Minimal value of the sum of the digits of a minimal puzzle

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Re: Minimal value of the sum of the digits of a minimal puzz

Postby coloin » Tue Apr 11, 2017 7:57 am

JPF wrote: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
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Re: Minimal value of the sum of the digits of a minimal puzz

Postby coloin » Wed Apr 12, 2017 7:38 pm

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 !!
coloin
 
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Re: Minimal value of the sum of the digits of a minimal puzz

Postby JPF » Wed Apr 12, 2017 11:10 pm

coloin wrote: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
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Re: Minimal value of the sum of the digits of a minimal puzz

Postby dobrichev » Tue Apr 18, 2017 11:16 am

coloin wrote: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.

JPF wrote: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 ;)
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Re: Minimal value of the sum of the digits of a minimal puzz

Postby coloin » Tue Apr 18, 2017 11:47 am

dobrichev wrote: 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
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