## A tough pattern ?

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

### A tough pattern ?

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. 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Ocean

Posts: 442
Joined: 29 August 2005

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

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

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

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     Swordfishr348    =  3     Swordfishr159    =  4     Swordfishr3c1    <> 8     [r3c1]=8 ... ,=>[r8]=INVALIDr3c8    <> 9     [r3c8]=9 ... ,=>[r2c7]=EMPTYr4c3    <> 7     [r4c3]=7 ... ,=>[c1]=INVALIDr7c1    <> 7     [r7c1]=7 ... ,=>[r7]=INVALIDr7c2    <> 2     [r7c2]=2 ... ,=>[r6]=INVALIDr7c2    =  5     [r7c2]=7 ... ,=>[r6]=INVALIDr7c7    =  7     Hidden Singler1c3    =  5     Hidden Singler7      =  19    Naked  Pair    b3  =  89    Naked  Pairr2c7    =  5     Naked  Singler1c7    =  9     [r1c7]=8 ... ,=>[r4c4]=EMPTYr3c9    =  8     Naked  Singler8c3    =  7     [r8c3]=8 ... ,=>[r1c8]=EMPTYr3c4    <> 7     [r3c4]=7 ... ,=>[r1c4]=EMPTYr3c4    =  2     [r3c4]=9 ... ,=>[r2]=INVALIDr4c8    <> 9     [r4c8]=9 ... ,=>[r5c5]=EMPTYr5c5    <> 9     [r5c5]=9 ... ,=>[r4c8]=EMPTYr5c7    <> 2     [r5c7]=2 ... ,=>[r2c4]=EMPTYr8c1    <> 8     [r8c1]=8 ... ,=>[c6]=INVALID    b7  =  8     Locked Candidate (1)r9c9    =  5     [r9c9]=6 ... ,=>[r5c5]=EMPTYr1c8    =  7     [r1c8]=4 ... ,=>[r4c4]=EMPTY                 Singles`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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?
Ocean

Posts: 442
Joined: 29 August 2005

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
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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.
Ruud

Posts: 664
Joined: 28 October 2005

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.

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.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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.

ravel

Posts: 998
Joined: 21 February 2006

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.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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
`081600090000000000004037600600400500030000070007002004005210300000000000070004810053070008000000003001300000060800009040090060200007010000004600500000000700050290000018400000700093803000500000800010000506000020001000004000906930005000005960000000006902000090000004002560800000103000403000302000005075600300000080000401500000085700020000000000020000109008140005002000040600000800000004000000560007090020350090001700000000800800007012207000000000506000000000903580300004001000000004800060000100207000040005080003000005007009010050030200900500000600040100070000802009000000070508090008300510020000800000000045060980000000004000090056001400070407050000000190000010000090000030801060004930005080100094500080903040000020000070000059000030020006009006020000050100060400900300000001001007050007090000040800200200040030`

Have fun

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

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?
Mike Barker

Posts: 458
Joined: 22 January 2006

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.
ravel

Posts: 998
Joined: 21 February 2006

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
Havard

Posts: 377
Joined: 25 December 2005

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.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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.