The New Sudoku Players' Forum

[coloin]

I was surprised because there were sol counts so low below the 550

These patterns [by red ed and Serg] are proven invalid /impossible .... and maximal ... any further clue can give a valid puzzle

Code: Select all

 +---+---+---+    +---+---+---+
 |xxx|xxx|xxx|    |...|..x|..x|
 |xxx|...|xxx|    |...|..x|..x|
 |xxx|...|xxx|    |..x|..x|..x|
 +---+---+---+    +---+---+---+
 |x..|...|..x|    |...|xxx|xxx|
 |x..|.x.|..x| -> |...|xxx|xxx|
 |x..|...|..x|    |xxx|xxx|xxx|
 +---+---+---+    +---+---+---+
 |xxx|...|xxx|    |...|xxx|xxx|
 |xxx|...|xxx|    |...|xxx|xxx|
 |xxx|xxx|xxx|    |xxx|xxx|xxx|
 +---+---+---+    +---+---+---+   [morph]

so 6 clues are always needed for the 5 boxes

Code: Select all

+---+---+---+    +---+---+---+
 |xxx|xxx|xxx|    |...|..x|.xx|
 |xxx|...|xxx|    |...|..x|.xx|
 |xxx|...|xxx|    |...|..x|.xx|
 +---+---+---+    +---+---+---+
 |x..|...|.xx|    |...|xxx|xxx|
 |x..|...|.xx| -> |...|xxx|xxx|
 |x..|...|.xx|    |xxx|xxx|xxx|
 +---+---+---+    +---+---+---+
 |xxx|...|xxx|    |...|xxx|xxx|
 |xxx|xxx|xxx|    |xxx|xxx|xxx|
 |xxx|xxx|xxx|    |xxx|xxx|xxx|
 +---+---+---+    +---+---+---+ [morph] 

if empty box 1 we need 7 clues

plenty of new/old challenges here !! ask for pattens that dont have puzzles 2

[JPF]

Thanks for the link. I didn't see it.
It contains lots of interesting posts.

Back to the current challenge: 117 sol. seems to be the lower bound.

Now a question regarding B1B5B9 patterns :
There are 237083 B1B5B9 ed.subgrids.
The number of solutions varies from 95514 to 283576.

Code: Select all

+---+---+---+
|123|...|...|
|456|...|...|
|789|...|...|
+---+---+---+
|...|124|...|
|...|358|...|
|...|769|...|
+---+---+---+
|...|...|139|
|...|...|487|
|...|...|526|
+---+---+---+   95514 sol.


Code: Select all

+---+---+---+
|123|...|...|
|456|...|...|
|789|...|...|
+---+---+---+
|...|123|...|
|...|456|...|
|...|789|...|
+---+---+---+
|...|...|123|
|...|...|456|
|...|...|789|
+---+---+---+  283576 sol.


In the same veine, what is the minimum number of solutions for a pattern B1B5B9 + 2 clues?
I gave this example above:

Code: Select all

+---+---+---+
|123|...|...|
|456|...|7..|
|897|...|...|
+---+---+---+
|...|625|...|
|...|914|.2.|
|...|783|...|
+---+---+---+
|...|...|851|
|...|...|342|
|...|...|697|
+---+---+---+   23  sol.


JPF

[coloin]

Yes there are many challenges there

A few months ago as an exercise I generated all the B1B5B9 ....
....and eventually got them all

An overnight {+2} confirmed no valid puzzles with adding 2 clues ( no surprise)
Starting a {+3} , a few puzzles came out early on , so despite being hard to find they are not rare.
Update ... so an initial {+3} on the first 5% resulted in 32 27plus3 puzzles ... so possibly around 640 puzzles in total ...

23 sol seems rather good ....

[coloin]

Code: Select all

614......598......372.........612......834.2..6.975.........871......956......432   28 sol
294......635......871........3846......917......235...9.....276......498......351   29 sol
417......362......895...2.....638.1....245......917.........631......975......842   32 sol


having processed 1/3 of all the B159s and tried to add 3 clues , these were the +2s with the least solutions ...
these 200 puzzles would still be on course for 600 total therefore

[JPF]

Edit :
B1B5B9 + 3 clues: moved here
.......
For B1B5B9 + 2 clues, my conjecture is Min sol. = 23

JPF

[m_b_metcalf]

For B1B5B9 + 2 clues, my conjecture is Min sol. = 23

Best after 10 minutes' run:

Code: Select all

 1 2 3 9 . . . . .
 4 5 6 . . . 2 . .
 7 8 9 . . . . . .
 . . . 5 7 1 . . .
 . . . 6 4 3 . . .
 . . . 2 9 8 . . .
 . . . . . . 6 2 3
 . . . . . . 4 5 9
 . . . . . . 7 8 1         134 solution(s)

Regards,

Mike

[m_b_metcalf]

Really close:

Code: Select all

 1 2 3 8 . . . . .
 4 5 6 . . . 7 . .
 7 8 9 . . . . . .
 . . . 5 6 7 . . .
 . . . 4 1 9 . . .
 . . . 2 3 8 . . .
 . . . . . . 4 2 8
 . . . . . . 6 5 3
 . . . . . . 9 7 1    25 solution(s)

and friends:

Code: Select all

1238.....456...7..789.........567......419......238.........428......653......971 25                1
1238.....456...9..789.........569......427......138.........418......653......792 39                2
1238.....456...7..789.........567......439......128.........418......653......972 38                3
1238.....456...7..789.........567......439......281.........421......658......973 32                4
1238.....456...7..789.........547......639......218.........628......451......973 34                5
1238.....456...7..789.........567......439......218.........428......653......971 35                6
1238.....456...7..789.........567......419......238.........458......623......971 28                7
1237.....456...8..789.........568......419......273.........423......657......981 31                8
1237.....456...9..789.........569......418......273.........423......657......891 39                9
1238.....456...7..789.........547......619......238.........628......451......973 37                10
1238.....456...7..789.........657......439......218.........428......563......971 38                11
1238.....456...9..789.........569......437......218.........428......653......791 37                12
1238.....456...9..789.........569......417......238.........458......623......791 33                13
1238.....456...7..789.........657......419......238.........428......563......971 39                14
1238.....456...7..789.........567......218......439.........428......653......971 35                15
1238.....456...7..789.........567......419......283.........423......658......971 38                16
1238.....456...7..789.........567......419......238.........623......458......971 28                17