How many 1-clue-box and 2-clue-box? : General

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Re: How many 1-clue-box and 2-clue-box?

by coloin » Tue Sep 20, 2022 2:02 pm

Code: Select all: +---+---+---+ |...|...|12.| |...|...|456| |...|...|789| +---+---+---+ |618|735|...| |34.|.21|...| |5.2|6.4|...| +---+---+---+ |8..|3.7|...| |1..|.58|...| |753|162|...| +---+---+---+ minimal 34 clues 26plus8

There are a few 27plus7 puzzles so perhaps a 35C 27plus8 cant be ruled out, but not holding breath either ! ...

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Re: How many 1-clue-box and 2-clue-box?

by m_b_metcalf » Wed Sep 21, 2022 7:52 am

Well done! I've pulled the plug on my search now.
Mike

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Re: How many 1-clue-box and 2-clue-box?

by blue » Sat Sep 24, 2022 10:39 pm

I've competed some exhaustive testing work, on the "B1269 empty, minimum clue count" problem.

Part 1, verified that no 19 clue puzzles exist, and allowed collecting all of the 20c puzzles with >= 6 clues in box 3.
Part 2, collected all of the 5plus15 puzzles -- 306 of them, in the end.

Part 1, started by producing all of the 9plus14 (and 9plus13) puzzles.
No 9plus12s or smaller were found.
There were 116 9plus13's, and 561204 9plus14s (including 2615 non-minimals).

In minimalizing the "9plus14" cases, 139 7plus13 and 2764 6plus14's were produced.
No 19c puzzles, and no 20c 8plus12s were found.

With at least 5 clues required in B3, if a 19c puzzle existed, it would have extension to a (non-minimal) 9plus14.
Since no 9plus14 puzzle reduced to a 19c, no 19s exist.

The final counts for 20c puzzles were:

Code: Select all: 5+15 : 306 6+14 : 2764 7+13 : 139 8+12 : 0 total: 3209

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coloin wrote:So - I found 114 9plus13s - [ with x9 = 1036 8plus13s, ands only 138 7plus13s - which were all minimal] - this could well be approaching the total.

Pretty close !

Along the way over 2500 6plus14s and 171 5plus15s [all minimal] puzzles were collected - and this is still expanding as - the search space is significantly larger still

That was > 90% of the 6plus14s, with a way to go, still, on the 5plus15s.

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Re: How many 1-clue-box and 2-clue-box?

by Serg » Sun Sep 25, 2022 9:16 am

Brilliant blue!
Great work, as usual!
How many ED 20-clue patterns did you find?
Please, describe in more details the step

blue wrote:Part 1, started by producing all of the 9plus14 (and 9plus13) puzzles.
No 9plus12s or smaller were found.

In what way did you produce all of the 9plus14 (and 9plus13) puzzles?

Serg

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Re: How many 1-clue-box and 2-clue-box?

by coloin » Sun Sep 25, 2022 11:48 am

Excellent blue and thanks for confirming I was just one puzzle out !!
The more amazing part would be to know how to chose the 13 clues out of the 36 in B4578 in each valid B34578. [ and 14 and 15 !!]

though I am pretty sure that you didnt add 11 clues to B4578

Code: Select all: +---+---+---+ |...|...|123| |...|...|456| |...|...|789| +---+---+---+ |...|..1|...| |...|...|...| |...|...|...| +---+---+---+ |..1|...|...| |...|...|...| |...|...|...| +---+---+---+ add 11 clues !!!

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Re: How many 1-clue-box and 2-clue-box?

by JPF » Sun Sep 25, 2022 4:29 pm

Well done!, of course.
Finding all the solutions to a problem has the disadvantage of having to answer many questions...

I only found three 21Cs B1269=0 having a box with only one clue.
Here are mine :

Code: Select all: .......12......345......67......1.......82.....56......9.7.....28.5.....61.34.... .......12......345......67......1.......82.....57......9.6.....28.5.....71.34.... .......12......345......67......1.......82.....57......9.3.....28.5.....71.64....

Are there others?

JPF

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Re: How many 1-clue-box and 2-clue-box?

by blue » Sun Sep 25, 2022 7:11 pm

JPF wrote:Finding all the solutions to a problem has the disadvantage of having to answer many questions...

Yeah, I suppose so

I only found three 21Cs B1269=0 having a box with only one clue.
(...)
Are there others?

My 21c list is only complete for 14 clues or less in B4578.
It has your 3 puzzles, and one more. I think this is the morph with the shape, that's closest to the other three.

Code: Select all: .......12......345......67....4.6.......21.....3.......1..4....59.8.....2.835....

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Serg wrote:How many ED 20-clue patterns did you find?

956 patterns ... one with 180 degree rotational symmetry (2 puzzles), and 7 with diagonal reflection symmetry (18 puzzles).
This shape has 7 puzzles (the max, for the 8 patterns):

Code: Select all: +-----+-----+-----+ | ... | ... | xxx | | ... | ... | .xx | | ... | ... | ..x | +-----+-----+-----+ | xxx | ... | ... | | x.. | x.. | ... | | ... | xx. | ... | +-----+-----+-----+ | .xx | ..x | ... | | ..x | ..x | ... | | ... | .xx | ... | +-----+-----+-----+

Last edited by blue on Sun Sep 25, 2022 8:40 pm, edited 1 time in total.

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Re: How many 1-clue-box and 2-clue-box?

by blue » Sun Sep 25, 2022 7:55 pm

For Colin and Serg,

The code that I used, was a modified version of my code for the 17-clue search.
A complete explanation would be long and complicated, but the basic idea, involves puzzles like this, in the first stage:

Code: Select all: +-------+-------+-------+ | . . . | . . . | x x x | | . . . | . . . | x x x | | . . . | . . . | x x x | +-------+-------+-------+ | | . . . | | <= 7 clues | . . . | | | . . . | +-------+-------+-------+ | g g g | g g g | g g g | | g g g | g g g | g g g | | g g g | g g g | g g g | +-------+-------+-------+

The 9c (or 5c) box, is the box with x's, and really it can be any of the 6 boxes in bands 1 & 2.

Band 3 is a band fill with one of the 44 "gangster (mini-column) signatures", and bands 1 & 2 in the puzzles' solution grids, are minlex with respect to transformations that preserve the gangster signature in band 3. There are 983,959,110 (ED) cases like that ... "gangster signature" + "compatible bands 1&2 fill".

For the first part of the search, band 3 can be any of the bands that have the required gangster signatures, and puzzles like the one above, are identified.

For the next part, there's a loop over the compatible band 3 fills, and an attempt to clear the band 3 box that's under the box with the x's, and then reduce the clue count in the other boxes, to be small enough to make a 9plus14 (or less) puzzle, or for the 5+15 search, to make a 5plus15.

I'm leaving a bunch of details out ... like having tables for each canonical band type, listing thier "5c one box puzzles", "7c <= two box puzzles", and so on.
and translating those to match the particular band 1 & band 2 fills.

Both problems (9+14 and 5+15) have a diagonal reflection symmetry, that I didn't exploit ... so I ended up finding each puzzle twice, basically.
The 9+14 search took 36 hours, and the 5+15 search took 45 hours, on a machine with 8 (physical) cores, running at 4.5 GHz.

Is this enough of an anwer ?

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Re: How many 1-clue-box and 2-clue-box?

by blue » Sun Sep 25, 2022 8:36 pm

For Mike and JPF:

20C cousins, with 180 degree symmetry.

Code: Select all: +-------+-------+-------+ +-------+-------+-------+ | 8 7 6 | . . . | . . . | | 8 7 6 | . . . | . . . | | 3 . . | . . . | 7 . . | | 3 . . | . . . | 7 . . | | . . . | . . . | 2 1 . | | . . . | . . . | 2 1 . | +-------+-------+-------+ +-------+-------+-------+ | . . . | 1 2 3 | . . . | | . . . | 1 2 3 | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | 4 5 6 | . . . | | . . . | 4 5 6 | . . . | +-------+-------+-------+ +-------+-------+-------+ | . 1 4 | . . . | . . . | | . 1 5 | . . . | . . . | | . . 2 | . . . | . . 5 | | . . 2 | . . . | . . 4 | | . . . | . . . | 8 9 6 | | . . . | . . . | 8 9 6 | +-------+-------+-------+ +-------+-------+-------+ 876......3.....7........21....123...............456....14........2.....5......896 876......3.....7........21....123...............456....15........2.....4......896

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Re: How many 1-clue-box and 2-clue-box?

by JPF » Sun Sep 25, 2022 9:54 pm

Here is a 20C with diagonal symmetry:

Code: Select all: +-------+-------+-------+ | . . . | . . . | . 1 2 | | . . . | . . . | 3 4 5 | | . . . | . . . | . 6 . | +-------+-------+-------+ | 3 7 . | . . . | . . . | | . 4 . | 8 6 . | . . . | | . 5 . | . 9 . | . . . | +-------+-------+-------+ | 1 . 9 | . . . | . . . | | . . . | 5 8 2 | . . . | | . . 2 | . . 7 | . . . | +-------+-------+-------+

JPF