Where do I go from here?????

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Where do I go from here?????

Postby Gee » Tue Mar 31, 2009 7:34 pm

I got this far with this puzzle and I cannot find another candidate to remove. The start of the puzzle is below followed by the as to where I gave up. This puzzle seemed easy until I got stuck. Your help will be appreciated. Thanks.

Code: Select all
 *-----------*
 |4..|..3|.7.|
 |...|...|...|
 |...|.8.|2..|
 |---+---+---|
 |..6|...|...|
 |.28|...|...|
 |...|..7|.3.|
 |---+---+---|
 |9..|...|8..|
 |1..|7.5|4..|
 |...|...|6..|
 *-----------*



Code: Select all
 *--------------------------------------------------------------------*
 | 4      159    2      | 6      159    3      | 159    7      8      |
 | 8      159    19     | 12459  7      1249   | 3      6      145    |
 | 6      3      7      | 1459   8      149    | 2      49     145    |
 |----------------------+----------------------+----------------------|
 | 37     19     6      | 13459  13459  149    | 1579   8      2      |
 | 37     2      8      | 1359   1359   6      | 1579   49     145    |
 | 5      4      19     | 8      2      7      | 19     3      6      |
 |----------------------+----------------------+----------------------|
 | 9      6      45     | 1234   134    124    | 8      15     7      |
 | 1      8      3      | 7      6      5      | 4      2      9      |
 | 2      7      45     | 149    149    8      | 6      15     3      |
 *--------------------------------------------------------------------*

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Postby 999_Springs » Tue Mar 31, 2009 10:53 pm

Code: Select all
9r2c6-9-r2c3=9=r6c3
||
9r4c6-9-r4c2=9=r6c3
||
9r3c6-9-r3c8=9=r5c8-9-r6c7=9=r6c3


Therefore, r6c3=9, and the puzzle solves with singles, a turbot fish or BUG, and more singles.

Perhaps the fish experts around here can give a name to this species of fish.
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Once upon a time I was a teenager who was active on here 2007-2011
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Postby daj95376 » Wed Apr 01, 2009 12:17 am

Code: Select all
 Sashimi Franken Jellyfish r169b5\c2457 w/2x fin cells  =>  [r4c2]<>9   -or-
 Sashimi Franken Jellyfish r159b4\c2457 w/2x fin cells  =>  [r6c7]<>9
 *--------------------------------------------------------------------*
 | 4      159    2      | 6      159    3      | 159    7      8      |
 | 8      159    19     | 12459  7      1249   | 3      6      145    |
 | 6      3      7      | 1459   8      149    | 2      49     145    |
 |----------------------+----------------------+----------------------|
 | 37     19     6      | 13459  13459  149    | 1579   8      2      |
 | 37     2      8      | 1359   1359   6      | 1579   49     145    |
 | 5      4      19     | 8      2      7      | 19     3      6      |
 |----------------------+----------------------+----------------------|
 | 9      6      45     | 1234   134    124    | 8      15     7      |
 | 1      8      3      | 7      6      5      | 4      2      9      |
 | 2      7      45     | 149    149    8      | 6      15     3      |
 *--------------------------------------------------------------------*

BUG+1 remains only obstacle to Singles completion.
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Postby Draco » Wed Apr 01, 2009 1:08 am

Another solution that also plays off all those 9's is this chain:

r4c2=9 r2c3=9 [r4c6<>9 + r2c6<>9] = r3c6=9 r3c8=4 r5c8=9 r6c7=1 r6c3=0

Makes the same elimiation as Daj's first Franken Fish: r4c2<>9. Several singles followed by a single-color exclusion on 9's (or you can use BUG+1 as 999_Springs noted) leaves you with singles to solve.

999_Springs: is the color exclusion on 9's (which is a single color move) what you were calling the Turbot Fish (I thought Turbot's required multiple colors, but I've thought lots of things that turned out to be not quite right:) )?

Cheers...

- drac

[edit: fixed typo]
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Postby DonM » Wed Apr 01, 2009 4:56 am

999_Springs wrote:
Code: Select all
9r2c6-9-r2c3=9=r6c3
||
9r4c6-9-r4c2=9=r6c3
||
9r3c6-9-r3c8=9=r5c8-9-r6c7=9=r6c3


Therefore, r6c3=9, and the puzzle solves with singles, a turbot fish or BUG, and more singles.

Perhaps the fish experts around here can give a name to this species of fish.


Rather than a fish, I think this fits more as an AAIC/column or Kraken/column depending on what terminology one prefers.
Last edited by DonM on Wed Apr 01, 2009 2:38 am, edited 1 time in total.
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Postby Gee » Wed Apr 01, 2009 5:46 am

Thanks for your replies. I do have a question about the cold from below.

999_Springs wrote:
9r2c6-9-r2c3=9=r6c3
||
9r4c6-9-r4c2=9=r6c3
||
9r3c6-9-r3c8=9=r5c8-9-r6c7=9=r6c3




I knew when I submitted the puzzle that there were a lot of (1) and (9) digits but I couldn’t make any elimination’s. I understand the notation, I think, but I have never seen a strategy like this before. I wonder if it could be explained in layman terms, if you will, to help me understand this logic as well as if all three of the steps shown are necessary. It is interesting.

Thanks again,

Gee
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Postby Luke » Wed Apr 01, 2009 6:59 am

Gee wrote:999_Springs wrote:
9r2c6-9-r2c3=9=r6c3
||
9r4c6-9-r4c2=9=r6c3
||
9r3c6-9-r3c8=9=r5c8-9-r6c7=9=r6c3

I wonder if it could be explained in layman terms, if you will, to help me understand this logic as well as if all three of the steps shown are necessary. It is interesting.

Hi, Gee, lately I too have been working on understanding this notation. Since no man around here is more lay than I, here's how I see it.

All three steps are needed. The move is an examination of what effect placing a 9 anywhere in column 6 has on the 9 in r6c3. All three possibilities lead to a common conclusion: r6c3 must be 9. Each chain starts with a weak inference, so one way to think of it is to follow each chain starting like this:
Code: Select all
If r2c6 is 9, then...
If r4c6 is 9, then...
If r3c6 is 9, then...
Note that no conclusions are made about c6, only r6c3.

I've probably made some mistakes in semantics, but I'll bet you can see that all roads lead to the same destination.
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Postby aran » Wed Apr 01, 2009 2:58 pm

Gee, just to add to Luke's post :
in the presentation
a
||
b
||
c

the vertical double bars are a reflection of the horizontal double bar strong link symbol =.
Just as a=b means at least one of a or b is true, so the vertical picture means that at least one of the items in the list linked by || is true. In the above : at least one of a or b or c is true, or in other words {a,b,c} is a strong set.

In the example given by the well-named 999 Springs, {999} at r234c6 is a strong set, since one of those must be true, hence
9r2c6
||
9r3c6
||
9r4c6

Strong sets can therefore be listed vertically and developed horizontally with the goal of seeking a common conclusion, which if found must be true.

Another example : imagine a deadly rectangle with corners 57, 571, 572, 573. Then {1,2,3} is a strong set (at least one must be true, and indeed all may be true) so
1
||
2
||
3.
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Postby Gee » Thu Apr 02, 2009 6:25 am

Thanks to all for your responses. Luke451, I understood where you were coming from. And Aran, your excellent clarification solidified my understanding of this concept.

I wonder if this strategy has a name. I have never seen it in anything I have ever read. It seems to be a rather esoteric strategy but it is certainly clever and something I would never have thought of in a million years. I will keep it in mind and thanks for your enlightenment.
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Postby DonM » Thu Apr 02, 2009 7:44 am

Gee wrote:Thanks to all for your responses. Luke451, I understood where you were coming from. And Aran, your excellent clarification solidified my understanding of this concept.

I wonder if this strategy has a name. I have never seen it in anything I have ever read. It seems to be a rather esoteric strategy but it is certainly clever and something I would never have thought of in a million years. I will keep it in mind and thanks for your enlightenment.


Repeating myself from above: AAIC/column or Kraken/column depending on what terminology one prefers.
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Postby Luke » Thu Apr 02, 2009 9:58 am

aran wrote:Strong sets can therefore be listed vertically and developed horizontally with the goal of seeking a common conclusion, which if found must be true.

I'd also like to thank aran for his consise presentation. It helped me out as well. Now I have to wonder why I've never seen him suggest such a move in his solutions:) .

Gee wrote:I have never seen it in anything I have ever read.

Check out the Eureka forum under "Puzzles From Others." There are several presentations from ttt and others that key on this concept. However, be prepared to woodshed a bit ... there are no concessions to us uninitiated, to say the least.

DonM wrote:Repeating myself from above: AAIC/column or Kraken/column depending on what terminology one prefers.

This made a small bulb flicker on in the dim room that is my Sudoku clarity:idea: :
Code: Select all
If the originating strong set is in a column, one could call the move a Kraken Column.
If the originating strong set is in a row, one could call the move a Kraken Row.
If the originating strong set is in a single cell, one could call the move a Kraken Cell.

I can only hope that the differing nomenclature was not the product some debate I can't seem to find. That would mean there's someone out there that would prefer to see AAIC/Column/Row/Cell.

Either way, I too find this very interesting.
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Postby storm_norm » Thu Apr 02, 2009 11:43 am

:idea::idea:
i'd also like to be included in the party that is thanking aran, don, luke and anyone else I am forgetting for taking the time to explain that in such a understanding way.
I think my learning curve jumped past verticle by simply reading this thread.
much thanx.

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Postby aran » Thu Apr 02, 2009 12:46 pm

Luke451 wrote:Now I have to wonder why I've never seen him suggest such a move in his solutions:) .

Up to now, I haven't been too keen on this approach...the idea of having to find a number of chains that all converge on a common conclusion seems somehow unattractive...That said I wouldn't hesitate to do so for a deadly pattern. And further we saw how effective 999 Springs approach was in Gee's example. So I may reconsider:)

As to Kraken : I think of it as a fin acting through a chain rather than directly on an elimination target. In that sense Kraken fin rather than Kraken fish would seem to me better terminology, but I think Kraken fish is orthodox.
In keeping with the "halieutic" context, the Kraken fin can be thought of as a tentacle and - tying in to Don's "Kraken column" term - maybe Kraken has developed to mean tentacular emanations from a common source such as a strong set, as in the case of those {999}.

To finish with a Kraken example (profiting from daj's excellent find of a two-finned Sashimi Franken Jellyfish)
Code: Select all
 Sashimi Franken Jellyfish r169b5\c2457 w/2x fin cells  =>  [r4c2]<>9   -or-
 Sashimi Franken Jellyfish r159b4\c2457 w/2x fin cells  =>  [r6c7]<>9
 *--------------------------------------------------------------------*
 | 4      159    2      | 6      159    3      | 159    7      8      |
 | 8      159    19     | 12459  7      1249   | 3      6      145    |
 | 6      3      7      | 1459   8      149    | 2      49     145    |
 |----------------------+----------------------+----------------------|
 | 37     19     6      | 13459  13459  149    | 1579   8      2      |
 | 37     2      8      | 1359   1359   6      | 1579   49     145    |
 | 5      4      19     | 8      2      7      | 19     3      6      |
 |----------------------+----------------------+----------------------|
 | 9      6      45     | 1234   134    124    | 8      15     7      |
 | 1      8      3      | 7      6      5      | 4      2      9      |
 | 2      7      45     | 149    149    8      | 6      15     3      |
 *--------------------------------------------------------------------*

we can also proceed as follows with respect to candidate 9 :
Base set units : rows 1,5,6,9
Cover set units : columns 2,4,6,7.
ie exactly four truths in the base, and exactly 4 in the cover.
When that is done, there are two members of the base set which remain uncovered : 9r6c3 and 9r5c8.
So those are fins.
Any candidate 9 in the cover sets and outside the base sets is a potential target.
Were there no fins, all such items would be eliminated.
Because of the fins, only those candidates seen by both fins are eliminated.
Take 9r4c2.
Lies in the cover column c2, lies outside base sets (not in rows 1,5,6,9)=>potential target.
Seen directly by fin 9r6c3.
Seen indirectly by fin 9r5c8 : 9r5c8-9r6c7=9r6c3-9r4c2. Which is therefore a Kraken fin.
So that creature is also a two-finned Sashimi Kraken jellyfish.
But it has lost its Franken status since there is no longer a box as one of the units covered or covering.
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Postby hobiwan » Thu Apr 02, 2009 1:47 pm

aran wrote:To finish with a Kraken example ...

Very nice find aran!

A shorter version (although not found by hand):
Code: Select all
.---------------.----------------------.----------------.
| 4   *159   2  | 6      *159     3    | *159   7   8   |
| 8    159   19 | 12459   7      *1249 |  3     6   145 |
| 6    3     7  | 1459    8      *149  |  2     49  145 |
:---------------+----------------------+----------------:
| 37  *1-9   6  | 13459   13459  *149  |  1579  8   2   |
| 37   2     8  | 1359    1359    6    |  1579  49  145 |
| 5    4    *19 | 8       2       7    | *19    3   6   |
:---------------+----------------------+----------------:
| 9    6     45 | 1234    134     124  |  8     15  7   |
| 1    8     3  | 7       6       5    |  4     2   9   |
| 2    7     45 | 149     149     8    |  6     15  3   |
'---------------'----------------------'----------------'

Kraken Fish Type 1:  => r4c2<>9
  Sashimi X-Wing: 9 r16 c27 fr1c5 fr6c3
  r1c5 -9- r23c6 =9= r4c6 -9- r4c2
  r6c3 -9- r4c2
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Postby ronk » Thu Apr 02, 2009 2:00 pm

The smallest "chainless fish" is a 2-finned mutant swordfish.

Code: Select all
 . #9  . |  . *9  . | *9  .  .
 .  9  9 |  9  . *9 |  .  .  .
 .  .  . |  9  . *9 |  .  9  .
---------+----------+----------
 . -9  . |  9  9 *9 |  9  .  .
 .  .  . |  9  9  . |  9  9  .
 .  . #9 |  .  .  . | *9  .  .
---------+----------+----------
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  9  9  . |  .  .  .

(9)r16c6\r4c7b2 plus fins r1c2 and r6c3 ==> r4c2<>9

Except for r1c2 and r6c3, the <9> candidates in r1, r6 and c6 are covered by r4, c7 and b2. Fins r1c2 and r6c3 each directly see r4c2.
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