The New Sudoku Players' Forum

[coloin]

What do you mean by single maximal 3-rookery?

999...... - 27 clues with all 9 digits of the three clues ..... and actually 999221110 non-minimal puzzles are quite common !

looking at any non minimal puzzle with 999221110 the ...221110 clues tend to be essential .
There are many ways of removing clues to give a minimal puzzle but the minimal 666221110 wasn't very common

And of course the 19 clues with 543221110 is 61

Will update

[coloin]

Removing clues from a few of the 999911110 puzzles from Fruitless Sudoku Discoveries

I got these [ minimal !] puzzles

Code: Select all

....1.5246..7.....3..2..1......4......1..8..........32.2......1.4...13.....3.....   20      544311110  = 63
...5.4....12.63....7.....1.....2.184.....1.2.........3..1..2.4.4..3...........3..   21      644311110  = 64
...512.3..1.6....247.3.........2..1...1.48...2.......3.3......1.....14.........2.   22      654311110  = 66
...512.3..1.6.....4723.........2..1...1.482..........3.3......1.2...14.........2.   23      664311110  = 68
...513.2..126....347.2.........32.1...1.48...3.........2......1.....14........23.   24      665311110  = 71
...513.2..126....347.2.........32.1...1.483............2.3....1.3...14........2..   25      666311110  = 74
...513.24.126....3.7........3...2.1......8...4..1...32.234....1.4..21......3.....   26      666411110  = 78
...543.21..2.613...7.2...4...3...18..2..14.3.4.......2.34..2.1....1....3.........   27      666511110  = 82
...51......2.634..3742...1...3...184.......3.14......2.31..2...2..4..3..4..1..2..   28      666611110  = 86

I think it would be difficult to find these puzzles any other way !!

[JPF]

Removing clues from a few of the 999911110 puzzles
.....
I think it would be difficult to find these puzzles any other way !!

Well, I got better or equal results for a number of clues less than 23 clues.
see here. For 22 clues, I got the same minimal sum of digits = 66;

I did it using the good old method : {-a+b} x n , starting with 17 clues-puzzles.
I stopped at 22 clues when I saw your numbers. The process is awfully boring.

Note that one can have different distributions for the same minimal result:
For example: 22 clues ; minimal sum = 66

Code: Select all

......8...1.....2..32.....1...1.724......2.....5..3.1.2...6...34...1....1...5...2   663221110
......8...2.....1..41....32.....71....2..1.....3..4.2.1...3....6...2.....3..5..41   654311110


JPF

[dobrichev]

Removing clues from a few of the 999911110 puzzles from Fruitless Sudoku Discoveries
I got these [ minimal !] puzzles...

Hi Coloin,
Nice to see that 999911110 templates helped in this research.

Note that 2648603 out of 10989384471 templates were checked; ~ 1:4000.
So we can expect ~ 2*4000=8000 999911110 templates in total
A possible less resource-consuming approach for exhaustive search for wxyz11110 or even xyz111110 or xyz211110 distributions is by progressively expanding the smaller 999991110 to 999911110 and so on.

Note that one can have different distributions for the same minimal result:
For example: 22 clues ; minimal sum = 66

Code: Select all

......8...1.....2..32.....1...1.724......2.....5..3.1.2...6...34...1....1...5...2   663221110
......8...2.....1..41....32.....71....2..1.....3..4.2.1...3....6...2.....3..5..41   654311110


JPF

Right, but the digit distributions alone is sufficiently interesting problem and from this perspective the sum metric only adds noise

[coloin]

8000 999911110 templates in total

ah ... hmmmm ... so there are more ....
well from your two 5-rookeries/templates which solved in 4 clues - there were several ways to put in a reciprocal 4-rookery/template [ 75 of these 999911110 puzzles]
i removed clues from all of these and a 999211110 wasn't found .... so this isnt proven

in this thread , however, the next challenging puzzle to find [if anyone can be bothered] is to find a minimal 666621110

C

[JPF]

in this thread , however, the next challenging puzzle to find [if anyone can be bothered] is to find a minimal 666621110

Right.I'm still working on it, softly.
Looking at the chart here and the metric "sum", we could also find a minimal 19 clues 633221110

JPF

[coloin]

Code: Select all

+---+---+---+
|1.2|5..|...|
|...|...|3..|
|..4|1..|...|
+---+---+---+
|.1.|...|6.5|
|...|812|...|
|...|..4|...|
+---+---+---+
|...|...|.2.|
|.3.|..1|...|
|...|.37|..1|
+---+---+---+
633221110

[JPF]

well done!
JPF

[JPF]

in this thread , however, the next challenging puzzle to find [if anyone can be bothered] is to find a minimal 666621110

Code: Select all

 1 . . | . . 3 | 5 . .
 . . . | 2 . 1 | . 4 .
 . . 4 | . . 7 | . . 3
-------+-------+-------
 2 . . | 3 . . | 4 . .
 5 . 3 | 1 . 4 | 2 . .
 . . 1 | . 2 . | . 3 .
-------+-------+-------
 4 . . | . . . | 1 2 6
 . . 2 | . . . | . . .
 3 1 . | 8 . . | . . 4    Sum of values of 29 clues = 91 - distribution : 666621110



[speter]

G'Day Folks,

Yesterday I rewrote my puzzle hole puncher to emphasise the min-sum.
None of my results are spectacular, but I thought I'd post some.

Code: Select all

...............21.2....4....5..1..4..3.....6..128............3.6..1.35..4..2.71..  min-sum = 71, 21 clues, 543322110
...........1......2.3.1.6.....4...1....3..28..1.5...34..2.6.1...4....5..1...2...7  min-sum = 72, 22 clues, 643322110
.........2...3....4......2..3..2.1.........4..156..3......4...365.1....8....72..1  min-sum = 73, 21 clues, 444322110
................5321.........3..1.....485..........2...4....1...35.12.4.1...37.62  min-sum = 73, 22 clues, 544331110
..........32..4.1..1..23...........2....1..65..4..2.3.....5.8..1...6.4...2.7.1...  min-sum = 73, 22 clues, 553322110


As you can probably guess from the puzzles, my hole-puncher has a strong bias towards removing the initial numbers in the puzzle.

[JPF]

Hi speter,

Good start!
Some improvements have to be done though to get the current lowest min-sums. They are given here at the beginning of the thread.

my hole-puncher has a strong bias towards removing the initial numbers in the puzzle

No problem, here are equivalent puzzles:

Code: Select all

8..21.....1..5.4......3.6..2.7..4.1.1.3..6.5.......3....4..2.........12..........   min-sum=   71   21 clues, 543322110
831......2..6..51..4......7354.........1...62..........1....4.....31..2....2....1   min-sum=   72   22 clues, 643322110
831.........4..2......31...6.....42.5...13.......5....1...6.....47..2.3...2......   min-sum=   73   21 clues, 444322110
85.4.......13...........2...37.1..62.125.3.4......41......21..........53.........   min-sum=   73   22 clues, 544331110
84..........63.1.....5.2...56.1...2...7........1.2.43..1.........2...31.....4.2..   min-sum=   73   22 clues, 553322110



JPF

[JPF]

Code: Select all

 . . . | . . 1 | . . .
 . . . | 3 . 4 | . 2 .
 . . 2 | . . . | 5 4 1
-------+-------+-------
 3 . . | 1 . . | . 7 .
 8 . 1 | 4 . 2 | 3 . .
 . 2 . | 6 3 . | . 1 4
-------+-------+-------
 2 . . | . . . | 4 3 .
 . . 3 | . . . | . . 5
 1 4 . | 5 . . | . . 2    Sum of values of 30 clues = 96 - distribution : 666631110


JPF

[coloin]

Code: Select all

+---+---+---+
|...|..1|...|
|6..|3.4|.2.|
|..2|..7|541|
+---+---+---+
|3..|1..|...|
|..1|4.2|35.|
|.2.|83.|.14|
+---+---+---+
|2..|...|43.|
|..3|...|..5|
|14.|5..|..2|
+---+---+---+   Sum of values of 31 clues = 101 - distribution : 666641110


[coloin]

Code: Select all

+---+---+---+
|...|..1|...|
|...|3.4|62.|
|..2|...|541|
+---+---+---+
|3..|1..|...|
|..1|4.2|3..|
|52.|73.|.14|
+---+---+---+
|25.|...|43.|
|..3|...|..5|
|14.|5..|.82|
+---+---+---+    Sum of values of 32 clues = 106 - distribution : 666651110


[coloin]

Code: Select all

+---+---+---+
|...|.6.|...|
|.7.|..1|.23|
|..2|..3|..1|
+---+---+---+
|..4|.52|3..|
|..5|4..|.1.|
|.2.|138|.45|
+---+---+---+
|.4.|.25|1..|
|.5.|6.4|.3.|
|2.6|31.|.54|
+---+---+---+      Sum of values of 35 clues = 123 - distribution : 666663110