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

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

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

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
coloin

Posts: 1839
Joined: 05 May 2005

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

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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Joined: 05 May 2005

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

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

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

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
coloin

Posts: 1839
Joined: 05 May 2005

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

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

Code: Select all
`+---+---+---+|1.2|5..|...||...|...|3..||..4|1..|...|+---+---+---+|.1.|...|6.5||...|812|...||...|..4|...|+---+---+---+|...|...|.2.||.3.|..1|...||...|.37|..1|+---+---+---+633221110`
coloin

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

well done!
JPF
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### Re: Minimal value of the sum of the digits of a minimal puzz

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

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.
speter

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Joined: 30 March 2017

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

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.

you wrote: 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, 543322110831......2..6..51..4......7354.........1...62..........1....4.....31..2....2....1   min-sum=   72   22 clues, 643322110831.........4..2......31...6.....42.5...13.......5....1...6.....47..2.3...2......   min-sum=   73   21 clues, 44432211085.4.......13...........2...37.1..62.125.3.4......41......21..........53.........   min-sum=   73   22 clues, 54433111084..........63.1.....5.2...56.1...2...7........1.2.43..1.........2...31.....4.2..   min-sum=   73   22 clues, 553322110`

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

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

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

Posts: 1839
Joined: 05 May 2005

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

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

Posts: 1839
Joined: 05 May 2005

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

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`
coloin

Posts: 1839
Joined: 05 May 2005

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