The New Sudoku Players' Forum

[coloin]

I think its possible to be sure that the max is reached

Code: Select all

+---+---+---+
|987|645|32.|
|654|32.|...|
|32.|...|...|
+---+---+---+
|89.|...|...|
|4..|.7.|9..|
|...|...|.6.|
+---+---+---+
|73.|9..|6..|
|...|786|...|
|...|...|5..|
+---+---+---+


an advance ... done by removing and adding clues - the first 17 clues in this one cant be improved on

Code: Select all

98765432.65372.............79.8.56..26.4..89..........5...6.9.......7.4..........  coloin
98765432.65423.............42.38.6..8937..2.............259.83........5..........  JPF
98764532.6543.....32.......89...3.........68.4...7....73.9..86.............7..4..  coloin2
98765432.6543.....32.......89..6..........75.5...3....2..9..57.............2...4.  JPF2
98764532.65432....32.......89.......4...7.9.........6.73.9..6.....786.........5..  coloin3


but my best and possibly max puzzle has quite a nice shape and 34 clues and ends with a 7....

any ideas on the min lexing problem ? !

[JPF]

coloin3 is not greater than JPF2 and I added a new one JPF3:

Code: Select all

98765432.65372.............79.8.56..26.4..89..........5...6.9.......7.4..........  coloin
98765432.65423.............42.38.6..8937..2.............259.83........5..........  JPF
98764532.6543.....32.......89...3.........68.4...7....73.9..86.............7..4..  coloin2
98765432.6543.....32.......89..6..........75.5...3....2..9..57.............2...4.  JPF2
98764532.65432....32.......89.......4...7.9.........6.73.9..6.....786.........5..  coloin3
....^............................................................................ 
98765432.65432....32.......89.....3.......8...........76.2..5..2..97..........6..  JPF3


JPF

[coloin]

Yes a slight slip but it was showing the 2 @r2c5
but essentially you keep trying the biggest clues row by row
c3r456789and col 9 has to be empty

Code: Select all

98765432.65432....32.......89.56..3..4....25..............9.58......6..........9.  coloin4

[JPF]

Code: Select all

98765432.65432....32.......89.56..3..4....25..............9.58......6..........9.  coloin4
98765432.65432....32.......89.73..5..6....28..............4.83......5..........9.  JPF4


JPF

[coloin]

Code: Select all

+---+---+---+
|987|654|32.|
|654|32.|...|
|32.|...|...|
+---+---+---+
|89.|76.|...|
|...|...|69.|
|...|...|...|
+---+---+---+
|74.|.8.|96.|
|...|..5|47.|
|...|...|...|
+---+---+---+


Yes it keeps improving ... and maybe gets easier now - except ive found another improvement ... 33C puzzle ends in 5..8

[JPF]

You should post it.
I will try to improve it if it's possible!

JPF

[coloin]

Ok ... another leap to get to extend the pattern ....

Code: Select all

+---+---+---+       +---+---+---+
|987|654|32.|       |xxx|xxx|xx.|
|654|32.|...|       |xxx|xx.|...|
|32.|...|...|       |xx.|...|...|
+---+---+---+       +---+---+---+
|89.|576|4..|       |xx.|xxx|xx.|
|76.|.4.|8..|       |xx.|xxx|xx.|
|4..|.8.|.9.|       |x..|xxx|xx.|
+---+---+---+       +---+---+---+
|5..|.6.|.7.|       |x..|xxx|xx.|
|2..|7.5|.6.|       |x..|xxx|xx.|
|...|...|...|       |...|...|...|
+---+---+---+  35C  +---+---+---+   


It is clear that c9 and r9 and the remains of r3 and c3 have to be empty to allow minimality in r1,c1 and box 1.....

These two symmetrical ones seem worthy and show advancing....

Code: Select all

+---+---+---+          +---+---+---+     
|987|654|32.|          |987|654|32.|     
|654|32.|...|          |654|32.|...|     
|32.|...|...|          |32.|...|...|     
+---+---+---+          +---+---+---+     
|89.|74.|6..|          |89.|76.|...|     
|76.|2..|.3.|          |76.|4.5|...|     
|4..|...|.9.|          |4..|.8.|...|     
+---+---+---+          +---+---+---+     
|5..|9..|...|          |5..|...|.8.|     
|2..|.76|.8.|          |2..|...|47.|     
|...|...|...|          |...|...|...|     
+---+---+---+  32C     +---+---+---+  30C

Note it is/was not possible to insert a 5 at r6c1 [r6c12 is 14 pair] .....

...but it was a big step up to get to this one ...

Code: Select all

+---+---+---+
|987|654|32.|
|654|32.|...|
|32.|...|...|
+---+---+---+
|89.|765|4..|
|76.|4..|95.|
|.4.|9..|...|
+---+---+---+
|.7.|5..|.8.|
|...|.9.|57.|
|...|...|...|
+---+---+---+  34C

...and another final leap to get to....

Code: Select all

+---+---+---+
|987|654|32.|
|654|32.|...|
|32.|...|...|
+---+---+---+
|89.|765|4..|
|76.|4..|98.|
|4..|9..|...|
+---+---+---+
|5..|.9.|.6.|
|...|5..|8..|
|...|...|...|
+---+---+---+  33C


which very likely is the maximum. It is difficult to see how it can be made larger ...