A tough pattern ?

Everything about Sudoku that doesn't fit in one of the other sections

A tough pattern ?

Postby Ocean » Fri May 19, 2006 1:53 pm

My logical solver had problem with these: No progress at all. Could be interesting to know if they are hard or not. Also, whether a similar solving strategy can be used for all, or if different strategies are needed.
Code: Select all
#
# M20. (Possibly Hard).
#
. . .|. 1 .|. . 2
. . 1|. . .|. 3 .
. 4 .|. . 5|6 . .
-----+-----+-----
. . .|. . 6|7 . .
3 . .|. . .|. . 5
. . 8|4 . .|. . .
-----+-----+-----
. . 7|8 . .|. 4 .
. 5 .|. . .|9 . .
2 . .|. 3 .|. . .


#
# The hard set: 411 M20s. Non-isomorphic. Identical pattern. 20 clues. Minimal.
#
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#
Ocean
 
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Postby Ruud » Fri May 19, 2006 3:10 pm

#254 is the odd one out. It solves with naked pairs and swordfish.

#9 is the toughest. 33 tabling steps for SudoCue.

Ruud.
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Postby daj95376 » Fri May 19, 2006 5:47 pm

Ocean,

Great collection of Swordfish puzzles. Too bad they require more. Another way of looking at puzzle #9. (Based on guessing.)

Code: Select all
Puzzle #9: 

....1...2..2....3..4...56.......21..5.......7..34.......63...8..1....4..9...7....

r267    =  1     Swordfish
r348    =  3     Swordfish
r159    =  4     Swordfish
r3c1    <> 8     [r3c1]=8 ... ,=>[r8]=INVALID
r3c8    <> 9     [r3c8]=9 ... ,=>[r2c7]=EMPTY
r4c3    <> 7     [r4c3]=7 ... ,=>[c1]=INVALID
r7c1    <> 7     [r7c1]=7 ... ,=>[r7]=INVALID
r7c2    <> 2     [r7c2]=2 ... ,=>[r6]=INVALID
r7c2    =  5     [r7c2]=7 ... ,=>[r6]=INVALID
r7c7    =  7     Hidden Single
r1c3    =  5     Hidden Single
r7      =  19    Naked  Pair
    b3  =  89    Naked  Pair
r2c7    =  5     Naked  Single
r1c7    =  9     [r1c7]=8 ... ,=>[r4c4]=EMPTY
r3c9    =  8     Naked  Single
r8c3    =  7     [r8c3]=8 ... ,=>[r1c8]=EMPTY
r3c4    <> 7     [r3c4]=7 ... ,=>[r1c4]=EMPTY
r3c4    =  2     [r3c4]=9 ... ,=>[r2]=INVALID
r4c8    <> 9     [r4c8]=9 ... ,=>[r5c5]=EMPTY
r5c5    <> 9     [r5c5]=9 ... ,=>[r4c8]=EMPTY
r5c7    <> 2     [r5c7]=2 ... ,=>[r2c4]=EMPTY
r8c1    <> 8     [r8c1]=8 ... ,=>[c6]=INVALID
    b7  =  8     Locked Candidate (1)
r9c9    =  5     [r9c9]=6 ... ,=>[r5c5]=EMPTY
r1c8    =  7     [r1c8]=4 ... ,=>[r4c4]=EMPTY
                 Singles
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Postby Ocean » Fri May 19, 2006 6:53 pm

Thanks, Ruud and daj95376, for analyzing the puzzle set.

Ruud wrote:#254 is the odd one out. It solves with naked pairs and swordfish.

#9 is the toughest. 33 tabling steps for SudoCue.

Ruud.

I couldn't catch the swordfishes... so it was almost expected some of them would slip through the net...
33 tabling steps sound much .... how does that compare to other puzzles in the forum?
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Postby ronk » Fri May 19, 2006 8:27 pm

Ruud wrote:#9 is the toughest. 33 tabling steps for SudoCue.

Does one "step" mean the exclusion of one candidate? Or might there be multiple steps per exclusion?

daj95376 wrote:Puzzle #9:
(...)
r3c1 <> 8 [r3c1]=8 ... ,=>[r8]=INVALID

Typically, does this mean no candidate available in r8 (empty row) ... or something else?

TIA, Ron
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Postby Ruud » Sat May 20, 2006 11:35 am

Ocean wrote:33 tabling steps sound much .... how does that compare to other puzzles in the forum?

It is much. The 'ancient toughest known' requires 19 steps. #1 in my top50000 requires 29.

ronk wrote:Does one "step" mean the exclusion of one candidate?

Yes. Each time a single candidate is eliminated, SudoCue tries all solving techniques before it tries another tabling step. There is a bias towards the cells with the smallest contraint size (bivalue, bilication, trivalue, trilocation, etc.), but not towards magic cells.

Ruud.
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Postby ronk » Sat May 20, 2006 1:06 pm

ronk wrote:
daj95376 wrote:Puzzle #9:
(...)
r3c1 <> 8 [r3c1]=8 ... ,=>[r8]=INVALID

Typically, does this mean no candidate available in r8 (empty row) ... or something else?

daj95376, never mind. I just noticed my solver -- with multi-coloring and almost-locked-sets both disabled -- takes exactly the same solution path, so I can just take a look at what it is doing.:D

It's (more verbose) solution path ...
swordfish1: excludes 1 from r3c1 = 1378
swordfish1: excludes 1 from r5c6 = 13689
swordfish1: excludes 1 from r9c6 = 1468
swordfish1: excludes 1 from r3c9 = 189
swordfish1: excludes 1 from r9c9 = 1356
swordfish1: excludes 3 from r1c1 = 3678
swordfish1: excludes 3 from r5c5 = 3689
swordfish1: excludes 3 from r9c9 = 356
swordfish1: excludes 4 from r4c3 = 4789
swordfish1: excludes 4 from r2c6 = 46789
swordfish1: excludes 4 from r7c6 = 149
swordfish1: excludes 4 from r4c8 = 4569
implication: excludes 8 from r3c1 = 378
implication: excludes 9 from r3c8 = 179
implication: excludes 7 from r4c3 = 789
implication: excludes 7 from r7c1 = 247
implication: excludes 2 from r7c2 = 257
implication: excludes 7 from r7c2 = 57
implication: r7c2 := 5
hidden single: r1c3 := 5
hidden single: r7c7 := 7
naked pair: excludes 89 from r1c8 = 479
naked pair: excludes 89 from r2c7 = 589
naked pair: r2c7 := 5
naked pair: excludes 89 from r2c9 = 1489
naked pair: excludes 19 from r7c5 = 249
implication: excludes 8 from r1c7 = 89
implication: r1c7 := 9
naked single: r3c9 := 8
implication: excludes 8 from r8c3 = 78
implication: r8c3 := 7
implication: excludes 7 from r3c4 = 279
implication: excludes 9 from r3c4 = 29
implication: r3c4 := 2
implication: excludes 9 from r4c8 = 569
implication: excludes 9 from r5c5 = 689
implication: excludes 2 from r5c7 = 238
implication: excludes 8 from r8c1 = 238
locked1: excludes 8 from r9c4 = 1568
locked1: excludes 8 from r9c6 = 468
implication: excludes 6 from r9c9 = 56
implication: r9c9 := 5
implication: excludes 4 from r1c8 = 47
implication: r1c8 := 7
... then a cascade of naked singles.

Enabling both multi-coloring and ALSs reduces the "implication chain steps" (guesses) from 16 to 12.
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Postby ravel » Mon May 22, 2006 8:23 am

Oceans #9 needs 3 brute force steps in my solver (r4c4<>5 or r8c5<>5 or r9c4<>5 or r9c4<>6, r1c6<>3, r1c7<>8).
In the moment i cannot check sudokus line by line (and the program is rather slow), but if i find some time, i will enable this to look at the others in the list.

Ruud, can you post your say 5 or 10 hardest from your list also, please ?
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Postby daj95376 » Mon May 22, 2006 6:07 pm

ronk wrote:
daj95376 wrote:Puzzle #9:
(...)
r3c1 <> 8 [r3c1]=8 ... ,=>[r8]=INVALID

Typically, does this mean no candidate available in r8 (empty row) ... or something else?

TIA, Ron


FWIW, the INVALID indicates that there are too few candidates in row 8 to fill all of the remaining cells.
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Postby Ruud » Mon May 22, 2006 6:30 pm

ravel wrote:Ruud, can you post your say 5 or 10 hardest from your list also, please ?


Here are the first 10 in my top50000 a.k.a. "Trials and Tabulations"

Code: Select all
081600090000000000004037600600400500030000070007002004005210300000000000070004810
053070008000000003001300000060800009040090060200007010000004600500000000700050290
000018400000700093803000500000800010000506000020001000004000906930005000005960000
000006902000090000004002560800000103000403000302000005075600300000080000401500000
085700020000000000020000109008140005002000040600000800000004000000560007090020350
090001700000000800800007012207000000000506000000000903580300004001000000004800060
000100207000040005080003000005007009010050030200900500000600040100070000802009000
000070508090008300510020000800000000045060980000000004000090056001400070407050000
000190000010000090000030801060004930005080100094500080903040000020000070000059000
030020006009006020000050100060400900300000001001007050007090000040800200200040030


Have fun

Ruud.
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Postby Mike Barker » Tue May 23, 2006 12:52 pm

Could you provide a link to what you mean by "tabling"? It seems that #2 cracks with nothing more than an ALS-xy rule and a finned X-wing:
    Hidden Single: r3c9 => r3c9=6,r3c156<>6
    Hidden Single: r5c9 => r5c9=2,r4c8<>2,r5c46<>2
    Locked Column: r45c1 => r7c1<>1
    Locked Column: r45c3 => r2c3<>7
    Locked Column: r89c3 => r2c3<>4
    Locked Column: r89c3 => r2c3<>6
    Locked Column: r12c7 => r8c7<>1
    Locked Column: r56c7 => r8c7<>8
    Locked Column Box: r2345c7|r234c8 => r8c7<>7,r78c8<>7
    Hidden Column Pair: r89c3 => r8c3=46,r9c3=46
    Naked Row Triple: r9c349 => r9c2<>1,r9c6<>16
    ALS xy-rule with B=1 cells: r4c378-4-r6c9-5-r8c79|r79c9 => r56c7<>3
    Locked Row: r4c78 => r4c156<>3
    Naked Single: r4c1 => r4c56<>1,r5c1<>1
    Row X-Wing Fillet-o-Fish: r5c16|r9c26 => r7c1<>3
    The Solution is completed with singles
If this right, how does tabling fit into the solution?
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Postby ravel » Tue May 23, 2006 1:00 pm

Ocean, i have scanned now the whole list with this 20 clue pattern. Nearly all are rather tough, numbers 40, 75 and 126 needed 4 steps.

Thanks Ruud, heavy food, for 6 of the puzzles my program needed unusually long to get the low step paths. But at the end only numbers 7 and 10 needed 4 steps.

I started scanning the top1465. After about 600 now i expect about 90 puzzles with at least 4 steps there. So i will have about 100 hardies then and i will rearrange my toughest list in a new thread in the next days.

BTW: i have also scanned Eppsteins list with 520 hard 17-clues, but none needed more than 3 steps.
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Postby Havard » Tue May 23, 2006 1:45 pm

Mike Barker wrote:Could you provide a link to what you mean by "tabling"? It seems that #2 cracks with nothing more than an ALS-xy rule and a finned X-wing:
    Hidden Single: r3c9 => r3c9=6,r3c156<>6
    Hidden Single: r5c9 => r5c9=2,r4c8<>2,r5c46<>2
    Locked Column: r45c1 => r7c1<>1
    Locked Column: r45c3 => r2c3<>7
    Locked Column: r89c3 => r2c3<>4
    Locked Column: r89c3 => r2c3<>6
    Locked Column: r12c7 => r8c7<>1
    Locked Column: r56c7 => r8c7<>8
    Locked Column Box: r2345c7|r234c8 => r8c7<>7,r78c8<>7
    Hidden Column Pair: r89c3 => r8c3=46,r9c3=46
    Naked Row Triple: r9c349 => r9c2<>1,r9c6<>16
    ALS xy-rule with B=1 cells: r4c378-4-r6c9-5-r8c79|r79c9 => r56c7<>3
    Locked Row: r4c78 => r4c156<>3
    Naked Single: r4c1 => r4c56<>1,r5c1<>1
    Row X-Wing Fillet-o-Fish: r5c16|r9c26 => r7c1<>3
    The Solution is completed with singles
If this right, how does tabling fit into the solution?


Yup, I found the same thing! Also #10 does not belong in that list according to my solver, since it solves using ALS.

Havard
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Postby ronk » Tue May 23, 2006 2:16 pm

Havard wrote:
Mike Barker wrote:Could you provide a link to what you mean by "tabling"? It seems that #2 cracks with nothing more than an ALS-xy rule and a finned X-wing:
(...)
If this right, how does tabling fit into the solution?

Yup, I found the same thing! Also #10 does not belong in that list according to my solver, since it solves using ALS.

I don't think there are many published solvers that employ ALS at this time, particularly the ALS xy-rule. I doubt that even Bob Hanson's Medusa uses the xy-rule.
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Postby Havard » Tue May 23, 2006 2:27 pm

ronk wrote:
Havard wrote:
Mike Barker wrote:Could you provide a link to what you mean by "tabling"? It seems that #2 cracks with nothing more than an ALS-xy rule and a finned X-wing:
(...)
If this right, how does tabling fit into the solution?

Yup, I found the same thing! Also #10 does not belong in that list according to my solver, since it solves using ALS.

I don't think there are many published solvers that employ ALS at this time, particularly the ALS xy-rule. I doubt that even Bob Hanson's Medusa uses the xy-rule.


With your point being that...?:)

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