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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Fri Aug 20, 2010 7:14 am Post subject: Puzzle 10/08/20: A |
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| Code: | +-----------------------+
| . 3 1 | . . 5 | . . . |
| 8 . 4 | 3 1 2 | 6 9 . |
| 9 2 5 | . . . | . . . |
|-------+-------+-------|
| . 1 . | . . 4 | 9 . . |
| . 9 . | . 5 . | . . . |
| 2 5 . | 6 . 9 | 4 . . |
|-------+-------+-------|
| . 4 . | 2 . 6 | 1 8 . |
| . 8 . | . . . | 3 4 . |
| . . . | . . . | . . . |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Fri Aug 20, 2010 10:36 am Post subject: |
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A conventional three steps solution ...
| Quote: | Type 1 UR(13)R36C89 : => r6c9<>13 UP54
X Wing : (3)R67/C35 : => r59c3<>3
XY Wing : (37)R4C1 (78)R4C4 (83)R6C5 : r6c3,r4c9<>3
Note : If a proof is wanted instead of a solution, the 2 1st steps may be replaced by a kraken Starfish (a NoFish, but not containing an impossible non-degenerate Fish !) on 7 removing (7)r7c9 ...  But this doesn't preclude the existence of a shorter solution 
More details tonight maybe, if needed. |
JC |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Fri Aug 20, 2010 4:29 pm Post subject: |
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I played the same as JC but read his post and went back to see what on earth a 'kraken starfish' might be! I am not any wiser and look forward to finding out.
Fwiw, I found a wing which avoided the UR but still left some work..
| Quote: | m-wing(78) with transport ; (7=8)r4c4 - r6c5=(8-7)r1c5=r3c6 - r8c6=r8c1 ; r4c1<>7
skyscraper(7) r4, r7 ; r6c5<>7, r9c4<>7
skyscraper(7) c5, c8 ; r7c9<>7 |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Aug 20, 2010 4:35 pm Post subject: |
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| JC Van Hay wrote: | A conventional three steps solution ...
Note : If a proof is wanted instead of a solution, the 2 1st steps may be replaced by a kraken Starfish (a NoFish, but not containing an impossible non-degenerate Fish !) on 7 removing (7)r7c9 ... But this doesn't preclude the existence of a shorter solution
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I understand that manual solvers encounter different steps and in a different order than my solver. Still, since I do review many puzzles for each one saved for posting, it's nice to occassionally see a solution that matches or comes close to the one from my solver. This way, I know that my selection criteria is actually possible for those working on my puzzles. Thanks for the conventional solution!
That said, I like seeing different solutions posted to know that everyone isn't locked into reporting the same solution. I also enjoy seeing where someone finds something interesting that my (boring ole) solver overlooked. I'd like to see your kraken Starfish as well! If it's not too much to ask, please show the Starfish and the kraken chain separately. I get confused easily if they are combined into one gruesome chain. Thanks!
Regards, Danny
Aside Note: When it comes to XY-Wings, I try to find puzzles where the XY-Wings occur in a manageable number of bivalue cells. An example would be with 18 bivalue cells and 15 polyvalue cells in the grid when my solver uses an XY-Wing step. This forces me to discard a large number of puzzles because the XY-Wing occurs when the ratio is weighted more towards the bivalue side. Does anyone want me to post puzzles where you have to search through more bivalue cells to find an elusive XY-Wing? |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Sat Aug 21, 2010 2:36 am Post subject: |
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After SSTS
| Code: | +--------------------------------------------------------+
| 6 3 1 | 9 78 5 | 278 27 4 |
| 8 7 4 | 3 1 2 | 6 9 5 |
| 9 2 5 | 4 6 78 | 78 13 13 |
|------------------+------------------+------------------|
| 37 1 6 | 78 2 4 | 9 5 378 |
| 4 9 378 | 178 5 1378 | 27 6 2378 |
| 2 5 378 | 6 378 9 | 4 13 1378 |
|------------------+------------------+------------------|
| 5 4 379 | 2 37 6 | 1 8 79 |
| 17 8 2 | 5 9 17 | 3 4 6 |
| 137 6 379 | 178 4 1378 | 5 27 279 |
+--------------------------------------------------------+ |
1. Determination of the superfluous candidates on 7
The distribution of the candidates for the digit 7 looks very fishy, if not "turboty".
| Code: | +-----------------------------------+
| . . . | . 7 . | 7 7 . |
| . . . | . . . | . . . |
| . . . | . . 7 | 7 . . |
|-----------+-----------+-----------|
| 7 . . | 7 . . | . . 7 |
| . . 7 | 7 . 7 | 7 . 7 |
| . . 7 | . 7 . | . . 7 |
|-----------+-----------+-----------|
| . . 7 | . 7 . | . . 7 |
| 7 . . | . . 7 | . . . |
| 7 . 7 | 7 . 7 | . 7 7 |
+-----------------------------------+ |
This is because of the 10 following Boolean Variables : 2 bi-locals in the rows r38, 5 empty rectangles in the boxes b23469 and 3 almost locked candidates in the lines r1c17.
These trigger a search for eventual extraneous candidate(s). To prevent wasting time, a crude and fast nishio/template analysis is done starting from one of the above Boolean Variable. The most promising starting point is the ER in B6 as there is only one solution for the digit 7 when r5c7 contains 7, to wit r5c7=7, r1c8=7, r3c6=7, r8c1=7, r6c3=7, r4c4=7, r7c5=7, r9c9=7.
| Code: | +-----------------------------------+
| . . . | . 7 . | 7 7b . |
| . . . | . . . | . . . |
| . . . | . . 7c | 7 . . |
|-----------+-----------+-----------|
| 7 . . | 7f . . | . . 7 |
| . . 7 | 7 . 7 | 7a . 7 |
| . . 7e | . 7 . | . . 7 |
|-----------+-----------+-----------|
| . . 7 | . 7g . | . . -7 |
| 7d . . | . . 7 | . . . |
| 7 . 7 | 7 . 7 | . 7 7h |
+-----------------------------------+ |
Therefore, one can write the following derived strong sets :(7)r456c9=r7c5 or r9c9 => r7c9<>7 => r9c1346,r5c6,r6c5<>7. In other words, 7 eliminations are obtained in a single shot ! A second run, from the bi-locals in c1 for example, shows that the resulting distribution of candidates is irreducible.2. Interpretation
It is clear that the derived strong sets result from a network of assignments. The shortest path is obtained by using the following SIS : (7)B6 R3 R8 B4 C5 where C5 is taken instead of B8 only because of a smaller number of candidates.
| Code: | +-----------------------------------+
| . . . | . *7 . | 7 7 . |
| . . . | . . . | . . . |
| . . . | . . *7B | *7 . . |
|-----------+-----------+-----------|
| *7 . . | 7 . . | . . *7 |
| . . *7 | 7 . 7 | *7A . *7 |
| . . *7D | . *7 . | . . *7 |
|-----------+-----------+-----------|
| . . 7 | . *7E . | . . -7 |
| *7C . . | . . *7 | . . . |
| 7 . 7 | 7 . 7 | . 7 7 |
+-----------------------------------+ |
So (7)R38C5B46 => (7)r456c9=r7c5 => r7c9<>7
The strong inferences are done inside the 5 SIS while the weak inferences are done inside the following WIS (7)[c7] [c6] [c1 & r5] [r6 & b2] [r7 & c9] where the fifth set of WIS is related to the elimination.
The 5 SIS and the 8 WIS simply locate where the Sudoku puzzle rules are applied. They are all needed to explain the elimination, no less no more.
This is the announced Rank 3 Kraken Mutant "Starfish" (7)R38 C5 B46/r567 c1679 b2. There are 5 base sets (SIS) and 8 cover sets (WIS). The difference of these numbers is the overall rank.3. Representation of the network
The simplest representation of the network is obtained by writing down a Forbiding Matrix where the SIS are put in the rows and the conflicts identified by the WIS in the columns.
Here it is.
| Code: | +--------------------------------------------------------+
| SIS\WIS | 7c9 7c7 7c6 7c1 7r6 |
| | 7r7 7r5 7b2 |
+--------------------------------------------------------+
| Elim |-779 |
+--------------------------------------------------------+
| 7B6 | 7(456)9 757 |
| 7R3 | . 737 736 |
| 7R8 | . . 786 781 |
| 7B4 | . @753 . 741 763 |
| 7C5 | #775 . @715 . 765 |
+--------------------------------------------------------+
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The notations are those of Allan Barker. In the nrc notation, the candidate 757 is equivalent to (7)r2c7, 7(456)9 is equivalent to (7)r456c9, ...
Here the Forbiding Matrix is a Triangular Matrix. The easiest way to read it is to start from the target 779 True, then row after row, False False ... False True. The last row is read False ... False, a contradiction.
Except for the presence of @753 and @715, the Triangular Matrix would reduce to a 5-SIS AIC : 7B6 7R3 7R8 7B4 7C5 : 7(456)9=775 : => -779, and the WIS 7r5 and 7b2 would be superfluous. But this is a Locally Finned Mutant Starfish : (7)R38 C5 B46/r6 c1679 + fin #775. @753 and @715 are therefore remote fins.
Finally, we have caught a Remotely Finned (or Kraken) Mutant Starfish. It is not however a NoFish, because a NoFish is represented by a SIS of 2 Triangular Matrices not reducible to a Pigeonhole Matrix.
Once a Forbiding Matrix is written down, it remains true independently of the target (it may eventually be devised independenly of a presupposed target). The implications of any entry supposed to be True may be read fom it. Furthermore, it may be reinterpreted by reading it from any row ("Interpretation at will" !!).
For example, if it is supposed that @715 is True, then 736 is False, 737 is True, 757 is False and 7(456)9 is True killing 779.
The usual interpretation of the Fish results : 779 is false whether the fins are False or True.
The same kind of reasoning may be done if we suppose that 765 or 775 is True. An alternative interpretation of the elimination results : a Kraken Column 7C5.
| Code: | A Kraken Column 7C5 (ttt's diagram) interpretation
of the Kraken Mutant Starfish (7)R38C5B46/r6c1679 + fins r7c5,r5c3,r1c5
775*
||
715---------736=737-757=7(456)9*
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|| 741-781=786
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765-763
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753-757=7(4 6)9*
+-----------------------------------+
| . . . | . @7 . | 7 7 . |
| . . . | . . . | . . . |
| . . . | . . *7 | *7 . . |
|-----------+-----------+-----------|
| *7 . . | 7 . . | . . *7 |
| . . @7 | 7 . 7 | *7 . *7 |
| . . *7 | . *7 . | . . *7 |
|-----------+-----------+-----------|
| . . 7 | . #7 . | . . -7 |
| *7 . . | . . *7 | . . . |
| 7 . 7 | 7 . 7 | . 7 7 |
+-----------------------------------+ |
4. An Xsudo illustration of the SIS & WIS
The bold lines represent the SIS, while the others the WIS.
5. Final remark
As is usual with Fishes, there are many other ("Kraken") Fishes of various type explaining the elimination of (7)r7c9. As I don't have a General Fish Finder, I don't yet know if there is a simpler interpretation of that elimination JC |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Aug 21, 2010 3:18 am Post subject: |
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A two stepper without a AUR move.......
| Quote: | Almost skyscraper (7)r1c58 with fin (7)r6c5
Skyscraper (7)r1c58=(7)r6c5-r4c4=(7)r4c19
(7)r4c1-r89c1=(7)r7c3; r7c9<>7
(7)r4c9-r79c9=(7)r9c8; r9c46<>7
xy-wing -378 vertex (78)r4c4; r6c3<>3 plus transport (3)r6c5-r7c5=(3)r9c6; r9c1<>3 |
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Aug 21, 2010 5:33 am Post subject: |
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JC, Thank You for the impressive presentation on your Kraken fish!
I followed your network in section 1. Then I was lost in section 2 and the start of section 3. I picked you up again at:
Kraken Mutant Starfish (7)R38C5B46/r6c1679 + fins r7c5,r5c3,r1c5
The three fin cells are easily linked to the r7c9 elimination cell of the Starfish.
| Quote: | As is usual with Fishes, there are many other ("Kraken") Fishes of various type explaining the elimination of (7)r7c9. As I don't have a General Fish Finder, I don't yet know if there is a simpler interpretation of that elimination.
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These three fish exist for your elimination:
| Code: | finned mutant Whale r348c58b6\r17c167b5 w/fins r567c9,r9c8
+-----------------------------------+
| * * * | * X * | * X * |
| * . . | . / * | * / . |
| X / / | / / X | X / / |
|-----------+-----------+-----------|
| X / / | X / * | / / # |
| * . . | * X * | X / # |
| * . . | * X * | X / # |
|-----------+-----------+-----------|
| * * * | * X * | * X ** |
| X / / | / / X | X / / |
| * . . | . / * | * # . |
+-----------------------------------+
+-----------------------------------+
| . . . | . 7 . | 7 7 . |
| . . . | . . . | . . . |
| . . . | . . 7 | 7 . . |
|-----------+-----------+-----------|
| 7 . . | 7 . . | . . 7 |
| . . 7 | 7 . 7 | 7 . 7 |
| . . 7 | . 7 . | . . 7 |
|-----------+-----------+-----------|
| . . 7 | . 7 . | . . -7 |
| 7 . . | . . 7 | . . . |
| 7 . 7 | 7 . 7 | . 7 7 |
+-----------------------------------+
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| Code: | finned mutant Whale r348c58b6\r1c1679b5 w/fins r4c9,r7c5,r9c8
+-----------------------------------+
| * * * | * X * | * X * |
| * . . | . / * | * / * |
| X / / | / / X | X / X |
|-----------+-----------+-----------|
| X / / | X / * | / / # |
| * . . | * X * | X / X |
| * . . | * X * | X / X |
|-----------+-----------+-----------|
| * . . | . # * | * / ** |
| X / / | / / X | X / X |
| * . . | . / * | * # * |
+-----------------------------------+
+-----------------------------------+
| . . . | . 7 . | 7 7 . |
| . . . | . . . | . . . |
| . . . | . . 7 | 7 . . |
|-----------+-----------+-----------|
| 7 . . | 7 . . | . . 7 |
| . . 7 | 7 . 7 | 7 . 7 |
| . . 7 | . 7 . | . . 7 |
|-----------+-----------+-----------|
| . . 7 | . 7 . | . . -7 |
| 7 . . | . . 7 | . . . |
| 7 . 7 | 7 . 7 | . 7 7 |
+-----------------------------------+
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| Code: | finned mutant Whale r348c58b6\r1c167b59 w/fins r456c9,r7c5
+-----------------------------------+
| * * * | * X * | * X * |
| * . . | . / * | * / . |
| X / / | / / X | X / / |
|-----------+-----------+-----------|
| X / / | X / * | / / # |
| * . . | * X * | X / # |
| * . . | * X * | X / # |
|-----------+-----------+-----------|
| * . . | . # * | * X ** |
| X / / | / / X | * / X |
| * . . | . / * | * X * |
+-----------------------------------+
+-----------------------------------+
| . . . | . 7 . | 7 7 . |
| . . . | . . . | . . . |
| . . . | . . 7 | 7 . . |
|-----------+-----------+-----------|
| 7 . . | 7 . . | . . 7 |
| . . 7 | 7 . 7 | 7 . 7 |
| . . 7 | . 7 . | . . 7 |
|-----------+-----------+-----------|
| . . 7 | . 7 . | . . -7 |
| 7 . . | . . 7 | . . . |
| 7 . 7 | 7 . 7 | . 7 7 |
+-----------------------------------+
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Sat Aug 21, 2010 8:14 am Post subject: |
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| tlanglet wrote: | | Quote: | Almost skyscraper (7)r1c58 with fin (7)r6c5
Skyscraper (7)r1c58=(7)r6c5-r4c4=(7)r4c19
(7)r4c1-r89c1=(7)r7c3; r7c9<>7
(7)r4c9-r79c9=(7)r9c8; r9c46<>7
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Ted, I tried to make this work too. Not sure I see your reasoning though.
I think you are saying if fin (7)r6c5 then one of r4c1 or r4c9 is 7? I follow the path for r4c9 and it makes the elimination - in fact both. But from r4c1 I still have a 7 in r9c3 so I don't see the strong link (7)r89c1=r7c3?
(Looking at it again, I can see the fin does make that link exist since:
(7)r6c5 - r7c5 &
(7)r6c5 - r1c5=r3c6 - r89c6 => r9c4=7 removing the (7)r9c3!) |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Sat Aug 21, 2010 8:26 am Post subject: |
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| JC, thanks also. Sadly you lost me! I should say not because of your description which seemed clear and comprehensive - but because just some of the basic terms are new to me. I will do some studying! (The xsudo diagram gave me a grasp of the intent!) |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Sat Aug 21, 2010 12:00 pm Post subject: |
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Danny, thank you for providing the 3 Locally Finned Mutant Whales. From a pure logical point of view, they "contain" a Mutant Starfish (7)R348C58/r1c16b59 with 2 local fins r7c5,r7c9 and 1 remote fin r3c7 removing (7)r7c9. The cover set b6 eliminates the need for a remote fin ! That's fine.
Danny, Peter, I designed the post on the Kraken Fish so as to easily pick up the essentials to one's need. I was well aware that you could be lost somewhere because the details I gave to whom it may concern are rather synthetic. In any case, they are to be taken as a line of thought.
JC |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Sat Aug 21, 2010 1:04 pm Post subject: |
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Down to earth ...
To reveal the XY Wing : (37)R4C1 (78)R4C4 (83)R6C5 : r6c3,r4c9<>3, only (7)r9c4 has to be removed. This is achieved by the following Almost Empty Rectangle (7)R4B9 : (7)r8c6=r8c1-r4c1=[ER R4B9] : => r9c4<>7.
JC |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Aug 21, 2010 2:11 pm Post subject: |
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| peterj wrote: | | tlanglet wrote: | | Quote: | Almost skyscraper (7)r1c58 with fin (7)r6c5
Skyscraper (7)r1c58=(7)r6c5-r4c4=(7)r4c19
(7)r4c1-r89c1=(7)r7c3; r7c9<>7
(7)r4c9-r79c9=(7)r9c8; r9c46<>7
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Ted, I tried to make this work too. Not sure I see your reasoning though.
I think you are saying if fin (7)r6c5 then one of r4c1 or r4c9 is 7? I follow the path for r4c9 and it makes the elimination - in fact both. But from r4c1 I still have a 7 in r9c3 so I don't see the strong link (7)r89c1=r7c3?
(Looking at it again, I can see the fin does make that link exist since:
(7)r6c5 - r7c5 &
(7)r6c5 - r1c5=r3c6 - r89c6 => r9c4=7 removing the (7)r9c3!) |
Peter,
I think I had one (or more) glasses of wine too many last night before working on this puzzle, and am assuming both my sight and thinking are better this morning.
Yes, you interpreted my horrible notation correctly as to my intented solution but, I now see at least two problems with my post.
1. My code after basics did not not have a 7 in r9c3 which, as you pointed out, is not deadly.
2. At the branch, r4c1=7 => r7c9<>7 and r4c9=7 =>r9c46<>7 but neither provides all three deletions.
I think the best approach is to show that r6c5<>7 and then take the three deletions from the resulting skyscraper.
If r6c5=7, then r3c6=7, then r9c4=7, then r8c1=7, then r7c9=7 leaving row 4 without a 7; thus r6c5<>7.
Ted |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Aug 21, 2010 4:45 pm Post subject: |
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| I struggled with a couple of ERs, W-Wing, Type 1 UR and multi-coloring. Then looked at the potential 78 Type 6 UR; r6c3<>3. |
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