The New Sudoku Players' Forum

by **storm_norm** » Sun Jun 29, 2008 7:57 am

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

Code: Select all: .---------------------.---------------------.---------------------. | 14 13 7 | 2 35 6 | 145 9 8 | | 149 139 6 | 58 358 7 | 145 15 2 | | 5 2 8 | 49 49 1 | 6 7 3 | :---------------------+---------------------+---------------------: | 189 189 4 | 6 189 5 | 3 2 7 | | 1289 5 3 | 189 7 29 | 18 6 4 | | 6 7 12 | 3 128 4 | 9 158 15 | :---------------------+---------------------+---------------------: | 3 16 15 | 7 156 8 | 2 4 9 | | 128 168 159 | 1459 14569 29 | 7 3 156 | | 7 4 1259 | 159 12569 3 | 158 158 156 | '---------------------'---------------------'---------------------'

I found the x-wing

anyone wanna take a stab from here? 7.8 SE

by **wintder** » Sun Jun 29, 2008 9:30 am

This is the best I could do.

Code: Select all: .---------------------.---------------------.---------------------. | 14 13 7 | 2 35 6 | 145 9 8 | | 149 139 6 | 58 358 7 | 45 15 2 | | 5 2 8 | 49 49 1 | 6 7 3 | :---------------------+---------------------+---------------------: | 189 189 4 | 6 189 5 | 3 2 7 | | 1289 5 3 | 189 7 29 | 18 6 4 | | 6 7 12 | 3 128 4 | 9 158 15 | :---------------------+---------------------+---------------------: | 3 16 15 | 7 156 8 | 2 4 9 | | 128 168 159 | 145 1456 29 | 7 3 156 | | 7 4 29 | 159 12569 3 | 158 158 16 | '---------------------'---------------------'---------------------'

From your markup I did these steps.
UR.

Code: Select all: .---------------------.---------------------.---------------------. | 14 13 7 | 2 35 6 | 145 9 8 | | 149 139 6 | 58 358 7 | 145 15 2 | | 5 2 8 |*49 *49 1 | 6 7 3 | :---------------------+---------------------+---------------------: | 189 189 4 | 6 189 5 | 3 2 7 | | 1289 5 3 | 189 7 29 | 18 6 4 | | 6 7 12 | 3 128 4 | 9 158 15 | :---------------------+---------------------+---------------------: | 3 16 15 | 7 156 8 | 2 4 9 | | 128 168 159 |*145-9 *1456-9 29 | 7 3 156 | | 7 4 1259 | 159 12569 3 | 158 158 156 | '---------------------'---------------------'---------------------'

Hidden UR.

Code: Select all: .---------------------.---------------------.---------------------. |#14 13 7 | 2 35 6 |#145 9 8 | |#149 139 6 | 58 358 7 |#45-1 15 2 | | 5 2 8 | 49 49 1 | 6 7 3 | :---------------------+---------------------+---------------------: | 189 189 4 | 6 189 5 | 3 2 7 | | 1289 5 3 | 189 7 29 | 18 6 4 | | 6 7 12 | 3 128 4 | 9 158 15 | :---------------------+---------------------+---------------------: | 3 16 15 | 7 156 8 | 2 4 9 | | 128 168 159 | 145 1456 29 | 7 3 156 | | 7 4 1259 | 159 12569 3 | 158 158 156 | '---------------------'---------------------'---------------------'

Sue de coq or ALS.

Code: Select all: .---------------------.---------------------.---------------------. | 14 13 7 | 2 35 6 | 145 9 8 | | 149 139 6 | 58 358 7 | 45 15 2 | | 5 2 8 | 49 49 1 | 6 7 3 | :---------------------+---------------------+---------------------: | 189 189 4 | 6 189 5 | 3 2 7 | | 1289 5 3 | 189 7 29 | 18 6 4 | | 6 7 12 | 3 128 4 | 9 158 15 | :---------------------+---------------------+---------------------: | 3 @16 @15 | 7 156 8 | 2 4 9 | |@128 @168 @159 | 145 1456 #29 | 7 3 156 | | 7 4 29-1-5| 159 12569 3 | 158 158 156 | '---------------------'---------------------'---------------------'

ALS.

Code: Select all: .---------------------.---------------------.---------------------. | 14 13 7 | 2 35 6 | 145 9 8 | | 149 139 6 | 58 358 7 | 45 15 2 | | 5 2 8 | 49 49 1 | 6 7 3 | :---------------------+---------------------+---------------------: | 189 189 4 | 6 189 5 | 3 2 7 | | 1289 5 3 | 189 7 29 | 18 6 4 | | 6 7 @12 | 3 128 4 | 9 158 @15 | :---------------------+---------------------+---------------------: | 3 16 15 | 7 156 8 | 2 4 9 | | 128 168 159 | 1459 14569 29 | 7 3 156 | | 7 4 *29 |*159 12569 3 |*158 *158 16-5 | '---------------------'---------------------'---------------------'

by **hobiwan** » Mon Jun 30, 2008 6:58 pm

I tried to build on wintder's solution and use mainly ALS, but it still needs lot of steps:
wintder's 1st and 3rd step combined:

Code: Select all: .----------------------.----------------------.---------------------. | 14 13 7 | 2 35 6 | 145 9 8 | | 149 139 6 | 58 358 7 | 145 15 2 | | 5 2 8 | 49 49 1 | 6 7 3 | :----------------------+----------------------+---------------------: | 189 189 4 | 6 189 5 | 3 2 7 | | 1289 5 3 | 189 7 29 | 18 6 4 | | 6 7 12 | 3 128 4 | 9 158 15 | :----------------------+----------------------+---------------------: | 3 C16 C15 | 7 156 8 | 2 4 9 | | A128 A168 A159 | 145-9 1456-9 B29 | 7 3 156 | | 7 4 -12-59 | 159 12569 3 | 158 158 156 | '----------------------'----------------------'---------------------' Sue de Coq: r8c123 - {125689} (r8c6 - {29}, r7c23 - {156}) => r9c3<>1, r9c3<>5, r8c45<>9

Code: Select all: Finned Franken Swordfish: 1 r47b1 c125 fr7c3 => r8c12<>1 .----------------------.----------------------.----------------------. | 14 13 7 | 2 35 6 | 145 9 8 | | 149 139 6 | 58 358 7 | 145 15 2 | | 5 2 8 | 49 49 1 | 6 7 3 | :----------------------+----------------------+----------------------: | 189 189 4 | 6 189 5 | 3 2 7 | | 1289 5 3 | 189 7 29 | 18 6 4 | | 6 7 12 | 3 128 4 | 9 158 B15 | :----------------------+----------------------+----------------------: | 3 16 15 | 7 156 8 | 2 4 9 | | C28 C68 159 | 145 1456 29 | 7 3 B156 | | 7 4 A29 | A159 12569 3 | A158 A158 -1-56 | '----------------------'----------------------'----------------------' Almost Locked Set XY-Wing: A=r9c3478 - {12589}, B=r68c9 - {156}, C=r8c12 - {268}, Y,Z=2,6, X=1,5 => r9c9<>1, r9c9<>5

Code: Select all: Naked Single: [r9c9]=6 W-Wing: 1/5 in r2c8,r8c9 connected by 5 in r6c89 => r9c8<>1 .------------------.-------------------.------------------. | 14 13 7 | 2 35 6 | 145 9 8 | | 149 139 6 | 58 358 7 | 145 15 2 | | 5 2 8 | A49 49 1 | 6 7 3 | :------------------+-------------------+------------------: | 189 189 4 | 6 189 5 | 3 2 7 | | 1289 5 3 | 18-9 7 B29 | 18 6 4 | | 6 7 12 | 3 128 4 | 9 158 15 | :------------------+-------------------+------------------: | 3 16 15 | 7 156 8 | 2 4 9 | | 28 68 C159 | C145 1456 C29 | 7 3 C15 | | 7 4 29 | 159 1259 3 | 158 58 6 | '------------------'-------------------'------------------' Almost Locked Set XY-Wing: A=r3c4 - {49}, B=r5c6 - {29}, C=r8c3469 - {12459}, Y,Z=2,4, X=9 => r5c4<>9

Code: Select all: Naked Pair: 1,8 in r5c47 => r5c1<>1, r5c1<>8 Locked Candidates Type 1 (Pointing): 8 in b4 => r4c5<>8 2-String Kite: 1 in r5c4,r8c9 (connected by r5c7,r6c9) => r8c4<>1 .-------------------.-------------------.------------------. | 14 B13 7 | 2 C35 6 | 145 9 8 | | 149 139 6 | C58 358 7 | 145 15 2 | | 5 2 8 | 49 49 1 | 6 7 3 | :-------------------+-------------------+------------------: | 18-9 18-9 4 | 6 D19 5 | 3 2 7 | | A29 5 3 | D18 7 2-9 | 18 6 4 | | 6 7 12 | 3 128 4 | 9 158 15 | :-------------------+-------------------+------------------: | 3 B16 15 | 7 156 8 | 2 4 9 | | A28 B68 159 | 45 1456 29 | 7 3 15 | | 7 4 29 | 159 1259 3 | 158 58 6 | '-------------------'-------------------'------------------' Almost Locked Set XY-Chain: A=r58c1 - {289}, B=r178c2 - {1368}, C=r1c5,r2c4 - {358}, D=r4c5,r5c4 - {189}, RCs=3,8, X=9 => r4c12,r5c6<>9 Singles

As always some steps are ambiguous. The last ALS-XY-Chain for example can be seen as a normal XY-Chain as well.

by **daj95376** » Mon Jun 30, 2008 8:01 pm

Five chains. I didn't convert them to NL-notation.

Code: Select all: ...2...98..6......528..1..3..46.5.2..5.....6..7.3.49..3..7..249......7..74...3... r3 b2 Naked Pair <> 49 [r1c5],[r2c456] c3b7 Locked Candidate 2 <> 9 [r8c12] X-Wing c16\r58 <> 2 [r8c35] -or- X-Wing r69\c35 <> 2 [r8c35] finned Franken Swordfish r47b1\c125 <> 1 [r8c12] -2r9c5 2r6c5 1r6c3 1r4c5 -1r9c5 <> 1 [r9c5] 5r9c5 5r8c9 1r6c9 2r6c3 2r9c5 <> 5 [r9c5] 6r9c5 6r7c2 8r8c2 2r8c1 2r9c5 <> 6 [r9c5] b8 Naked Pair <> 29 [r8c45],[r9c4] r9 Naked Triple <> 158 [r9c3] 9r3c5 2r9c5 2r8c1 8r8c2 6r8c5 4r3c5 <> 9 [r3c5] r5 Naked Pair <> 18 [r5c1] r4 b4 Locked Candidate 1 <> 8 [r4c5] X-Wing finned c47\r29 <> 5 [r2c8] c7b3 Naked Pair <> 45 [r9c7] 1r4c1 2r6c3 2r8c1 8r4c1 <> 1 [r4c1] 137256498496837512528941673814695327953172864672384951365718249281469735749523186

by **storm_norm** » Mon Jun 30, 2008 8:44 pm

how did I miss the UR 49? I should have seen that

by **ronk** » Tue Jul 01, 2008 1:04 pm

hobiwan wrote:
Code: Select all
.----------------------.----------------------.---------------------. | 14 13 7 | 2 35 6 | 145 9 8 | | 149 139 6 | 58 358 7 | 145 15 2 | | 5 2 8 | 49 49 1 | 6 7 3 | :----------------------+----------------------+---------------------: | 189 189 4 | 6 189 5 | 3 2 7 | | 1289 5 3 | 189 7 29 | 18 6 4 | | 6 7 12 | 3 128 4 | 9 158 15 | :----------------------+----------------------+---------------------: | 3 C16 C15 | 7 156 8 | 2 4 9 | | A128 A168 A159 | 145-9 1456-9 B29 | 7 3 156 | | 7 4 -12-59 | 159 12569 3 | 158 158 156 | '----------------------'----------------------'---------------------' Sue de Coq: r8c123 - {125689} (r8c6 - {29}, r7c23 - {156}) => r9c3<>1, r9c3<>5, r8c45<>9

Your "Sue de Coq" -- with an AAALS (A) doubly-linked to one ALS (B) and triply-linked to a second (C) -- is legitimate, but quite unconventional. I wonder how frequently that pattern occurs.

by **daj95376** » Tue Jul 01, 2008 3:24 pm

Does the Sue de Coq simplify after ... ?

Code: Select all: finned Franken Swordfish r47b1\c125 <> 1 [r8c12] => +-----------------------------------------------------------------------+ | 14 13 7 | 2 35 6 | 145 9 8 | | 149 139 6 | 58 358 7 | 145 15 2 | | 5 2 8 | 49 49 1 | 6 7 3 | |-----------------------+-----------------------+-----------------------| | 189 189 4 | 6 189 5 | 3 2 7 | | 1289 5 3 | 189 7 29 | 18 6 4 | | 6 7 12 | 3 128 4 | 9 158 15 | |-----------------------+-----------------------+-----------------------| | 3 16 15 | 7 156 8 | 2 4 9 | | 28 68 159 | 1459 14569 29 | 7 3 156 | | 7 4 1259 | 159 12569 3 | 158 158 156 | +-----------------------------------------------------------------------+

At this point, these two URs have been used:

Code: Select all: (49) UR [r38c45] => [r8c45]<>9 (14) UR [r12c17] => [r2c7 ]<>1

Code: Select all: +-----------------------------------------------------------------------+ | 14 13 7 | 2 35 6 | 145 9 8 | | 149 139 6 | 58 358 7 | 145 15 2 | | 5 2 8 | 49 49 1 | 6 7 3 | |-----------------------+-----------------------+-----------------------| | 189 189 4 | 6 189 5 | 3 2 7 | | 1289 5 3 | 189 7 29 | 18 6 4 | | 6 7 12 | 3 128 4 | 9 158 15 | |-----------------------+-----------------------+-----------------------| | 3 16 15 | 7 156 8 | 2 4 9 | | 28 68 159 | 1459 14569 29 | 7 3 156 | | 7 4 1259 | 159 12569 3 | 158 158 156 | +-----------------------------------------------------------------------+

There's also ...

Code: Select all: (15) UR [r69c89] => [r9c8 ]<>1

However, I'm surprised that someone hasn't found a useful UR in (15) or (59) in [r789c345] for eliminations there? Heck, I'll even settle for a MUG in (159).

by **hobiwan** » Tue Jul 01, 2008 5:52 pm

ronk wrote:Your "Sue de Coq" -- with an AAALS (A) doubly-linked to one ALS (B) and triply-linked to a second (C) -- is legitimate, but quite unconventional. I wonder how frequently that pattern occurs.

I don't have any numbers, but "non-standard" Sue de Coqs do pop up once in a while. Again without numbers I think that the variant with digits in B or C that are not part of A does happen more often than something like the above.

by **hobiwan** » Tue Jul 01, 2008 6:04 pm

daj95376 wrote:Does the Sue de Coq simplify after ... ?

No, exactly the same, but as often with different flavors:
Sue de Coq: r8c123 - {125689} (r8c6 - {29}, r7c23 - {156}) => r9c3<>1, r9c3<>5, r8c45<>9
Sue de Coq: r8c13 - {12589} (r8c6 - {29}, r7c23,r8c2 - {1568}) => r9c3<>1, r9c3<>5, r8c45<>9
Sue de Coq: r8c23 - {15689} (r8c16 - {289}, r7c23 - {156}) => r9c3<>1, r9c3<>5, r8c45<>9

The last one is different but not easier:
Sue de Coq: r9c45 - {12569} (r9c789 - {1568}, r8c6 - {29}) => r8c45<>9, r9c3<>1, r9c3<>5

Even applying all your URs does not change the Sue de Coqs (only the eliminations).

by **hobiwan** » Wed Jul 02, 2008 8:21 am

Another example (original puzzle posted here):

Code: Select all: 100000007020400060003000500090040000000062040000900800005000003060200080700001000 Silver Plate .-------------------------.------------------------.--------------------------. | 1 458 4689 | 3568 23589 35689 | 2349 239 7 | | 589 2 789 | 4 135789 35789 | 139 6 189 | | 4689 478 3 | 678 12789 6789 | 5 129 12489 | :-------------------------+------------------------+--------------------------: | B26 9 B126 | 3578 4 3578 | A12367 A12357 A1256 | | 358 3578 78 | 1 6 2 | C379 4 C59 | | 23456 13457 12467 | 9 357 357 | 8 12-3-5-7 12-56 | :-------------------------+------------------------+--------------------------: | 2489 148 5 | 678 789 46789 | 124679 1279 3 | | 349 6 149 | 2 3579 34579 | 1479 8 1459 | | 7 348 2489 | 3568 3589 1 | 2469 259 24569 | '-------------------------'------------------------'--------------------------' Sue de Coq: r4c789 - {123567} (r4c13 - {126}, r5c79 - {3579}) => r6c8<>357, r6c9<>5

AAALS, B and C triply-linked (C with additional candidate)

Other possibility (even more complicated and does the same eliminations):
Sue de Coq: r6c123 - {1234567} (r6c56 - {357}, r4c13 - {126}) => r6c8<>357, r6c9<>5

by **Steve K** » Wed Jul 02, 2008 11:38 am

Another view of the same elimination: multi-hub, rim, spokes:
ALS 126 r4c13 is the rim, (126)r6 Box6=Box4 are the spokes.
Multi-Hub is (126) at r6 c89. => r6c89 limited to (126), if any of (126) existed in box 4 outside of the spokes and the ALS, they would be eliminated at those locations. The overlap between Hub,Rim, Spoke and Sue de Coq is frequent. The first example in this thread is also a single hub, two spokes, ALS rim configuration.

by **ronk** » Wed Jul 02, 2008 2:06 pm

hobiwan, AFAIK the ALS xz-rule subsumes the Sue de Coq technique. Looking at these patterns as one ALS and one AALS would simplify things IMO.

Code: Select all: .-------------------------.------------------------.--------------------------. | 1 458 4689 | 3568 23589 35689 | 2349 239 7 | | 589 2 789 | 4 135789 35789 | 139 6 189 | | 4689 478 3 | 678 12789 6789 | 5 129 12489 | :-------------------------+------------------------+--------------------------: | B26 9 B126 | 3578 4 3578 | A12367 A12357 A1256 | | 358 3578 78 | 1 6 2 | C379 4 C59 | | D23456 D13457 D12467 | 9 E357 E357 | 8 12-3-5-7 12-56 | :-------------------------+------------------------+--------------------------: | 2489 148 5 | 678 789 46789 | 124679 1279 3 | | 349 6 149 | 2 3579 34579 | 1479 8 1459 | | 7 348 2489 | 3568 3589 1 | 2469 259 24569 | '-------------------------'------------------------'--------------------------'

AB is an ALS triply-linked to AALS C
AC is an AALS triply-linked to ALS B

BD is an AALS triply-linked to ALS E
DE is an AALS triply-linked to ALS B

by **hobiwan** » Wed Jul 02, 2008 5:12 pm

Steve K wrote:Another view of the same elimination: multi-hub, rim, spokes:

I am not familiar with the terminology. Do you have a link?

ronk wrote:hobiwan, AFAIK the ALS xz-rule subsumes the Sue de Coq technique. Looking at these patterns as one ALS and one AALS would simplify things IMO.

Agreed on "simplify", but since my solver can't handle AALS I am stuck with the Sue de Coq version for now. Besides if eliminations were present in r4 or b4 (the AC-E and DE-B variants) you would have two steps instead of one.

by **ronk** » Wed Jul 02, 2008 8:42 pm

hobiwan wrote:Besides if eliminations were present in r4 or b4 (the AC-E and DE-B variants) you would have two steps instead of one.

I don't believe that is correct. The sets are truly locked ... whether the viewpoint is two sets or three sets.

by **Steve K** » Thu Jul 03, 2008 3:38 am

Perhaps the multi-hub is not fully explained, albeit the extensions should be obvious. Here is a link: http://forum.enjoysudoku.com/viewtopic.php?t=5251

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