No new 17s within {-2+2}

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Re: No new 17s within {-2+2}

Postby coloin » Mon Mar 31, 2014 11:35 am

champagne i'm sure that all your patterns will stem from the 15 puzzles/patterns i posted. Though - i looked at the asymmetric one and removed 9 clues - no resultant pattern satisfied the conditions
The point that maybe you are missing is that given the 2 diagonal clues in a box - this dictates where the third clue would be.
C
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Re: No new 17s within {-2+2}

Postby champagne » Mon Mar 31, 2014 12:11 pm

coloin wrote:champagne i'm sure that all your patterns will stem from the 15 puzzles/patterns i posted. Though - i looked at the asymmetric one and removed 9 clues - no resultant pattern satisfied the conditions
The point that maybe you are missing is that given the 2 diagonal clues in a box - this dictates where the third clue would be.
C


Hi coloin,

Could you clarify your point?

Here is the first pattern in the 72 patterns list

Code: Select all
1.. 1.. ...
.1. ... 1..
... .1. .1.

1.. ... ..1
..1 .1. ...
... ..1 1..

.1. ..1 ...
..1 ... .1.
... 1.. ..1


In each box, you can reorganize rows and columns to have a diagonal pattern, but I am not sure that you have one rows/columns valid permutation giving a diagonal pattern in each box.
As you can see, the pattern fits with the only constraint: max lexical starting by 1.. 1.. ...

EDIT : I pushed to the last pattern in the list


1..1.....
.1..1....
..1..1...
1.....1..
.1.....1.
..1.....1
...1..1..
....1..1.
.....1..1

Can not that one be derived from your 15 patterns??
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Re: No new 17s within {-2+2}

Postby coloin » Mon Mar 31, 2014 12:48 pm

The first pattern expands to this - which is in the 15 ......
Code: Select all
+---+---+---+
|1..|1..|..1|
|.1.|..1|1..|
|..1|.1.|.1.|
+---+---+---+
|1..|1..|..1|
|..1|.1.|.1.|
|.1.|..1|1..|
+---+---+---+
|.1.|..1|1..|
|..1|.1.|.1.|
|1..|1..|..1|
+---+---+---+

Code: Select all
+---+---+---+
|1..|1..|...|
|.1.|.1.|...|
|..1|..1|...|
+---+---+---+
|1..|...|1..|
|.1.|...|.1.|
|..1|...|..1|
+---+---+---+
|...|1..|1..|
|...|.1.|.1.|
|...|..1|..1|
+---+---+---+

There are multiple instances of this pattern in many perhaps [poss not the asmmetric one] of the 15 patterns......
certainly you can make some of the 15 patterns by filling in B3B5B7 with 3 staggered/diagonal clues [all ways] [6^3]

But yes i had overlooked the posssibility that there could be 3 clues still in a box.

There are obviously even less patterns which have row/column/box each with counts of 222222222
Added
In fact the first 18 patterns in the list are the ones which have 222222222 in all rows columns and boxes.
Hidden Text: Show
Code: Select all
1..1......1....1......1..1.1.......1..1.1.........11...1...1.....1....1....1....1
1..1......1....1......1..1.1....1.....1...1......1...1.1...1.....1....1....1....1
1..1......1....1......1..1.1...1......1.....1.....1.1..1.1.......1...1.......1..1
1..1......1....1......1..1.1...1......1.....1.....11...1...1.....1....1....1....1
1..1......1....1......1..1.1...1......1.....1.....11...1.1.......1....1......1..1
1..1......1....1......1..1.1...1......1...1.......1..1.1......1..1..1......1...1.
1..1......1....1......1..1.1...1......1...1.......1..1.1......1..11..........1.1.
1..1......1....1......1..1.1...1......1...1.......1..1.1.....1...1..1......1....1
1..1......1....1......1..1.1...1......1...1.......1..1.1...1.....1.....1...1...1.
1..1......1....1......1..1.1...1......1...1.......1..1.1...1.....1....1....1....1
1..1......1....1......1..1.1...1......1...1.......1..1.1.1.......1.....1.....1.1.
1..1......1....1......1..1.1..1.......1....1......1..1.1......1..1.1.........11..
1..1......1....1......1..1.1..1.......1....1......1..1.1....1....1.1.........1..1
1..1......1....1......1..1.1..1.......1....1......1..1.1...1.....1...1......1...1
1..1......1....1......1..1.1..1.......1...1.......1..1.1...1.....1.....1....1..1.
1..1......1....1......1..1.1..1.......1...1.......1..1.1...1.....1....1.....1...1
1..1......1....1......1..1.1..1.......1...1.......1..1.1..1......1.....1.....1.1.
1..1......1....1......1..1.1..1.......1...1.......1..1.1..1......1....1......1..1
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Re: No new 17s within {-2+2}

Postby Serg » Tue Apr 01, 2014 10:59 am

hi, champagne!
Your 72-patterns list looks quite reasonable. I am planning to write a program, generating "222222222" patterns (to cross-check your list), coming days. Unfortunately I don't see a way to calculate number of such patterns mathematically.

Serg
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Re: No new 17s within {-2+2}

Postby champagne » Tue Apr 01, 2014 2:08 pm

Serg wrote:hi, champagne!
Your 72-patterns list looks quite reasonable. I am planning to write a program, generating "222222222" patterns (to cross-check your list), coming days. Unfortunately I don't see a way to calculate number of such patterns mathematically.

Serg


I agree that effect of such "symmetries" is not easy to evaluate.
An independent generation will be welcome to check the file.

I started the 18 clues generation and so far, 2 patterns have been finished (a little more than one day for one pattern/core with my generation process).

I got one 17 clue already in the file. A kind of validation of the process. The pattern having the second puzzle should be finished soon.

I thought a little more about other starts in row 1. Even if we still have a "symmetry" reduction factor, the number of patterns will increase sharply. One possibility to consider is to use the 18 puzzles coming out of that process as seeds.
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Re: No new 17s within {-2+2}

Postby Serg » Fri Apr 04, 2014 7:25 am

Hi, champagne!
I cross-checked your 72-patterns list by writing generating program and confirm now correctness of your list.
It was very surprising for me that constraint "no minirow and no minicolumn may contain more than 1 clue" can decrease number of possible 18-clue patterns, containing 2 clues in every row and every column, from millions to 72 patterns only.

Serg
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Re: No new 17s within {-2+2}

Postby champagne » Fri Apr 04, 2014 8:15 am

Serg wrote:Hi, champagne!
I cross-checked your 72-patterns list by writing generating program and confirm now correctness of your list.
It was very surprising for me that constraint "no minirow and no minicolumn may contain more than 1 clue" can decrease number of possible 18-clue patterns, containing 2 clues in every row and every column, from millions to 72 patterns only.

Serg


Hi Serg,

Thank you for that check.
The generation process for the 18 clues is ongoing with till now the following partial results on the head part of the file :

11 patterns have been scanned (including the 2 patterns with known 17 clues puzzles)
The over all number of 18 clues puzzles is very small and 5 patterns gave no puzzle at all.
The generation uses now 7 cores and ongoing batches have a poor yield (empty till now for 4 of them).

The 72 patterns could be covered by the end of the next week.
Again, cross checking these results would be good at least on part of the 72 patterns.
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Re: No new 17s within {-2+2}

Postby Serg » Fri Apr 04, 2014 12:36 pm

Hi, champagne!
champagne wrote:The over all number of 18 clues puzzles is very small and 5 patterns gave no puzzle at all.

Please, publish five 18-clue patterns from your list, not having valid puzzles.

Serg
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Re: No new 17s within {-2+2}

Postby champagne » Fri Apr 04, 2014 2:46 pm

Serg wrote:Please, publish five 18-clue patterns from your list, not having valid puzzles.

Serg


Hi Serg,

Meantime, I have six. For these 6 patterns, my scan generator (a modified code starting from an existing process) did not find any 18 clues valid puzzle.
The patterns immediately following the 3 last in the global list seem to be dry as well, but the process is not over.

1..1......1..1......1...1..1......1...1..1.......1...1.1......1...1...1......11..
1..1......1..1......1...1..1......1...1.1.........1..1.1......1...1...1......11..
1..1......1..1......1...1..1....1.....1....1.....1...1.1......1...1..1.......1.1.
1..1......1..1......1...1..1....1.....1....1.....1...1.1.....1....1....1.....11..
1..1......1..1......1...1..1....1....1.....1....1....1..1.....1....1..1......11..
1..1......1..1......1...1..1...1.......1...1......1..1.1......1..1....1......11..
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Postby Afmob » Thu Apr 10, 2014 6:41 am

The following 55 patterns from the 72-list do not produce a valid puzzle
Code: Select all
1..1......1....1......1..1.1...1......1.....1.....1.1..1.1.......1...1.......1..1
1..1......1....1......1..1.1..1.......1....1......1..1.1....1....1.1.........1..1
1..1......1..1......1...1..1......1...1..1.......1...1.1......1...1...1......11..
1..1......1..1......1...1..1......1...1.1.........1..1.1......1...1...1......11..
1..1......1..1......1...1..1......1..1......1.....11....1..1......1....1....1..1.
1..1......1..1......1...1..1......1..1......1.....11....1..1......1...1.....1...1
1..1......1..1......1...1..1....1......1...1.....1...1.1......1..1....1......11..
1..1......1..1......1...1..1....1......1...1.....1...1.1.....1...1.....1.....11..
1..1......1..1......1...1..1....1.....1....1.....1...1.1......1...1...1......11..
1..1......1..1......1...1..1....1.....1....1.....1...1.1......1...1..1.......1.1.
1..1......1..1......1...1..1....1.....1....1.....1...1.1.....1....1....1.....11..
1..1......1..1......1...1..1....1.....1....1....1....1.1......1....1..1......11..
1..1......1..1......1...1..1....1.....1....1....1....1.1.....1.....1...1.....11..
1..1......1..1......1...1..1....1.....1....1....1....1.1.....1.....1.1.......1..1
1..1......1..1......1...1..1....1....1.....1.....1...1..1.....1...1...1......11..
1..1......1..1......1...1..1....1....1.....1.....1...1..1....1....1....1.....11..
1..1......1..1......1...1..1....1....1.....1.....1...1..1....1....1..1.......1..1
1..1......1..1......1...1..1....1....1.....1.....1...1..1...1.....1....1.....1.1.
1..1......1..1......1...1..1....1....1.....1....1....1..1.....1....1..1......11..
1..1......1..1......1...1..1....1....1.....1....1....1..1....1.....1...1.....11..
1..1......1..1......1...1..1....1....1.....1....1....1..1....1.....1.1.......1..1
1..1......1..1......1...1..1....1....1.....1....1....1..1...1......1...1.....1.1.
1..1......1..1......1...1..1....1....1.....1....1....1..1...1......1..1......1..1
1..1......1..1......1...1..1...1.......1...1......1..1.1......1..1....1......11..
1..1......1..1......1...1..1...1.......1...1......1..1.1.....1...1.....1.....11..
1..1......1..1......1...1..1...1.......1...1......1..1.1....1....1.....1.....1.1.
1..1......1..1......1...1..1...1......1....1......1..1.1......1...1..1.......1.1.
1..1......1..1......1...1..1...1......1....1......1..1.1.....1....1....1.....11..
1..1......1..1......1...1..1...1.....1.....1......1..1..1.....1...1...1......11..
1..1......1..1......1...1..1...1.....1.....1......1..1..1....1....1....1.....11..
1..1......1..1......1...1..1...1.....1.....1......1..1..1...1.....1....1.....1.1.
1..1......1..1......1...1..1..1.........1..1......1..1.1......1..1....1......11..
1..1......1..1......1...1..1..1.........1..1......1..1.1.....1...1.....1.....11..
1..1......1..1......1...1..1..1.........1..1......1..1.1.....1...1...1.......1..1
1..1......1..1......1...1..1..1.........1..1......1..1.1....1....1.....1.....1.1.
1..1......1..1......1...1..1..1.........1..1......1..1.1....1....1....1......1..1
1..1......1..1......1...1..1..1.......1....1......1..1.1......1....1..1......11..
1..1......1..1......1...1..1..1.......1....1......1..1.1.....1.....1...1.....11..
1..1......1..1......1...1..1..1.......1....1......1..1.1.....1.....1.1.......1..1
1..1......1..1......1...1..1..1.......1....1......1..1.1....1......1...1.....1.1.
1..1......1..1......1...1..1..1......1.....1......1..1..1.....1....1..1......11..
1..1......1..1......1...1..1..1......1.....1......1..1..1....1.....1...1.....11..
1..1......1..1......1...1..1..1......1.....1......1..1..1....1.....1.1.......1..1
1..1......1..1......1...1..1..1......1.....1......1..1..1...1......1...1.....1.1.
1..1......1..1......1...1..1..1......1.....1......1..1..1...1......1..1......1..1
1..1......1..1......1..1...1.....1...1.....1......1..1..1.....1...1...1.....1.1..
1..1......1..1......1..1...1.....1...1.....1......1..1..1.....1...1..1......1..1.
1..1......1..1......1..1...1.....1...1.....1....1....1..1.....1....1..1......11..
1..1......1..1......1..1...1.....1...1.....1....1....1..1.....1....1.1.......1.1.
1..1......1..1......1..1...1.....1...1.....1....1....1..1....1.....1...1.....11..
1..1......1..1......1..1...1.....1...1.....1....1....1..1...1......1...1.....1.1.
1..1......1..1......1..1...1.....1...1.....1....1....1..1...1......1..1......1..1
1..1......1..1......1..1...1.....1...1.....1...1.....1...1...1.....1...1.....11..
1..1......1..1......1..1...1.....1...1.....1...1.....1...1..1......1...1.....1.1.
1..1......1..1......1..1...1.....1...1.....1...1.....1...1..1......1..1......1..1
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Re: No new 17s within {-2+2}

Postby champagne » Thu Apr 10, 2014 7:24 am

Hi afmob,

So you got the same empty patterns and, clearly, you are ahead of me for the full process.

So far, I did not find a new 17. What about you?

Another interesting point will be to compare our lists of 18 ED puzzles coming out of that process.

I have currently 222 "18 clues" in the closed batches and a small number of other puzzles have been produced, but in ongoing runs.
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Postby Afmob » Thu Apr 10, 2014 9:02 am

I have a total of 283 ED puzzles (with 18 clues) but I haven't checked them for 17s since I'm only interested in analyzing patterns.
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Re:

Postby champagne » Fri Apr 11, 2014 11:57 am

Afmob wrote:I have a total of 283 ED puzzles (with 18 clues) but I haven't checked them for 17s since I'm only interested in analyzing patterns.


I have currently 272 "18 clues" puzzles including the 2 known 17. I doubt that a new 17 will be in the missing 11 "18 clues" puzzles.
My own generation will not be over before the beginning of the next week.
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Re: No new 17s within {-2+2}

Postby champagne » Tue Apr 15, 2014 6:12 am

I have now 283 "18 clues" and no new "17 clue"
Relying on afmob finished scan, we can say that there is no new "17" with the start 1.. 1.. in max lex canonical form.

If I stay in the same line, the next question should be

'is there a "17" with the start 1.. 1.. 1.. where no "17" has been identified so far.

I did not evaluate the number of patterns, but it should be many more than for the start 1.. 1..

The results of the scan of the 72 patterns (55 dry patterns out of the 72 and only 283 "18" puzzles in total) pushes to think of other investigations
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Re: No new 17s within {-2+2}

Postby coloin » Thu Apr 24, 2014 9:12 pm

Well done in completing that search. You have shown that there are no new 17s which have a maximum of 2 clues [ not 3] in all rows or columns or boxes in the puzzle.

Edit
unfortunatly it is not that easy - as usual
One would need to search all the max lex 18 clue patterns which begin with
11. ... ... and also max 2 clues in a box
one example ....
Code: Select all
+---+---+---+
|12.|...|...|
|...|34.|...|
|...|...|56.|
+---+---+---+
|7..|..1|...|
|..8|...|..2|
|...|.9.|..3|
+---+---+---+
|.4.|...|.9.|
|..5|...|8..|
|...|6.7|...|
+---+---+---+ 

which probably is a bigger task

If we were to find all known 17s [surely the objective of the thread ] .....

we would "simply" have to generate "all" the 9plus12s, 9plus13s and 9plus14s.
removing clues from the 9 to give 5plus12s, 4plus13s and 3plus14s.
posssibly all the 9plus14s are within a {-1+1] [?]

The 9 clues are either 9 clues in the first row or 9 clues in the central box

9plus12s are relatively remote - but this is not the case with 9plus13s ......
At the present time even adding 9plus11 clues is too big a task [ ? none exist] - even with reductions.
A clever way to do it might be out there

Avoiding dealing with 9plus15s would be a prerequisite / start ......

C
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