Puzzles related to Patterns Game patterns

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Re: Puzzles related to Patterns Game patterns

Postby JPF » Sun Feb 19, 2017 7:53 pm

Here are some more minimal 74 s(pattern 280) and their distribution:
Code: Select all
2..1....3.1..5..4...4...1..1....3.2..7..1.6.....2.......5.4.....2.3...183......5.    6 4 4 3 3 1 1 1 0
3..2....1.1..5..4...4...2..2....1.3..4..2.5.....3.......6.4.....8.1...231......7.    5 5 4 4 2 1 1 1 0
3..1....5.1..5..2...2...7..1....3.4..2..1.5.....8.......1.2.....6.3...144......3.    6 4 4 3 3 1 1 1 0
4..5....1.1..2..6...2...3..1....4.2..3..1.8.....3.......1.6.....7.2...152......4.    6 5 3 3 2 2 1 1 0
2..1....3.1..5..2...4...1..1....3.6..7..1.2.....4.......8.2.....5.3...143......5.    6 4 4 3 3 1 1 1 0

and a sum = 72 ; distribution : 7 4 4 2 2 2 1 1 0

Code: Select all
 5 . . | 1 . . | . . 3
 . 1 . | . 4 . | . 7 .
 . . 2 | . . . | 1 . .
-------+-------+-------
 1 . . | . . 5 | . 3 .
 . 2 . | . 1 . | 6 . .
 . . . | 2 . . | . . .
-------+-------+-------
 . . 1 | . 6 . | . . .
 . 4 . | 3 . . | . 1 2
 3 . . | . . . | . 8 .
not minimal...

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Re: Puzzles related to Patterns Game patterns

Postby m_b_metcalf » Sun Feb 19, 2017 8:51 pm

... and, FWIW,
Code: Select all
 2 . . 5 . . . . 1
 . 3 . . 4 . . 2 .
 . . 1 . . . 6 . .
 1 . . . . 5 . 3 .
 . 4 . . 1 . 2 . .
 . . . 8 . . . . .
 . . 4 . 2 . . . .
 . 2 . 1 . . . 5 7
 3 . . . . . . 1 .
Sum of values of clues =  73, with just 3 solutions
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Re: Puzzles related to Patterns Game patterns

Postby JPF » Sun Feb 19, 2017 9:34 pm

... and finally this minimal:
Code: Select all
 4 . . | 1 . . | . . 2
 . 1 . | . 2 . | . 6 .
 . . 3 | . . . | 1 . .
-------+-------+-------
 1 . . | . . 3 | . 2 .
 . 7 . | . 1 . | 5 . .
 . . . | 2 . . | . . .
-------+-------+-------
 . . 5 | . 3 . | . . .
 . 3 . | 6 . . | . 1 8
 2 . . | . . . | . 4 .   Sum of values of clues = 73

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Re: Puzzles related to Patterns Game patterns

Postby m_b_metcalf » Mon Feb 20, 2017 8:38 am

JPF wrote:... and finally this minimal:
Code: Select all
 2 . . | . . . | . 4 .   Sum of values of clues = 73

JPF

Brilliant. :D (My search made the wrong assumption that there would be only one 6.)
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Re: Puzzles related to Patterns Game patterns

Postby JPF » Mon Feb 20, 2017 11:09 am

Thanks,
Some improvement:
Code: Select all
 3 . . | 8 . . | . . 1
 . 1 . | . 2 . | . 4 .
 . . 2 | . . . | 5 . .
-------+-------+-------
 4 . . | . . 2 | . 1 .
 . 2 . | . 1 . | 6 . .
 . . . | 3 . . | . . .
-------+-------+-------
 . . 3 | . 5 . | . . .
 . 4 . | 1 . . | . 3 7
 1 . . | . . . | . 2 .   Sum of values of clues = 71 - distribution  6 5 4 3 2 1 1 1 0

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Re: Puzzles related to Patterns Game patterns

Postby blue » Mon Feb 20, 2017 12:03 pm

Nice timing JPF :!:

I think 71 is the best sum for this shape, and that there are only 8 such puzzles (up to isomorphisms).
Edit: It's only 5 puzzles -- see the next post.

Code: Select all
5..7....1.1..4..8...2...3..2....3.1..3..1.4.....2.......6.3.....2.1...451......2.
3..8....1.1..2..4...2...5..4....2.1..2..1.7.....3.......3.5.....4.1...361......2.
3..4....1.1..2..4...2...3..8....3.1..2..1.5.....2.......5.6.....4.1...321......7.
5..2....1.1..3..2...2...8..7....2.1..4..1.3.....3.......3.4.....6.1...421......5.
2..4....1.1..5..3...8...2..4....2.1..6..1.3.....7.......2.3.....4.1...231......5.
2..4....1.1..7..4...8...2..4....6.1..5..1.3.....2.......2.3.....3.1...251......3.
1..3....2.4..1..3...2...5..8....1.2..2..3.1.....4.......5.6.....1.2...473......1.
8..5....1.3..1..2...2...4..7....1.3..4..3.1.....2.......5.2.....1.4...632......1.

They all have the distribution: (6 5 4 3 2 1 1 1 0)
Your's matches #2 in this list, with 6 and 7 swapped.

Cheers,
Blue.

PS: The same code, is saying that there are no minimal puzzles with sum=72, for thier "best case" digit mapping(s) ... odd !
Did you see any counterexamples ?
Last edited by blue on Mon Feb 20, 2017 6:19 pm, edited 1 time in total.
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Re: Puzzles related to Patterns Game patterns

Postby m_b_metcalf » Mon Feb 20, 2017 2:16 pm

A stunning result, blue :!: (Just a little niggle that your puzzles 3, 4 and 6 are transposed isomorphs of preceding ones.)

Regards,

Mike
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Re: Puzzles related to Patterns Game patterns

Postby blue » Mon Feb 20, 2017 6:17 pm

m_b_metcalf wrote:(Just a little niggle that your puzzles 3, 4 and 6 are transposed isomorphs of preceding ones.)

Ha ha ha ...
Thanks Mike.

The last thing I did before putting the code to rest, was add "#ifdef TRANSPOSE_INVARIANT" around a part of it, along with a note that it wasn't a guarantee that a puzzle would only be found once. It was the symmetric placement for the 1's in the first 6 puzzles, that proved that out.

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Re: Puzzles related to Patterns Game patterns

Postby JPF » Mon Feb 20, 2017 7:20 pm

blue wrote:PS: The same code, is saying that there are no minimal puzzles with sum=72, for thier "best case" digit mapping(s) ... odd !
Did you see any counterexamples ?

No, all my 72s are not minimal.
Congratulations for your five 71s (I have only 2 puzzles, both in your list)

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Re: Puzzles related to Patterns Game patterns

Postby m_b_metcalf » Tue Feb 21, 2017 1:56 pm

For Game 281, I postulate that the uneven distribution of givens between boxes will result in a higher minimum. Is it perhaps the case that a low minimum requires an even spread?

My best yet:
Code: Select all
 4 1 . 3 . . . . .
 3 . 2 . . . 4 . .
 . 5 6 . . . . . .
 1 . . 2 . . 7 . .
 . . . . . 3 . . 2
 . . . . 5 . . 1 .
 . 4 . 1 . . 3 . .
 . . . . . 8 . 2 1
 . . . . 2 . . 5 .   Sum of values of clues= 75, 55433111
Last edited by m_b_metcalf on Tue Feb 21, 2017 5:29 pm, edited 1 time in total.
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Re: Puzzles related to Patterns Game patterns

Postby JPF » Tue Feb 21, 2017 5:05 pm

blue wrote:I think 71 is the best sum for this shape

Well, this one is not minimal:
Code: Select all
 4 . . | 2 . . | . . 1
 . 1 . | . 5 . | . 2 .
 . . 3 | . . . | 6 . .
-------+-------+-------
 1 . . | . . 2 | . 7 .
 . 2 . | . 1 . | 4 . .
 . . . | 3 . . | . . .
-------+-------+-------
 . . 1 | . 4 . | . . .
 . 5 . | 1 . . | . 3 8
 3 . . | . . . | . 1 .   Sum of values of clues = 70 - distribution  7 4 4 3 2 1 1 1 0


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Re: Puzzles related to Patterns Game patterns

Postby blue » Tue Feb 21, 2017 7:52 pm

Hi JPF,

JPF wrote:
blue wrote:I think 71 is the best sum for this shape

Well, this one is not minimal:
(...)

Right ... Congratulations !

There's (only) one more like that (AFAIK):

Code: Select all
7 . . | 2 . . | . . 1
. 2 . | . 3 . | . 8 .
. . 1 | . . . | 6 . .
------+-------+------
1 . . | . . 2 | . 3 .
. 4 . | . 5 . | 1 . .
. . . | 1 . . | . . .
------+-------+------
. . 6 | . 1 . | . . .
. 1 . | 5 . . | . 2 4
3 . . | . . . | . 1 .   Sum of values of clues = 70 - distribution  8 4 3 2 2 2 1 1 0

Cheers,
Blue.
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Re: Puzzles related to Patterns Game patterns

Postby JPF » Tue Feb 21, 2017 11:56 pm

m_b_metcalf wrote:For Game 281, I postulate that the uneven distribution of givens between boxes will result in a higher minimum. Is it perhaps the case that a low minimum requires an even spread?
My best yet:
Sum of values of clues= 75, 55433111

Just to line up:
Code: Select all
 2 7 . | 3 . . | . . .
 5 . 3 | . . . | 1 . .
 . 1 4 | . . . | . . .
-------+-------+-------
 3 . . | 1 . . | 5 . .
 . . . | . . 4 | . . 1
 . . . | . 2 . | . 4 .
-------+-------+-------
 . 6 . | 5 . . | 3 . .
 . . . | . . 2 | . 1 8
 . . . | . 1 . | . 2 .   Sum of values of clues = 74 - distribution  644331110

Edit - improvement:
Code: Select all
 6 3 . | 5 . . | . . .
 4 . 2 | . . . | 1 . .
 . 1 7 | . . . | . . .
-------+-------+-------
 5 . . | 1 . . | 4 . .
 . . . | . . 3 | . . 2
 . . . | . 2 . | . 1 .
-------+-------+-------
 . 4 . | 3 . . | 2 . .
 . . . | . . 2 | . 3 1
 . . . | . 1 . | . 8 .   Sum of values of clues = 71 - distribution  654321110

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Re: Puzzles related to Patterns Game patterns

Postby blue » Fri Feb 24, 2017 6:55 am

Nice work again, JPF :!:

I didn't play, because after the last shape, I would have been cheating -- using an exhaustive search.

m_b_metcalf wrote:For Game 281, I postulate that the uneven distribution of givens between boxes will result in a higher minimum. Is it perhaps the case that a low minimum requires an even spread?

Comparing results with the last shape, I get:

Code: Select all
<=70: none of any kind - down from 2 non-minimals with sum=70
71: one minimal - down from 5
72: no minimals - same as before
73: one minimal - down from 48
74: 58 minimals - down from 463

This is the one for "73":

Code: Select all
3 7 . 1 . . . . .
4 . 1 . . . 8 . .
. 5 2 . . . . . .
1 . . 2 . . 3 . .
. . . . . 5 . . 1
. . . . 4 . . 2 .
. 2 . 3 . . 1 . .
. . . . . 6 . 5 2
. . . . 1 . . 4 .   Sum of clue values: 73, Distribution: 653331110
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Re: Puzzles related to Patterns Game patterns

Postby m_b_metcalf » Fri Feb 24, 2017 7:59 am

blue wrote:
m_b_metcalf wrote:For Game 281, I postulate that the uneven distribution of givens between boxes will result in a higher minimum. Is it perhaps the case that a low minimum requires an even spread?

Comparing results with the last shape, I get:

Code: Select all
71: one minimal - down from 5


So, I was wrong: the minimum is the same, it was just harder to get there.

Regards,

Mike
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