The New Sudoku Players' Forum

by **daj95376** » Sat May 31, 2008 4:27 pm

Hobiwan,

An impressive attack on those stubborn puzzles. My solver resorted to networks because I only have UR Type 1&2 implemented.

I thought I'd post a couple of nicer puzzles before the final two difficult ones.

Code: Select all: ....617..8............2.......5...8...38......7....2..42....1.....4....35........ #47289 +--------------------------------------------------------------+ | 2 9 5 | 3 6 1 | 7 4 8 | | 8 16 7 | 9 45 45 | 36 136 2 | | 3 16 4 | 7 2 8 | 5 169 169 | |--------------------+--------------------+--------------------| | 169 4 2 | 5 379 679 | 369 8 1679 | | 169 5 3 | 8 79 2 | 4 1679 1679 | | 69 7 8 | 1 349 469 | 2 3569 569 | |--------------------+--------------------+--------------------| | 4 2 9 | 6 8 3 | 1 57 57 | | 7 8 16 | 4 159 59 | 69 2 3 | | 5 3 16 | 2 179 79 | 8 69 4 | +--------------------------------------------------------------+

Code: Select all: .7....4.82...9........3.6...6.7..5.........92..1......9......1....8.....3........ #47505 +-----------------------------------------------------------------------+ | 156 7 9 | 1256 256 256 | 4 3 8 | | 2 34 346 | 46 9 8 | 7 5 1 | | 145 18 458 | 145 3 7 | 6 2 9 | |-----------------------+-----------------------+-----------------------| | 8 6 2 | 7 1 9 | 5 4 3 | | 457 345 3457 | 56 8 456 | 1 9 2 | | 45 9 1 | 3 245 245 | 8 67 67 | |-----------------------+-----------------------+-----------------------| | 9 28 45678 | 256 24567 2456 | 3 1 4567 | | 14567 12 4567 | 8 24567 3 | 9 67 45 | | 3 45 4567 | 9 4567 1 | 2 8 4567 | +-----------------------------------------------------------------------+

by **hobiwan** » Sat May 31, 2008 4:36 pm

#47289:

Discontinuous Nice Loop [r6c8]=3=[r6c5]=4=[r6c6]-4-[r2c6]-5-[r8c6]-9-[r8c7]=9=[r4c7]=3=[r6c8] => [r6c8]<>569
Singles

by **hobiwan** » Sat May 31, 2008 4:52 pm

#47505:

Forcing Chain Contradiction in c3 => [r1c1]=1
[r1c1]<>1=>[r1c4]=1=>[r7c4]=2=>[r7c2]=8=>[r3c3]=8=>[r3c3]<>5
[r1c1]<>1=>[r1c4]=1=>[r7c4]=2=>[r8c2]=2=>[r8c1]=1=>[r1c1]=6=>[r2c4]=6=>[r5c4]=5=>[r5c3]<>5
[r1c1]<>1=>[r1c4]=1=>[r7c4]=2=>[r8c2]=2=>[r8c1]=1=>[r1c1]=6=>[r2c4]=6=>[r5c4]=5=>[r9c2]=5=>[r789c3]<>5
Singles

There are several other Foring Chains, that all lead to the same contradiction but leave a slightly more complicated solution:
Forcing Chain Contradiction in c3 => [r1c4]=2 or
Forcing Chain Contradiction in c3 => [r2c3]=6 or
Forcing Chain Contradiction in c3 => [r2c4]=4 or
Forcing Chain Contradiction in c3 => [r3c2]=8 or
Forcing Chain Contradiction in c3 => [r3c4]=1 or
Singles plus Remote Pair

by **daj95376** » Sat May 31, 2008 6:33 pm

#47505 ... also ...

Code: Select all: r3c4 =1= r1c4 =2= r7c4 -2- r7c2 =2= r8c2 =1= r8c1 => [r3c1]<>1 4- r2c4 -6- r5c4 -5- r5c23 =5= r6c1 =4= r3c1 => [r2c23],[r3c4]<>4 SSTS

[edit: corrected typo.]

by **daj95376** » Sun Jun 01, 2008 12:25 am

Final two.

Code: Select all: .2....4.....5.7......3.....5.....713.8..2.............1...6..8.3.7.........4..... #47303 +--------------------------------------------------------------------------------+ | 789 2 1359 | 689 189 689 | 4 3579 15789 | | 4689 13 13469 | 5 1489 7 | 12689 2369 12689 | | 46789 17 14569 | 3 1489 2 | 15689 5679 15689 | |--------------------------+--------------------------+--------------------------| | 5 49 2 | 689 89 4689 | 7 1 3 | | 4679 8 13469 | 179 2 13459 | 569 4569 4569 | | 4679 137 13469 | 179 37 13459 | 25689 24569 245689 | |--------------------------+--------------------------+--------------------------| | 1 459 49 | 279 6 39 | 2359 8 24579 | | 3 469 7 | 1289 5 189 | 1269 2469 12469 | | 2 569 8 | 4 37 139 | 13569 5679 15679 | +--------------------------------------------------------------------------------+

Code: Select all: .7....3.....61.......2.8...2...5....4.....7........18....4...62..1.......3....... #47416 +-----------------------------------------------------------------------+ | 8 7 2 | 59 49 459 | 3 1 6 | | 59 4 59 | 6 1 3 | 2 7 8 | | 1 6 3 | 2 7 8 | 59 459 49 | |-----------------------+-----------------------+-----------------------| | 2 189 789 | 13 5 479 | 6 49 349 | | 4 15 569 | 13 8 69 | 7 2 359 | | 3 59 5679 | 79 2469 24679 | 1 8 459 | |-----------------------+-----------------------+-----------------------| | 7 589 589 | 4 3 1 | 59 6 2 | | 569 2 1 | 8 69 569 | 4 3 7 | | 569 3 4 | 579 269 25679 | 8 59 1 | +-----------------------------------------------------------------------+

by **hobiwan** » Sun Jun 01, 2008 1:38 pm

#47303 Without Forcing Chains:

Almost Locked Set XY-Wing: A=[r7c236] - {3459}, B=[r789c7],[r8c89],[r9c89] - {12345679}, C=[r9c5] - {37}, Y,Z=3,7, X=4,5,9 => [r8c2]<>4, [r7c9]<>459
Almost Locked Set XY-Wing: A=[r7c236] - {3459}, B=[r4c456],[r56c4],[r6c5] - {1346789}, C=[r489c2] - {4569}, Y,Z=4,5, X=3 => [r56c6],[r9c5]<>3
Singles

by **hobiwan** » Sun Jun 01, 2008 1:53 pm

#47416: Stubborn! I couldn't find a solution in one step.

Forcing Net Contradiction in [r7c7] => [r6c4]=7
[r6c4]<>7=>[r6c4]=9(=>[r5c6]<>9=>[r5c6]=6=>[r5c3]<>6=>[r5c3]=9=>[r4c2]<>9)(=>[r6c9]<>9)=>[r6c2]<>9=>
[r6c2]=5=>[r6c9]<>5=>[r6c9]=4=>[r4c8]<>4=>[r4c8]=9=>[r9c8]<>9=>[r7c7]=9=>[r7c2]<>9=>[r6c2]=9=>[r6c4]<>9=>[r6c4]=7
Singles to:

Code: Select all: .---------------.--------------------.----------------. | 8 7 2 | 59 49 459 | 3 1 6 | | 59 4 59 | 6 1 3 | 2 7 8 | | 1 6 3 | 2 7 8 | 59 459 49 | :---------------+--------------------+----------------: | 2 8 7 | 1 5 A49 | 6 C49 3 | | 4 1 569 | 3 8 A69 | 7 2 59 | | 3 59 569 | 7 4-69 2 | 1 8 459 | :---------------+--------------------+----------------: | 7 59 8 | 4 3 1 | 59 6 2 | | 59 2 1 | 8 B69 5-6-9| 4 3 7 | | 6 3 4 | B59 2 7 | 8 C59 1 | '---------------'--------------------'----------------'

Almost Locked Set XY-Wing: A=[r45c6] - {469}, B=[r8c5],[r9c4] - {569}, C=[r49c8] - {459}, Y,Z=4,5, X=6,9 => [r6c5]<>6, [r8c6]<>69
Singles

by **daj95376** » Sun Jun 01, 2008 5:37 pm

hobiwan wrote:#47416: Stubborn! I couldn't find a solution in one step.

It all depends upon your perspective about where a contradiction can occur and if it's okay for SSTS to complete the puzzle. The following (forcing ?) network leads to a simple SSTS completion of the puzzle.

In shorthand:

Code: Select all: 9r3c9 4r3c8 5r9c8 5r8c6 5r2c1 9r2c3 9r5c6 4r1c6 [b5]~7

In more detail:

Code: Select all: 9= r3c9 =4= r3c8 =5= r9c8 -5- r9c46 =5= r8c6 -5- r8c1 =5= r2c1 =9= r2c3 -9- ... -9- [r1c6] -4- [r4c6] -7- / \ ... r5c3 =9= r5c6 contradiction! => [r3c9]<>9 \ / -9- [r6c4] -7-

by **Draco** » Mon Jun 02, 2008 5:35 pm

daj95376 wrote:It all depends upon your perspective about where a contradiction can occur and if it's okay for SSTS to complete the puzzle. The following (forcing ?) network leads to a simple SSTS completion of the puzzle.
...

In more detail:

Code: Select all
9= r3c9 =4= r3c8 =5= r9c8 -5- r9c46 =5= r8c6 -5- r8c1 =5= r2c1 =9= r2c3 -9- ... -9- [r1c6] -4- [r4c6] -7- / \ ... r5c3 =9= r5c6 contradiction! => [r3c9]<>9 \ / -9- [r6c4] -7-

Danny I can't quite parse your chain/net/loop. From the branch at r5c6, why isn't r6c4=6 a valid move? I am missing whatever prevents that in your PM's and chain.

Cheers...

- drac

by **hobiwan** » Mon Jun 02, 2008 6:18 pm

daj95376 wrote:It all depends upon your perspective about where a contradiction can occur and if it's okay for SSTS to complete the puzzle. The following (forcing ?) network leads to a simple SSTS completion of the puzzle.

In shorthand:

Code: Select all
9r3c9 4r3c8 5r9c8 5r8c6 5r2c1 9r2c3 9r5c6 4r1c6 [b5]~7

You are right of course. How many nets I find depends on how far my tabling algorithm looks ahead when constructing the initial tables. With my standard setting I don't get your elimination. When I look farther ahead I get (in abbreviated notation):

Forcing Net Contradiction in [c9] => [r3c9]<>9
[r3c9]=9=>[r7c7]=9=>[r6c2]=9=>[r6c4]=7=>[r9c6]=7=>[r6c6]=2=>[r5c6]=6=>[r5c9]=9

[edit: [r9c4]=9 does not belong to the main chain]

or:

Forcing Net Verity => [r3c9]<>9
[r5c3]=9=>[r7c2]=9=>[r3c7]=9=>[r3c9]<>9
[r5c6]=9=>[r6c4]=7=>[r4c6]=4=>[r1c6]=5=>[r9c4]=5=>[r7c7]=5=>[r3c7]=9=>[r3c9]<>9
[r5c9]=9=>[r3c9]<>9

As to SSTS, I am still not really clear on which techniques are covered by it. Singles, Locked Candidates, Hidden and Naked Subsets of course. But what about Two String Kite, Skyscraper, UR, W-Wing, XY-Wing...? Is there a real definition?

by **daj95376** » Mon Jun 02, 2008 7:48 pm

Draco wrote:From the branch at r5c6, why isn't r6c4=6 a valid move? I am missing whatever prevents that in your PM's and chain.

Draco, I can only presume that you have a typo above. There's no way [r6c4]=6 is possible because [r2c4]=6 is a given.

by **daj95376** » Mon Jun 02, 2008 8:14 pm

hobiwan wrote:As to SSTS, I am still not really clear on which techniques are covered by it. Singles, Locked Candidates, Hidden and Naked Subsets of course. But what about Two String Kite, Skyscraper, UR, W-Wing, XY-Wing...? Is there a real definition?

Hobiwan: In diagnostic mode, my old solver lists which candidate eliminations will solve a PM through n-tuples and locked candidates. I refer to this subset of SSTS as simple SSTS.

Code: Select all: ===== ===== ===== ===== Simple Sudoku Technique Set (SSTS) by Hierarchy - Naked Singles - Hidden Singles - Naked Pairs - Locked Candidates - Naked Triples - Naked Quads - Hidden Pairs - X-Wing - Swordfish - Colors - Multi-Colors - Hidden Triples - XY-Wing - Hidden Quads

As for your abbreviated nets, a bit too abbreviated for me.

by **hobiwan** » Mon Jun 02, 2008 8:54 pm

daj95376 wrote:Hobiwan: In diagnostic mode, my old solver lists which candidate eliminations will solve a PM through n-tuples and locked candidates. I refer to this subset of SSTS as simple SSTS...

thanks.

daj95376 wrote:As for your abbreviated nets, a bit too abbreviated for me.

Forcing Net Contradiction in [c9] => [r3c9]<>9
[r3c9]=9(=>[r456c9]<>9=>[r4c8]=9=>[r9c8]<>9=>[r9c8]=5=>[r9c4]<>5)...
...(=>[r456c9]<>9=>[r4c8]=9=>[r4c2]<>9)=>[r3c7]<>9=>[r7c7]=9=>[r7c2]<>9=>[r6c2]=9...
...(=>[r5c3]<>9)=>[r6c4]<>9=>[r6c4]=7=>[r9c4]<>7=>[r9c4]=9(=>[r8c5]<>9=>[r8c5]=6=>[r6c5]<>6)=>...
...[r9c4]<>7=>[r9c6]=7=>[r9c6]<>2=>[r6c6]=2=>[r6c6]<>6=>[r5c6]=6=>[r5c6]<>9=>[r5c9]=9

[edit: first parenthesis was incomplete]

Forcing Net Verity => [r3c9]<>9
[r5c3]=9(=>[r4c2]<>9)=>[r6c2]<>9=>[r7c2]=9=>[r7c7]<>9=>[r3c7]=9=>[r3c9]<>9
[r5c6]=9(=>[r1c6]<>9)(=>[r4c6]<>9)=>[r6c4]<>9=>[r6c4]=7=>[r4c6]<>7=>[r4c6]=4=>...
...[r1c6]<>4=>[r1c6]=5(=>[r8c6]<>5)=>[r9c6]<>5=>[r9c4]=5=>[r9c8]<>5=>[r7c7]=5=>[r3c7]<>5=>[r3c7]=9=>[r3c9]<>9
[r5c9]=9=>[r3c9]<>9

by **hobiwan** » Mon Jun 02, 2008 9:09 pm

hobiwan wrote:#47137: This is a tough one!

One possibility:

Forcing Net Verity => [r3c1]=5
[r6c5]=2=>[r4c6]=3=>[r9c5]=3=>[r7c5]=5=>[r3c1]=5
[r6c5]=7=>[r6c2]=5=>[r7c9]=5=>[r3c1]=5
[r6c5]=9(=>[r9c5]<>9)(=>[r7c5]<>9)=>[r8c7]=9=>[r9c6]=9=>[r9c5]=3=>[r7c5]=5=>[r3c1]=5
After that a Remote Pair, Sashimi X-Wing, XY-Wing and Skyscraper

Alternative: Forcing Net (see above) plus Singles, then:
Finned Whale: 7 r235689 c234589 f[r8c6] f[r9c6] => [r7c5]<>7
Finned Whale: 9 r235689 c345789 f[r8c6] f[r9c6] => [r7c5]<>9
After that Singles plus 1 Remote Pair

Obviously I have a problem with my sorting algorithm for fishes. Instead of

Finned Whale: 7 r235689 c234589 f[r8c6] f[r9c6] => [r7c5]<>7
Finned Whale: 9 r235689 c345789 f[r8c6] f[r9c6] => [r7c5]<>9

it should be

Sashimi X-Wing: 7 c16 r17 f[r8c6] f[r9c6] => [r7c5]<>7
Sashimi X-Wing: 9 c16 r17 f[r8c6] f[r9c6] => [r7c5]<>9

by **Draco** » Mon Jun 02, 2008 10:32 pm

daj95376 wrote:
Draco wrote:From the branch at r5c6, why isn't r6c4=6 a valid move? I am missing whatever prevents that in your PM's and chain.

Draco, I can only presume that you have a typo above. There's no way [r6c4]=6 is possible because [r2c4]=6 is a given.

Sigh -- more like a "read-o". I was misreading your network.

Cheers...

- drac

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