Aug 26, 2007 9:07 pm

from the SudokuArchitect team:

Code: Select all
..1.3764..........6.4.913.7..2..6..314..235.63...1542.2.5..97.441..72..5.7..5.26.
....3......36.7..16.4.913.75....3.2414..625.3..2..517.2.51764..4.6.29715........2


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Postby Mauricio » Sun Aug 26, 2007 9:10 pm

So they did exist, wow. Very nice findings.
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Postby gsf » Sun Aug 26, 2007 9:30 pm

Havard wrote:from the SudokuArchitect team:

nice job
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Postby coloin » Sun Aug 26, 2007 10:07 pm

Well done on the two 39s

I forgot to congratulate you for all your 38s

But I think this puts this subject to rest !

I was rather hoping that all the clues might have 2 solutions......

But no !

[Edit ....Every clue in both puzzles has 3 solutions !!!]
A glich in the dat file
Code: Select all
#1
3 sol.4 sol.5 sol.4 sol.4 sol.5 sol.3 sol.4 sol.15 sol.12 sol.
9 sol.7 sol.22 sol9 sol.3 sol.3 sol.4 sol.8 sol.8 sol.7 sol.10 sol.5 sol.
2 sol.4 sol.5 sol.3 sol.4 sol.4 sol.4 sol.5 sol.2 sol.11 sol.2 sol.
2 sol.9 sol.21 sol.2 sol.8 sol.14 sol.

#2
2 sol.2 sol.3 sol.2 sol.8 sol.9 sol.3 sol.4 sol.7 sol.39 sol.5 sol.6 sol.
3 sol.11 sol.12 sol2 sol.6 sol.3 sol.5 sol.19 sol.7 sol.3 sol.
6 sol.3 sol.38 sol.3 sol.5 sol.4 sol.3 sol.5 sol.2 sol.4 sol.
3 sol.7 sol.2 sol.4 sol.2 sol.5 sol.6 sol.

C
Last edited by coloin on Sun Aug 26, 2007 7:34 pm, edited 3 times in total.
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Postby gsf » Sun Aug 26, 2007 10:15 pm

coloin wrote:Every clue in both puzzles has 3 solutions !!!

do you mean: remove 1 clue, count the solutions => that clue has that many solutions
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Postby JPF » Sun Aug 26, 2007 10:25 pm

well done !

Here is my contribution ::)
Code: Select all
 
 *-----------*
 |..1|.37|64.|
 |...|...|...|
 |6.4|.91|3.7|
 |---+---+---|
 |..2|..6|..3|
 |14.|.23|5.6|
 |3..|.15|42.|
 |---+---+---|
 |2.5|..9|7.4|
 |41.|.72|..5|
 |.7.|.5.|26.|
 *-----------*

 *-----------*
 |...|.3.|...|
 |..3|6.7|..1|
 |6.4|.91|3.7|
 |---+---+---|
 |5..|..3|.24|
 |14.|.62|5.3|
 |..2|..5|17.|
 |---+---+---|
 |2.5|176|4..|
 |4.6|.29|715|
 |...|...|..2|
 *-----------*

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Postby udosuk » Mon Aug 27, 2007 7:52 am

Great going the SudokuArchitect team & Harvard. Please try to find a 40. It's the number of my favourite baseball player (for now)!:)
JPF wrote:Here is my contribution ::)
Code: Select all
 
 *-----------*
 |..1|.37|64.|
 |...|...|...|
 |6.4|.91|3.7|
 |---+---+---|
 |..2|..6|..3|
 |14.|.23|5.6|
 |3..|.15|42.|
 |---+---+---|
 |2.5|..9|7.4|
 |41.|.72|..5|
 |.7.|.5.|26.|
 *-----------*

 *-----------*
 |...|.3.|...|
 |..3|6.7|..1|
 |6.4|.91|3.7|
 |---+---+---|
 |5..|..3|.24|
 |14.|.62|5.3|
 |..2|..5|17.|
 |---+---+---|
 |2.5|176|4..|
 |4.6|.29|715|
 |...|...|..2|
 *-----------*

Umm... May I ask what are they different from the 2 grids above, except for the added symbols and layout? If so, I can make another "contribution":
Code: Select all
*--------------------------------------------------------------------*
| 589    2589   1      | 258    3      7      | 6      4      289    |
| 5789   23589  3789   | 24568  468    48     | 189    1589   1289   |
| 6      258    4      | 258    9      1      | 3      58     7      |
|----------------------+----------------------+----------------------|
| 5789   589    2      | 4789   48     6      | 189    1789   3      |
| 1      4      789    | 789    2      3      | 5      789    6      |
| 3      689    6789   | 789    1      5      | 4      2      89     |
|----------------------+----------------------+----------------------|
| 2      368    5      | 1368   68     9      | 7      138    4      |
| 4      1      3689   | 368    7      2      | 89     389    5      |
| 89     7      389    | 1348   5      48     | 2      6      189    |
*--------------------------------------------------------------------*

*--------------------------------------------------------------------*
| 789    125789 1789   | 2458   3      48     | 2689   45689  689    |
| 89     2589   3      | 6      458    7      | 289    4589   1      |
| 6      258    4      | 258    9      1      | 3      58     7      |
|----------------------+----------------------+----------------------|
| 5      6789   789    | 789    18     3      | 689    2      4      |
| 1      4      789    | 789    6      2      | 5      89     3      |
| 389    3689   2      | 489    48     5      | 1      7      689    |
|----------------------+----------------------+----------------------|
| 2      389    5      | 1      7      6      | 4      389    89     |
| 4      38     6      | 38     2      9      | 7      1      5      |
| 3789   13789  1789   | 3458   458    48     | 689    3689   2      |
*--------------------------------------------------------------------*

Well I guess the first one is a pretty big "pearl".:?:
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Postby coloin » Mon Aug 27, 2007 9:18 am

Final points tally for this thread, points allocated IMO according to the degree of difficulty. Bearing in mind at each stage it was felt that a bigger minimal puzzle was unlikely !

Code: Select all
dukuso   32 clues  1
Ocean    33 clues  10
Ocean    34 clues  100
Ocean    35 clues  1000
coloin   36 clues  100000
coloin   37 clues  10000000
ravel    38 clues  10000000000
Havard   39 clues  1000000000000000


For example a rough guess for the chances of finding a 39 clue minimal puzzle if there is only one of these in any one particular grid = 81! / [42!*39!] = 2^10^23

The clue frequency pattern is 66555520 in both, which is slightly tricky but not impossible to work out how many ways to do this and multiply by the number of grids !

Two very improbable finds I think

Well done again

C
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Postby JPF » Mon Aug 27, 2007 9:46 am

udosuk wrote:Umm... May I ask what are they different from the 2 grids above, except for the added symbols and layout?

Umm...:(
of course you may, but I don't understand why you ask as it seems that you already got the answer.

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Postby Ocean » Mon Aug 27, 2007 10:35 am

Havard wrote:from the SudokuArchitect team:

Code: Select all
..1.3764..........6.4.913.7..2..6..314..235.63...1542.2.5..97.441..72..5.7..5.26.
....3......36.7..16.4.913.75....3.2414..625.3..2..517.2.51764..4.6.29715........2


Havard


Very nice job!
Congratulations with the minimal 39s!

As illustrated by coloin, I was lucky to be in this business at the times when "life was easy":
coloin wrote:
Code: Select all
dukuso   32 clues  1
Ocean    33 clues  10
Ocean    34 clues  100
Ocean    35 clues  1000
coloin   36 clues  100000
coloin   37 clues  10000000
ravel    38 clues  10000000000
Havard   39 clues  1000000000000000
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Postby udosuk » Mon Aug 27, 2007 11:41 am

JPF wrote:
udosuk wrote:Umm... May I ask what are they different from the 2 grids above, except for the added symbols and layout?

Umm...:(
of course you may, but I don't understand why you ask as it seems that you already got the answer.

Sorry, I didn't mean to sound mean.:) I was just remotely hoping that you've found another 2 non-isomorphic 39-clue minimal grids through those #-on-#-off searches but has accidentally pasted the wrong grids (the original 2) onto here. Please pardon my unintentional meanness.
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Postby daj95376 » Mon Aug 27, 2007 3:16 pm

When I first became interested in Sudoku, it was often believed that finding a puzzle with fewer clues would result in a more difficult puzzle to solve. I believe that the collection of 17s has (in general) disproven that. Since you folks have been looking for puzzles with 32 clues and beyond, I don't recall any of the puzzles I tested as easy. What a dichotomy on expected vs. results when correlating number of clues to difficulty.

FWIW, both of the 39 puzzles are missing <8> as a clue. This approach was how I created the #E series fish puzzles. Now, it appears that the fish hunters have two new puzzles to tackle.

(Yes, I realize that there's only a small sampling for 32+ clues, but the USA advertising industry makes big $$$ each year off such statistics! Say, just how many classes of vehicles are there, because so many models seem to be tops in their class?)
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re: more clues does _not_ imply easier puzzles

Postby Pat » Mon Aug 27, 2007 3:54 pm

daj95376 wrote:When I first became interested in Sudoku, it was often believed that finding a puzzle with fewer clues would result in a more difficult puzzle to solve.

I believe that the collection of 17s has (in general) disproven that.

Since you folks have been looking for puzzles with 32 clues and beyond, I don't recall any of the puzzles I tested as easy.

What a dichotomy on expected vs. results when correlating number of clues to difficulty.



yes.

in 952 minimal 38s,
i saw only 4 Ulterior puzzles (and none that could be solved by "singles"),
with 262 puzzles gsf-rated above 94000.


kat (2005.Jul.21) wrote:as they get harder does it just mean that you are given less and less numbers to work it out from

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Postby ronk » Mon Aug 27, 2007 5:40 pm

daj95376 wrote:FWIW, both of the 39 puzzles are missing <8> as a clue. This approach was how I created the #E series fish puzzles. Now, it appears that the fish hunters have two new puzzles to tackle.

For the second 39-clue minimal, there are several fish at the outset.

Code: Select all
....3......36.7..16.4.913.75....3.2414..625.3..2..517.2.51764..4.6.29715........2

sashimi mutant x-wing: (8)r8c6\r1b8 plus fin r8c2, implies r1c2<>8 (2-stringed kite, turbot fish)
finned swordfish: (8)r358\c248 plus fin r5c3 implies r46c2<>8
finned swordfish: (8)r378\c248 plus fin r7c9 implies r9c8<>8
finned jellyfish: (8)c1567\r1269 plus fin r4c7 implies r6c9<>8
sashimi franken x-wing: (8)c69\r1b9 plus fin r9c6, implies r9c7<>8 (skyscraper, turbot fish)
sashimi franken swordfish (8)r38b6\c248 plus fin r4c7, implies r4c4<>8
sashimi mutant swordfish (8)b458\r69c4 plus fin r45c3, implies r9c3<>8

The above fish -- along with an opening single and a later locked candidate step -- advance the puzzle to this:
Code: Select all
 789   12579 1789  | 2458  3     48    | 2689  45689 689
 89    2589  3     | 6     458   7     | 289   4589  1
 6     258   4     | 258   9     1     | 3     58    7
-------------------+-------------------+------------------
 5     679   789   | 79    1     3     | 689   2     4
 1     4     789   | 789   6     2     | 5     89    3
 389   369   2     | 489   48    5     | 1     7     69
-------------------+-------------------+------------------
 2     39    5     | 1     7     6     | 4     389   89
 4     38    6     | 38    2     9     | 7     1     5
 3789  13789 179   | 3458  458   48    | 69    369   2
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Postby ravel » Sun Sep 09, 2007 2:40 pm

Late congratulations on your excellent work and the great finds of the two minimal 39's, Havard & Co!

Opposite to the 17 clue search, where we could be quite sure for almost 2 years, that no 16 would exist and which seems to go to an end now with an amount of about 50000 puzzles (or maybe 60000, not a big difference), this search is still open. Is there a 40 clue out there or even a 41 ?

I hope, you will provide us with more details of your search, which might help to estimate the chances.

2 weeks ago i thought, that a 40 clue search would not be realistic at all, also if done on very fast computers. But when i saw the amazing results by anon17 with an improved method for finding 17's, i changed my mind.

But of course the times are over, when you could write a program in a few days, run it on a 1.5 GHz notebook for some weeks (making slight improvements only) and find a new record. I do know, that my program would not have been good enough for finding a 39 in this time even on high speed cpu's.
Now its the time for professionals (or a genius) to make more progress.
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