Are the Times puzzles minimal?

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Are the Times puzzles minimal?

Postby 999_Springs » Sat Aug 16, 2008 5:08 pm

Just wondering... are they minimal, symetrically minimal or just not minimal? Are there any constraints on the minimality of Times puzzles?
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Postby Glyn » Sat Aug 16, 2008 10:55 pm

The Times puzzles are not minimal. I randomly picked one from an old copy of the paper. Easy #2082 from August 12. ER 1.2
Code: Select all
. 7 .|. . .|. 8 .
1 . .|5 7 8|. . 9
4 . 3|. . .|5 . 6
-----+-----+-----
. 5 .|. 6 .|. 2 .
. 1 4|2 . 7|6 5 .
. 9 .|. 3 .|. 1 .
-----+-----+-----
7 . 8|. . .|1 . 2
9 . .|3 1 2|. . 8
. 6 .|. . .|. 9 .

r2c5,r5c2,r5c8,r8c5 can be removed without significantly affecting difficulty or destroying the symmetry.

Breaking symmetry we can lose a few more givens and this is still solvable with singles. ER 1.5

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


With different tweaking we could get ER 4.6 which would rank as Fiendish-Super Fiendish in Times ratings.

Code: Select all
. . .|. . .|. 8 .
1 . .|. 7 8|. . 9
. . 3|. . .|5 . 6
-----+-----+-----
. . .|. . .|. . .
. . .|2 . 7|6 . .
. 9 .|. 3 .|. 1 .
-----+-----+-----
7 . .|. . .|1 . 2
9 . .|3 1 2|. . 8
. 6 .|. . .|. . .
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Postby Pat » Sun Aug 17, 2008 5:03 am

    on minimality, there has never been any constraint in The Times (nor in any other newspaper as far as i know).

    The Times does continue to require symmetry of the givens.

    also as far as i know, the difficulty in The Times won't exceed Swordfish. (not quite as tough as our "superior plus".)
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Postby JPF » Thu Aug 21, 2008 7:20 pm

There is at least one newspaper giving minimal puzzles, but without symmetry :


Image

Minimality is invariant by isomorphism, symmetry is not.

By the way, I don't see any reason to give redundant informations in any puzzle.


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Postby tarek » Sat Aug 23, 2008 4:23 pm

Without minimality...

You could have more symmetric puzzles.

You could symmetrize & reduce difficulty of minimal puzzles generated from a symmetric template.

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Postby JPF » Sat Aug 23, 2008 5:13 pm

tarek wrote:Without minimality...
You could have more symmetric puzzles.
Right.
But as far as puzzles in newspapers (books, etc...) are concern :
lots are poorly built (tons of rough outputs from computers)

The Patterns Game proves that one can produce minimal puzzles at almost any level of difficulty for any pattern, even for symmetric ones.

But that needs a bit of work...

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re: minimality

Postby Pat » Mon Aug 25, 2008 6:01 am

JPF wrote:The Patterns Game proves that one can produce minimal puzzles at almost any level of difficulty for any pattern, even for symmetric ones.


look again at the 28-clue pattern (full symmetry)
which i posted 2008.Feb.20
    m_b_metcalf found a minimal 1.5
    and you found a minimal 8.9,

    but i thought we agreed that this pattern has too few minimal puzzles
    and would not suit the "patterns game"
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Postby JPF » Mon Aug 25, 2008 3:13 pm

Pat wrote:but i thought we agreed that this pattern has too few minimal puzzles
and would not suit the "patterns game"

I'm not sure we agreed.
A quick survey of minimal puzzles :
Code: Select all
9.0/1.2/1.2 # 010000020304000506050407080001050800000801000003090200020906040605000902030000060
8.9/1.2/1.2 # 010000020304000506050307080009020800000809000003010200020406010605000402030000060
8.8/1.2/1.2 # 010000020304000506070504030007030600000401000003050100040807060809000207030000090
8.6/1.2/1.2 # 010000020304000506070308090009020800000705000003080200020406010607000402030000060
8.5/1.2/1.2 # 010000020304000506050307080009040700000805000003070200020406010605000402030000060
8.4/1.2/1.2 # 010000020304000506050307080009020700000809000003010200020406010605000402030000060
8.3/1.2/1.2 # 010000020304000105060701080007060800000807000003090200020405090506000402030000050
7.8/1.2/1.2 # 010000020304000506050307040008030100000104000003090200020406010605000402030000060
7.7/1.2/1.2 # 010000020304000105060301070002080700000702000003040900080405090506000408030000050
7.6/2.0/2.0 # 010000020304000506020306010007010600000408000001030800040907060905000207070000090
7.5/1.2/1.2 # 010000020304000506070603080009060800000709000006010200020405010507000402060000050
7.3/1.2/1.2 # 010000020304000506050307040008020700000409000003010200080906010605000902030000060
7.2/1.2/1.2 # 010000020304000506050307080009050800000809000003010200090406010601000405030000060
7.1/1.2/1.2 # 010000020304000506050307010008020100000108000003040200030206090605000402080000060
6.7/1.2/1.2 # 010000020304000506050307040008020900000905000003010200020406080605000402030000060
6.6/1.2/1.2 # 010000020304000506070308040009020400000409000003010200040706010605000702030000060
4.5/1.2/1.2 # 010000020304000506050307080005070800000805000003010200020506010607000402030000060
4.2/1.2/1.2 # 010000020304000506050304070001050600000408000007030800040501060509000201070000090
3.2/1.2/1.2 # 010000020304000501020604070008090100000208000009060800040507010503000207090000050
2.6/1.2/1.2 # 010000020304000506020304070008050700000708000003010200080906010605000902030000060
2.0/1.2/1.2 # 010000020304000506050306070002070800000802000003060700070409010905000207030000090
1.7/1.2/1.2 # 010000020304000105020604030007040500000708000003060800040907050901000207030000090
1.5/1.2/1.2 # 010000020304000501020304060007020100000408000006030800040705010509000207060000050

of course, all the (valid) patterns don't have the same density of minimal puzzles (density = minimal/total)
For example, patterns with more than 40 clues have probably a density equal to zero.
At the other end, patterns with 17 clues have probably a density equal to 1...

In this thread, Mauricio and ravel mentionned some subpatterns forbidden in minimal puzzles.

Now, back to the toppic : minimal puzzles (or not) in the newspapers.
In this thread :
  • Red Ed gave an estimation of the number of minimal puzzles per grid : 6.6 x 10^15
  • Coloin reported dukuso's estimation of the total number of essentially different minimal puzzles : 10^25
Assuming one page (0.1 mm) per puzzle, what would be the thickness of the book of all the minimal puzzles:?:
Not enough space in our galaxy...

Who said that it's hard to find minimal puzzles for a newspaper ?

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