4-leaf clover 8.4

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4-leaf clover 8.4

Postby denis_berthier » Fri Jan 08, 2021 8:02 am

.
Here is a (non-minimal) puzzle with the 4-leaf clover pattern. I couldn't find a minimal puzzle for this pattern.
Code: Select all
. X X . . . X X .
X . . X . X . . X
X . . . X . . . X
. X . . . . . X .
. . X . . . X . .
. X . . . . . X .
X . . . X . . . X
X . . X . X . . X
. X X . . . X X .

28 givens

Code: Select all
   +-------+-------+-------+
   ! . 3 2 ! . . . ! 6 8 . !
   ! 5 . . ! 3 . 8 ! . . 2 !
   ! 9 . . ! . 7 . ! . . 1 !
   +-------+-------+-------+
   ! . 9 . ! . . . ! . 6 . !
   ! . . 5 ! . . . ! 1 . . !
   ! . 2 . ! . . . ! . 4 . !
   +-------+-------+-------+
   ! 2 . . ! . 8 . ! . . 4 !
   ! 3 . . ! 7 . 6 ! . . 5 !
   ! . 1 7 ! . . . ! 9 3 . !
   +-------+-------+-------+
.32...68.5..3.8..29...7...1.9.....6...5...1...2.....4.2...8...43..7.6..5.17...93.
SER 8.4
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Re: 4-leaf clover 8.4

Postby champagne » Fri Jan 08, 2021 10:44 am

.21...34.4..1.2..68...6...2.8.....6...6...7...7.....9.3...7...97..3.1..5.59...13.

this one is minimal but stte
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Re: 4-leaf clover 8.4

Postby pjb » Sat Jan 09, 2021 2:02 am

A couple of very messy chains?
Code: Select all
a47      3       2      | 145    459    159-4  | 6      8      79     
 5      b67      1      | 3     f69     8      | 4     e79     2     
 9       68      48     |g246    7     h24     | 3      5      1     
------------------------+----------------------+---------------------
 147     9       348    | 1458   345    1457   | 2      6      378   
 67-4   c78      5      | 2468   23469 i2479   | 1     d79     3789   
 167     2       38     | 168    369    179    | 5      4      3789   
------------------------+----------------------+---------------------
 2       5       6      | 9      8      3      | 7      1      4     
 3       4       9      | 7      1      6      | 8      2      5     
 8       1       7      | 245    245    245    | 9      3      6     

(4=7)r1c1 - (7)r2c2 = (7*)r5c2 - (7=9^)r5c8 - (9)r2c8 = (9-6)r2c5 = (6-2)r3c4 = (2)r3c6 - (2|7*|9^=4)r5c6 => -4 r1c6, -4 r5c1
4s at r5c456 only ones in row/column => -4 r4c456. =>

Code: Select all
 7-4     3       2      |l145    459    159    | 6      8      79     
 5      c67      1      | 3     e69     8      | 4     d79     2     
 9      b68     a48     |f26-4   7      2-4    | 3      5      1     
------------------------+----------------------+---------------------
 147     9       348    | 158    35     157    | 2      6      378   
 67      78      5      | 2468  j23469  2479   | 1      79    i3789   
 167     2       38     |g168    369    179    | 5      4     h3789   
------------------------+----------------------+---------------------
 2       5       6      | 9      8      3      | 7      1      4     
 3       4       9      | 7      1      6      | 8      2      5     
 8       1       7      | 245   k245    245    | 9      3      6     

Then:
(4=8*)r3c3 - (8=6)r3c2 - (6=7)r2c2 - (7=9^)r2c8 - (9=6)r2c5 - (6)r3c4 = (6-8)r6c4*3 = (8-9)r6^1c9 = (9-3)r5c9 = (3-2)r5c5 = (2-4)r9#5c5 = (4)r1c5 => -4 r1c1, -4 r3c4, -4 r3c6; stte

Phil
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Re: 4-leaf clover 8.4

Postby denis_berthier » Sat Jan 09, 2021 6:35 am

pjb wrote:A couple of very messy chains?

If you like long and messy chains, after the basics give the following PM:

Code: Select all
   47        3         2         145       459       1459      6         8         79       
   5         67        1         3         69        8         4         79        2         
   9         68        48        246       7         24        3         5         1         
   147       9         348       1458      345       1457      2         6         378       
   46        78        5         2468      23469     249       1         79        389       
   167       2         38        168       369       179       5         4         3789     
   2         5         6         9         8         3         7         1         4         
   3         4         9         7         1         6         8         2         5         
   8         1         7         245       245       245       9         3         6         

you can do it in a single sweep:

FORCING-T&E applied to bivalue candidates 433 and 443 :
.. 34 values decided by 433 : (433 711 622 832 752 958 728 925 919 236 456 596 116 746 966 651 161 441 634 864 363 769 665 843 349 859 545 144 415 295 494 355 514 254)
.. 31 values decided by 443 : (443 833 363 632 722 852 928 758 625 965 869 349 959 545 415 295 355 236 456 596 494 719 651 254 514 116 766 161 664 741 144)
==> 16 values decided in both cases: (236 456 596 116 651 161 363 349 545 144 415 295 494 355 514 254)
==> 48 candidates eliminated in both cases: (411 114 414 515 915 416 516 916 234 434 436 141 343 444 544 844 345 445 146 446 546 749 849 451 454 654 854 255 455 655 955 256 956 359 661 761 863 164 365 166 369 969 294 594 495 595 296 496)
Code: Select all
CURRENT RESOLUTION STATE:
   7         3         2         5         4         1         6         8         79       
   5         67        1         3         69        8         4         79        2         
   9         68        48        6         7         2         3         5         1         
   47        9         48        1         5         7         2         6         3         
   6         78        5         2         3         4         1         79        89       
   1         2         3         68        69        79        5         4         78       
   2         5         6         9         8         3         7         1         4         
   3         4         9         7         1         6         8         2         5         
   8         1         7         4         2         5         9         3         6         

stte

Of course, this is not how I would solve it.
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Re: 4-leaf clover 8.4

Postby DEFISE » Sat Jan 09, 2021 10:53 am

Happy New Year all !

there is a solution with several whips [<= 5] but here is a solution with only one whip [10]:

Hidden Text: Show
Single: 5r3c8
Single: 7r7c7
Single: 4r2c7
Single: 3r3c7
Single: 1r7c8
Single: 2r8c8
Single: 8r8c7
Single: 5r6c7
Single: 2r4c7
Single: 4r8c2
Single: 9r8c3
Single: 6r7c3
Single: 1r2c3
Single: 5r7c2
Single: 9r7c4
Single: 3r7c6
Single: 1r8c5
Single: 8r9c1
Single: 6r9c9
Alignment: 6-c1-b4 => -6r5c2
XWing: 7-c28-r25 => -7r5c1 -7r5c6 -7r5c9
whip[10]: r2c5{n9 n6}- r2c2{n6 n7}- r1c1{n7 n4}- c3n4{r3 r4}- c3n3{r4 r6}- r6c5{n3 n9}- r1c5{n9 n5}- r4c5{n5 n3}- c9n3{r4 r5}- r5n9{c9 .} => -9r2c8

STTE
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Re: 4-leaf clover 8.4

Postby coloin » Sat Jan 09, 2021 1:41 pm

denis_berthier wrote:...I couldn't find a minimal puzzle for this pattern.
more than 99.9 % are non-minimal but overnight more than 6000 minimal puzzles found and the best two were
Code: Select all
.63...24.4..2.8..65...4...7.1.....7...6...9...4.....6.3...9...56..3.1..9.59...73. ED=9.0/1.2/1.2
.27...84.1..2.4..34...6...7.7.....9...6...3...1.....8.2...9...87..5.1..9.94...13. ED=8.9/1.2/1.2

using gridchecker it would be possible to get a good estimate of the total number of minimal 28C puzzles with this pattern ...
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Re: 4-leaf clover 8.4

Postby denis_berthier » Sat Jan 09, 2021 1:52 pm

Hi Defise
Happy New Year to you also

DEFISE wrote:there is a solution with several whips [<= 5]

Yes and it's my preferred one.
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Re: 4-leaf clover 8.4

Postby denis_berthier » Sat Jan 09, 2021 2:15 pm

coloin wrote:
denis_berthier wrote:...I couldn't find a minimal puzzle for this pattern.
more than 99.9 % are non-minimal but overnight more than 6000 minimal puzzles found and the best two were
Code: Select all
.63...24.4..2.8..65...4...7.1.....7...6...9...4.....6.3...9...56..3.1..9.59...73. ED=9.0/1.2/1.2
.27...84.1..2.4..34...6...7.7.....9...6...3...1.....8.2...9...87..5.1..9.94...13. ED=8.9/1.2/1.2

Great. They are respectively in W6 and W5.
I tried with gsf's program, but I didn't let it run long enough.
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Re: 4-leaf clover 8.4

Postby DEFISE » Sat Jan 09, 2021 5:07 pm

denis_berthier wrote:Hi Defise
Happy New Year to you also

DEFISE wrote:there is a solution with several whips [<= 5]

Yes and it's my preferred one.


Hi Denis,
so here is a short solution with whips[<=5]:

Hidden Text: Show
Single: 5r3c8
Single: 7r7c7
Single: 4r2c7
Single: 3r3c7
Single: 1r7c8
Single: 2r8c8
Single: 8r8c7
Single: 5r6c7
Single: 2r4c7
Single: 4r8c2
Single: 9r8c3
Single: 6r7c3
Single: 1r2c3
Single: 5r7c2
Single: 9r7c4
Single: 3r7c6
Single: 1r8c5
Single: 8r9c1
Single: 6r9c9
Alignment: 6-c1-b4 => -6r5c2
XWing: 7c28-r25 => -7r5c1 -7r5c6 -7r5c9
whip[4]: r3n6{c4 c2}- r2c2{n6 n7}- r1c1{n7 n4}- r5c1{n4 .} => -6r5c4
whip[5]: r5c8{n9 n7}- r5c2{n7 n8}- r3c2{n8 n6}- c4n6{r3 r6}- r6n8{c4 .} => -9r6c9
Alignment: 9-r6-b5 => -9r5c5 -9r5c6
Naked pair: 24-r3c6-r5c6 => -4r1c6 -4r4c6 -2r9c6 -4r9c6
Single: 5r9c6
whip[5]: r3n6{c4 c2}- c2n8{r3 r5}- c4n8{r5 r4}- c4n1{r4 r1}- c4n5{r1 .} => -6r6c4

STTE
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Re: 4-leaf clover 8.4

Postby coloin » Sun Jan 10, 2021 2:25 pm

Out of 100K random grids there were found 10 minimal puzzles .... therefore probably there are around 55000 minimal puzzles with this pattern.
Of course there are probably more than a billion non-minimals
As of now ... the puzzle count is at 28000 and still expanding [but only 2 of the 10 random puzzles above identified]

A few more 9.0 and the only near diamond
Code: Select all
.91...54.3..9.5..18...1...2.8.....5...6...2...7.....3.4...6...97..4.8..5.28...47. ED=7.3/7.1/7.1
.21...45.4..1.5..35...4...2.6.....3...2...8...7.....9.2...9...87..3.8..9.89...36. ED=9.0/1.2/1.2
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Re: 4-leaf clover 8.4

Postby denis_berthier » Sun Jan 10, 2021 4:49 pm

Hi Coloin,

This is clearly a hard pattern for minimals. It's great you persevered in exploring it.

coloin wrote:A few more 9.0 and the only near diamond
Code: Select all
.91...54.3..9.5..18...1...2.8.....5...6...2...7.....3.4...6...97..4.8..5.28...47. ED=7.3/7.1/7.1
.21...45.4..1.5..35...4...2.6.....3...2...8...7.....9.2...9...87..3.8..9.89...36. ED=9.0/1.2/1.2


Respectively W=4 and W=6

The puzzles with this pattern seem to be relatively easily in their SER class.
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Re: 4-leaf clover 8.4

Postby m_b_metcalf » Sun Jan 10, 2021 5:21 pm

coloin wrote: and the only near diamond
Code: Select all
.91...54.3..9.5..18...1...2.8.....5...6...2...7.....3.4...6...97..4.8..5.28...47. ED=7.3/7.1/7.1

I played around with your near diamond, and found these minimal cousins:
Code: Select all
.12...34.5..3.2..16...1...7.6.....3...5...7...8.....5.4...9...38..4.6..9.26...48.   ED=2.6/1.2/1.2   
.12...34.5..3.2..16...1...7.6.....3...8...7...9.....5.4...8...29..4.6..3.76...49.   ED=7.2/7.1/3.4   
.12...34.5..2.4..16...1...7.6.....3...8...7...9.....5.3...8...29..4.6..3.76...49.   ED=7.2/7.2/2.8   
.12...34.5..1.4..26...2...7.6.....3...8...7...9.....5.3...8...19..4.6..3.76...49.   ED=7.3/7.3/2.8   
.12...34.5..1.3..26...2...7.5.....3...8...1...9.....7.4...8...19..6.4..3.76...49.   ED=8.3/1.2/1.2   
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Re: 4-leaf clover 8.4

Postby JPF » Sun Jan 10, 2021 5:22 pm

My puzzle count is at 73950.
Here are some examples:
Code: Select all
.12...34.4..1.3..25...4...6.2.....7...4...6...5.....8.2...6...73..7.8..1.79...56.   ED=9.1/7.5/2.6
.12...34.4..5.2..66...4...7.6.....7...1...8...4.....9.2...9...81..2.7..9.79...26.   ED=9.0/1.2/1.2
.12...34.3..1.4..56...2...1.7.....8...6...5...4.....6.4...5...87..8.9..6.68...15.   ED=9.0/1.2/1.2
.12...34.3..2.4..55...1...6.5.....6...1...7...8.....9.1...4...28..6.3..9.93...65.   ED=9.0/1.2/1.2
.12...34.5..1.4..64...2...7.2.....6...1...7...4.....8.1...3...82..9.5..3.93...67.   ED=9.0/1.2/1.2
.12...34.4..3.2..56...4...7.6.....7...1...5...4.....8.1...8...69..5.7..2.76...95.   ED=9.0/1.2/1.2
.12...34.4..5.2..63...4...7.2.....3...1...6...4.....7.2...8...31..7.6..8.87...56.   ED=9.0/1.2/1.2
.12...34.4..3.1..53...2...1.2.....6...3...7...5.....8.5...6...72..8.7..6.67...15.   ED=9.0/1.2/1.2
.12...34.3..4.1..54...2...1.2.....6...3...7...5.....8.5...6...72..8.7..6.67...15.   ED=9.0/1.2/1.2
.12...34.3..4.1..54...2...1.2.....6...3...7...5.....8.5...6...72..7.8..6.67...15.   ED=9.0/1.2/1.2
.12...34.5..6.4..74...1...8.5.....9...1...8...4.....7.9...8...21..7.9..3.65...78.   ED=9.0/1.2/1.2
.12...34.5..1.4..26...7...5.6.....8...1...9...3.....5.3...8...91..9.2..8.98...27.   ED=9.0/1.2/1.2
.12...34.5..2.3..67...8...5.3.....9...8...6...7.....5.3...9...14..1.6..9.91...56.   ED=9.0/1.2/1.2
.12...34.3..2.4..54...3...1.6.....7...1...5...8.....9.1...7...96..9.5..7.79...85.   ED=9.0/1.2/1.2
.12...34.3..2.4..54...3...1.6.....7...1...5...8.....9.1...7...96..9.5..7.97...85.   ED=9.0/1.2/1.2
.12...34.5..4.3..63...2...7.5.....2...1...6...4.....7.4...8...21..6.9..8.83...56.   ED=9.0/1.2/1.2
.12...34.5..6.4..14...2...7.6.....8...4...9...2.....7.1...7...92..9.8..3.95...71.   ED=9.0/1.2/1.2
.12...34.4..1.3..25...4...6.5.....7...1...8...3.....6.3...7...91..5.2..7.67...25.   ED=9.0/1.2/1.2
.12...34.4..3.5..16...4...7.4.....1...1...8...9.....7.2...8...61..2.9..8.68...72.   ED=9.0/1.2/1.2
.12...34.5..3.1..63...2...7.2.....8...3...7...9.....6.2...8...48..7.5..1.61...57.   ED=9.0/1.2/1.2
.12...34.5..1.4..64...7...5.4.....5...1...6...8.....9.1...8...98..9.6..3.39...56.   ED=9.0/1.2/1.2
.12...34.5..1.4..64...7...5.4.....5...1...6...8.....9.1...8...38..3.6..9.39...56.   ED=9.0/1.2/1.2
.12...34.5..4.6..78...1...5.8.....3...1...5...6.....7.1...9...34..8.7..9.97...85.   ED=9.0/1.2/1.2
.12...34.5..4.1..64...2...7.3.....7...4...6...8.....9.9...6...13..1.8..9.51...76.   ED=8.8/7.2/2.8
.12...34.5..4.6..74...2...5.5.....8...1...9...3.....5.1...9...83..8.7..2.68...47.   ED=7.3/7.3/2.8
.12...34.5..3.6..73...2...5.4.....7...1...8...5.....9.4...8...91..9.7..2.69...73.   ED=7.3/7.3/2.8
.12...34.5..3.6..73...2...5.4.....8...1...9...5.....7.4...9...81..8.7..2.68...73.   ED=7.3/7.3/2.8
.12...34.5..3.6..73...2...5.3.....8...1...9...4.....5.4...9...81..8.7..2.68...57.   ED=7.3/7.1/7.1
.12...34.5..3.6..73...2...5.4.....8...1...9...3.....5.4...9...81..8.7..2.68...57.   ED=7.3/7.1/7.1
.12...34.5..4.6..74...2...5.3.....5...1...8...4.....9.1...8...93..9.7..2.69...57.   ED=7.3/7.1/7.1
.12...34.5..4.6..74...2...5.3.....8...1...9...4.....5.1...9...83..8.7..2.68...57.   ED=7.3/7.1/7.1

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Re: 4-leaf clover 8.4

Postby denis_berthier » Mon Jan 11, 2021 6:34 am

DEFISE wrote:here is a short solution with whips[<=5]:

Hidden Text: Show
Single: 5r3c8
Single: 7r7c7
Single: 4r2c7
Single: 3r3c7
Single: 1r7c8
Single: 2r8c8
Single: 8r8c7
Single: 5r6c7
Single: 2r4c7
Single: 4r8c2
Single: 9r8c3
Single: 6r7c3
Single: 1r2c3
Single: 5r7c2
Single: 9r7c4
Single: 3r7c6
Single: 1r8c5
Single: 8r9c1
Single: 6r9c9
Alignment: 6-c1-b4 => -6r5c2
XWing: 7c28-r25 => -7r5c1 -7r5c6 -7r5c9
whip[4]: r3n6{c4 c2}- r2c2{n6 n7}- r1c1{n7 n4}- r5c1{n4 .} => -6r5c4
whip[5]: r5c8{n9 n7}- r5c2{n7 n8}- r3c2{n8 n6}- c4n6{r3 r6}- r6n8{c4 .} => -9r6c9
Alignment: 9-r6-b5 => -9r5c5 -9r5c6
Naked pair: 24-r3c6-r5c6 => -4r1c6 -4r4c6 -2r9c6 -4r9c6
Single: 5r9c6
whip[5]: r3n6{c4 c2}- c2n8{r3 r5}- c4n8{r5 r4}- c4n1{r4 r1}- c4n5{r1 .} => -6r6c4
STTE

Hi Defise,
Good, you have fewer rule applications than in the simplest-first strategy (with the same max length of whips).
Can you remind me your criterion for choosing the next target (within a fixed Wn)? I can't find the post where you told it. Was it the maximum number of candidates that would be subsequently eliminated by Singles and ECP (or maybe also Whips[1] and Subsets) if the target was eliminated? Did you also consider the number of candidates turned into solution values?
denis_berthier
2010 Supporter
 
Posts: 1983
Joined: 19 June 2007
Location: Paris

Re: 4-leaf clover 8.4

Postby denis_berthier » Mon Jan 11, 2021 7:04 am

JPF wrote:My puzzle count is at 73950.
Here are some examples:
Code: Select all
.12...34.4..1.3..25...4...6.2.....7...4...6...5.....8.2...6...73..7.8..1.79...56.   ED=9.1/7.5/2.6
.12...34.4..5.2..66...4...7.6.....7...1...8...4.....9.2...9...81..2.7..9.79...26.   ED=9.0/1.2/1.2
.12...34.3..1.4..56...2...1.7.....8...6...5...4.....6.4...5...87..8.9..6.68...15.   ED=9.0/1.2/1.2
.12...34.3..2.4..55...1...6.5.....6...1...7...8.....9.1...4...28..6.3..9.93...65.   ED=9.0/1.2/1.2
.12...34.5..1.4..64...2...7.2.....6...1...7...4.....8.1...3...82..9.5..3.93...67.   ED=9.0/1.2/1.2
.12...34.4..3.2..56...4...7.6.....7...1...5...4.....8.1...8...69..5.7..2.76...95.   ED=9.0/1.2/1.2
.12...34.4..5.2..63...4...7.2.....3...1...6...4.....7.2...8...31..7.6..8.87...56.   ED=9.0/1.2/1.2
.12...34.4..3.1..53...2...1.2.....6...3...7...5.....8.5...6...72..8.7..6.67...15.   ED=9.0/1.2/1.2
.12...34.3..4.1..54...2...1.2.....6...3...7...5.....8.5...6...72..8.7..6.67...15.   ED=9.0/1.2/1.2
.12...34.3..4.1..54...2...1.2.....6...3...7...5.....8.5...6...72..7.8..6.67...15.   ED=9.0/1.2/1.2

.12...34.5..6.4..74...1...8.5.....9...1...8...4.....7.9...8...21..7.9..3.65...78.   ED=9.0/1.2/1.2
.12...34.5..1.4..26...7...5.6.....8...1...9...3.....5.3...8...91..9.2..8.98...27.   ED=9.0/1.2/1.2
.12...34.5..2.3..67...8...5.3.....9...8...6...7.....5.3...9...14..1.6..9.91...56.   ED=9.0/1.2/1.2
.12...34.3..2.4..54...3...1.6.....7...1...5...8.....9.1...7...96..9.5..7.79...85.   ED=9.0/1.2/1.2
.12...34.3..2.4..54...3...1.6.....7...1...5...8.....9.1...7...96..9.5..7.97...85.   ED=9.0/1.2/1.2
.12...34.5..4.3..63...2...7.5.....2...1...6...4.....7.4...8...21..6.9..8.83...56.   ED=9.0/1.2/1.2
.12...34.5..6.4..14...2...7.6.....8...4...9...2.....7.1...7...92..9.8..3.95...71.   ED=9.0/1.2/1.2
.12...34.4..1.3..25...4...6.5.....7...1...8...3.....6.3...7...91..5.2..7.67...25.   ED=9.0/1.2/1.2
.12...34.4..3.5..16...4...7.4.....1...1...8...9.....7.2...8...61..2.9..8.68...72.   ED=9.0/1.2/1.2
.12...34.5..3.1..63...2...7.2.....8...3...7...9.....6.2...8...48..7.5..1.61...57.   ED=9.0/1.2/1.2

.12...34.5..1.4..64...7...5.4.....5...1...6...8.....9.1...8...98..9.6..3.39...56.   ED=9.0/1.2/1.2
.12...34.5..1.4..64...7...5.4.....5...1...6...8.....9.1...8...38..3.6..9.39...56.   ED=9.0/1.2/1.2
.12...34.5..4.6..78...1...5.8.....3...1...5...6.....7.1...9...34..8.7..9.97...85.   ED=9.0/1.2/1.2
.12...34.5..4.1..64...2...7.3.....7...4...6...8.....9.9...6...13..1.8..9.51...76.   ED=8.8/7.2/2.8
.12...34.5..4.6..74...2...5.5.....8...1...9...3.....5.1...9...83..8.7..2.68...47.   ED=7.3/7.3/2.8
.12...34.5..3.6..73...2...5.4.....7...1...8...5.....9.4...8...91..9.7..2.69...73.   ED=7.3/7.3/2.8
.12...34.5..3.6..73...2...5.4.....8...1...9...5.....7.4...9...81..8.7..2.68...73.   ED=7.3/7.3/2.8
.12...34.5..3.6..73...2...5.3.....8...1...9...4.....5.4...9...81..8.7..2.68...57.   ED=7.3/7.1/7.1
.12...34.5..3.6..73...2...5.4.....8...1...9...3.....5.4...9...81..8.7..2.68...57.   ED=7.3/7.1/7.1
.12...34.5..4.6..74...2...5.3.....5...1...8...4.....9.1...8...93..9.7..2.69...57.   ED=7.3/7.1/7.1

.12...34.5..4.6..74...2...5.3.....8...1...9...4.....5.1...9...83..8.7..2.68...57.   ED=7.3/7.1/7.1

JPF


I must correct my first impression, based on a very small sample, that the minimal puzzles with this pattern were relatively easy (wrt their SER).
I get the following W ratings:
Code: Select all
W9, W7, W7, W7, W6, W8, W8, W7, W7, W7,
W8, W8, W8, W6, W6, W6, W8, W5, W6, W7,
W6, W6, W6, W4, W5, W5, W5, W4, W4, W4,
W4
denis_berthier
2010 Supporter
 
Posts: 1983
Joined: 19 June 2007
Location: Paris

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