The New Sudoku Players' Forum

[daj95376]

Here is another example of where the same cell is the (#) cell whether it's a row-fish or a column-fish supporting the elimination in a box. Am I the last person to know that this is always the case ... or does someone have a counter example? TIA!!!

[ronk]

this layout is interesting. If you look at the complementary finned fish in r126/c149
[...]
you get a 231 structure in rows which probably does qualify as sashimi.

That's a bit of a wakeup call. The complementary fish are so often both finned or both sashimi, that I was beginning to believe that was the rule.

You can also describe it with
r5c1 = r12/c19 - r2c4 = r6c4 => r5c6 & r6c3 <> 4 [edit: typos corrected]
if you don't mind using fish/constraint groups in AICs

Another POV uses the strong inferences in r3, b4 and b5.

Code: Select all

 4  .  . | .  .  . | .  .  4
 4  .  . | 4  .  . | .  .  4
 /  / *4 | /  / *4 | /  /  /
---------+---------+---------
 /  /  . | /  /  . | .  .  .
#4  . *4 | /  / -4 | .  .  .
 /  / -4 |#4  . *4 | .  .  .
---------+---------+---------
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .

r5c1 = r56c3 - r3c3 = r3c6 - r56c6 = r6c4 => r5c6 & r6c3 <> 4

Which is merely the combination of these simpler chains:
r5c1 = r56c3 - r3c3 = r3c6 => r5c6 <> 4
r3c3 = r3c6 - r56c6 = r6c4 => r6c3 <> 4

In ultimate fish terms:
finned franken x-wing r3b4\c36 plus fin r5c1, implies r5c6<>4
finned franken x-wing r3b5\c36 plus fin r6c4, implies r6c3<>4

Here is another example of where the same cell is the (#) cell whether it's a row-fish or a column-fish supporting the elimination in a box. Am I the last person to know that this is always the case ... or does someone have a counter example? TIA!!!

I think "always" is correct for finned basic (row-col) fish. It has been known for some time that complementary fish cause the same eliminations. Indeed it may be part of the basis for the "complementary" term. I don't see how the addition of a single fin would alter that concept.

[daj95376]

While reviewing this thread, I came across a reference to Ocean's Hidden Pattern thread in the Programmers Forum. Below is my interpretation of the first pattern presented in that thread.

Code: Select all

# mutant Starfish c1256b9/r34789 -or-
# mutant Starfish r1256b9/c34789
*-----------------------------------*
|  .  .  1  |  1  .  .  |  1  1  1  |
|  .  .  1  |  1  .  .  |  1  1  1  |
|  1  1 -1  | -1  1  1  | -1 -1 -1  |
|-----------+-----------+-----------|
|  1  1 -1  | -1  1  1  | -1 -1 -1  |
|  .  .  1  |  1  .  .  |  1  1  1  |
|  .  .  1  |  1  .  .  |  1  1  1  |
|-----------+-----------+-----------|
|  1  1 -1  | -1  1  1  |  1  1  1  |
|  1  1 -1  | -1  1  1  |  1  1  1  |
|  1  1 -1  | -1  1  1  |  1  1  1  |
*-----------------------------------*


What I find interesting is that there are four columns [c1256] with five values and four rows [r1256] with five values. Is there any significance to this -- besides the fact that three of the rows and three of the columns completely cover [b9]?

[ronk]

# mutant Starfish c1256b9/r34789 -or-
# mutant Starfish r1256b9/c34789

Without a mix of both rows and columns in either the base set or cover set, those are franken fish. However, an alternate POV is mutant (exemplar Fig 4E2):

mutant jellyfish b1245\r34c34

[ronk]

Exemplars updated to include:

Code: Select all

 *  X  * |  .  .  . |  .  *  .        /  X  / |  .  .  . |  .  /  .
 X  /  X |  /  /  / |  /  X  /        X *X  X |  *  *  * |  *  X  *
 *  X  * |  .  .  . |  .  *  .        /  X  / |  .  .  . |  .  /  .
---------+----------+----------      ---------+----------+----------
 .  /  . |  .  .  . |  .  *  .        .  *  . |  .  .  . |  .  /  .
 .  /  . |  .  .  . |  .  *  .        .  *  . |  .  .  . |  .  /  .
 .  /  . |  .  .  . |  .  *  .        .  *  . |  .  .  . |  .  /  .
---------+----------+----------      ---------+----------+----------
 .  /  . |  .  .  . |  .  *  .        .  *  . |  .  .  . |  .  /  .
 .  #  . |  .  .  . |  . **  .        . **  . |  .  .  . |  .  #  .
 .  /  . |  .  .  . |  .  *  .        .  *  . |  .  .  . |  .  /  .
Fig 2C: rc\cb                         Fig 2C inverse: cb\rc
 rc\rb transpose                      rb\rc transpose
 turbot fish (2-stringed kite)        turbot fish (ER + conjugate link)
 sashimi mutant x-wing


Code: Select all

 *  X  * | .  .  . | .  /  .          /  X  / | .  .  . | .  *  .
**  X ** | .  .  . | .  #  .          #  X  # | .  .  . | . **  .
 *  X  * | .  .  . | .  /  .          /  X  / | .  .  . | .  *  .
---------+---------+---------        ---------+---------+---------
 .  /  . | .  .  . | .  /  .          .  *  . | .  .  . | .  *  .
 .  /  . | .  .  . | .  /  .          .  *  . | .  .  . | .  *  .
 .  /  . | .  .  . | .  /  .          .  *  . | .  .  . | .  *  .
---------+---------+---------        ---------+---------+---------
 .  /  . | .  .  . | .  /  .          .  *  . | .  .  . | .  *  .
 *  X  * | *  *  * | *  X  *          /  X  / | /  /  / | /  X  /
 .  /  . | .  .  . | .  /  .          .  *  . | .  .  . | .  *  .
 Fig 2D: cc\rb                        Fig 2D inverse: rb\cc
 rr\cb transpose                      cb\rr transpose
 turbot fish (skyscraper)             turbot fish (ER + conjugate link)
 sashimi mutant x-wing


Code: Select all

 /  X  / |  X  /  X |  /  /  /        *  X  * |  X  *  X |  *  *  * 
 /  *  . |  *  /  * |  .  .  /        *  /  . |  /  *  / |  .  .  * 
 X  *  * |  *  X  * |  *  *  X        X  /  / |  /  X  / |  /  /  X 
---------+----------+----------      ---------+----------+---------- 
*X  *  * |  *  X  * |  *  *  X        /  /  / |  /  X  / |  /  /  X 
 / *X  X |  X  /  X |  /  /  /       *X  /  X |  X  *  X |  *  *  * 
 X  *  * |  *  /  * |  .  .  /        X  /  / |  /  *  / |  .  .  * 
---------+----------+----------      ---------+----------+---------- 
 /  *  . |  X  /  X |  .  .  /        *  /  . |  X  *  X |  .  .  * 
 /  *  . |  X  /  X |  .  .  /        *  /  . |  X  *  X |  .  .  * 
 /  *  . |  X  /  X |  .  .  /        *  /  . |  X  *  X |  .  .  * 
 Fig 6C: rrcccb\rrcccb                Fig 6C inverse: rrcccb\rrcccb
 rrcccb\rrcccb transpose              rrcccb\rrcccb transpose
 NOT self-transpose
 mutant whale


[Figure based on Obi-Wahn's post here]

Most sashimi exemplars revised to illustrate fin positions that actually yield an exclusion ... as opposed to showing all fin positions that prevented degeneration.

A special thanks to daj95376 for checking the accuracy of the exemplars.

[tarek]

apologies for the dealy in updating the head post........

I'll try to find some time over the next 10 days to do that


tarek

[Myth Jellies]

Jigsaw techniques and examples.

Jigsaws seem to offer up a lot of interesting takes on some otherwise old techniques for standard sudoku puzzles, as well as perhaps a few new techniques.

To help make discussions on jigsaw nonet blocks go a little easier, I offer the following definition. Let a nonet block number be identified by its relative proximity to first the top row, and then the leftmost column by that nonet's topmost and then rightmost cell. The boxes (nonets) in a standard sudoku retain their legacy numeration under this scheme. Below you can see how a particular jigsaw configuration would have its nonets numbered. The starred number indicates the topmost then leftmost cell in the nonet.

Code: Select all

+---+---+---+---+---+---+---+---+---+
|*1   1   1   1   1 |*2   2   2   2 |
+   +   +---+---+---+---+---+   +   +
| 1   1 |*3   3 |*4 |*5   5 | 2   2 |
+   +---+   +---+   +---+   +---+   +
| 1 | 3   3 | 4   4   4 | 5   5 | 2 |
+   +   +---+   +   +   +---+   +   +
| 1 | 3 | 4   4   4   4   4 | 5 | 2 |
+---+   +---+---+---+---+---+   +   +
|*6 | 3 |*7   7   7   7   7 | 5 | 2 |
+   +   +---+   +   +   +---+   +---+
| 6 | 3   3 | 7   7   7 | 5   5 |*8 |
+   +   +---+---+   +---+---+   +   +
| 6 | 3 |*9   9 | 7 | 9   9 | 5 | 8 |
+   +---+   +   +---+   +   +---+   +
| 6   6 | 9   9   9   9   9 | 8   8 |
+   +   +---+---+---+---+---+   +   +
| 6   6   6   6 | 8   8   8   8   8 |
+---+---+---+---+---+---+---+---+---+

I thought this was an interesting application of a finned constraint set in a recent jigsaw sudoku

Code: Select all

+---+---+---+---+---+---+---+---+---+
|                   |               |
+   +   +---+---+---+---+---+   +   +
|       |       | x | x   4 |-4     |
+   +---+   +---+   +---+   +---+   +
|   |       |#4   x  #4 |-4   4 |   |
+   +   +---+   +   +   +---+   +   +
|   |   |*4   x   x   x  *4 | 4 |   |
+---+   +---+---+---+---+---+   +   +
|   |   |                   | x |   |
+   +   +---+   +   +   +---+   +---+
|   |       |           | x   x |   |
+   +   +---+---+   +---+---+   +   +
|   |   | x   x |   | x   x | x |   |
+   +---+   +   +---+   +   +---+   +
| x   x | 4a  x   x   x   4A| x   x |
+   +   +---+---+---+---+---+   +   +
|               |                   |
+---+---+---+---+---+---+---+---+---+

Note that (4)r48c37 would form a (4)b4b9/c3c7 constraint group that would eliminate all other 4's in c3 & c7 if not for the fin in r3c46. Since the 4 in r3c7 sees both the constraint group and the fin, it can be eliminated. Once that is gone, the 4 in r2c8 sees all the 4's in b5, so it can be eliminated too.

Note that a fair number of jigsaw grids feature only two nonets each in rows 1 and 9 and columns 1 and 9. It turns out that we can use our old friend the rrcc/bbbb constraint group to note some things without any digits filled in.

Code: Select all

+---+---+---+---+---+---+---+---+---+
|                   |               |
+   +   +---+---+---+---+---+   +   +
|       |       |   |       |       |
+   +---+   +---+   +---+   +---+   +
|   |       |           |       |   |
+   +   +---+   +   +   +---+   +   +
|   |   |                   |   |   |
+---+   +---+---+---+---+---+   +   +
|   |   |                   |   |   |
+   +   +---+   +   +   +---+   +---+
|   |       |           |       |   |
+   +   +---+---+   +---+---+   +   +
|   |   |       |   |       |   |   |
+   +---+   +   +---+   +   +---+   +
|       |                   |       |
+   +   +---+---+---+---+---+   +   +
|               |                   |
+---+---+---+---+---+---+---+---+---+

r19c19/b1268 makes up a constraint group. If you recall (check this post), when a constraint set has internal intersections like r19c19 does, then those internal intersections (r1c1, r1c9, r9c1, & r9c9) are removed from the other constraint set (b1268). Thus we have...

Code: Select all

+---+---+---+---+---+---+---+---+---+
| A   X   X   X   X | X   X   X   A |
+   +   +---+---+---+---+---+   +   +
| X   B |       |   |       | B   X |
+   +---+   +---+   +---+   +---+   +
| X |       |           |       | X |
+   +   +---+   +   +   +---+   +   +
| X |   |                   |   | X |
+---+   +---+---+---+---+---+   +   +
| X |   |                   |   | X |
+   +   +---+   +   +   +---+   +---+
| X |       |           |       | X |
+   +   +---+---+   +---+---+   +   +
| X |   |       |   |       |   | X |
+   +---+   +   +---+   +   +---+   +
| X   B |                   | B   X |
+   +   +---+---+---+---+---+   +   +
| A   X   X   X | X   X   X   X   A |
+---+---+---+---+---+---+---+---+---+

...The cells marked A now belong solely to the r19c19 set. The cells marked B belong only to the b1268 set. The cells marked X belong to the intersection of both sets. Thus the cells marked X form the r19c19/b1268 constraint group with A's being the potential fins for the r19c19 set, and B's being the matching potential fins for the b1268 set. Now any digit for which the r19c19/b1268 constraint set is not true, must have a digit true in both the A and B groups. Thus you get a set of relationships like (n)r1c1 => (n)r2c8|r8c28. I find these to be a big help when solving these types of grids.

[daj95376]

In the pattern below, conventional finned Swordfish easily explain [r7c79]<>7. However, the elimination [r7c8]<>7 needs an unusual cover set. I use to think that the cover set always included a cell from the base set. Obviously, I was wrong. Are there any other examples besides finned Swordfish?

Code: Select all

 .91..2.4664.1.9.35......1...8.6......6..5..1......1.2...6......51.4.6.8283.2..96.

# Finned Swordfish r289\c357 w/fin cell         [r9c9] => [r7c7]<>7
# Finned Swordfish r289\c359 w/fin cell  [r8c7]        => [r7c9]<>7
# Finned Swordfish r289\c358 w/fin cells [r8c7],[r9c9] => [r7c8]<>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  .  .  |  .  .  7  |
|-----------+-----------+-----------|
|  7  7  .  |  7  7  7  | -7 -7 -7  |
|  .  . *7  |  . *7  .  | @7  .  .  |
|  .  . *7  |  . *7  .  |  .  . @7  |
*-----------------------------------*


BTW, I guess tarek never got around to updating the head post.

[ronk]

In the pattern below, conventional finned Swordfish easily explain [r7c79]<>7. However, the elimination [r7c8]<>7 needs an unusual cover set. I use to think that the cover set always included a cell from the base set. Obviously, I was wrong. Are there any other examples besides finned Swordfish?

daj95376, nice catch It's the ultimate (pun) sashimi with no candidates at all in one cover sector (unit), c8 in this case. I don't recall anyone posting such a step ... unless it's the elusive "skinny swordfish" one reads about occasionally.

Of course, the (unfinned) franken swordfish r289\c35b9 gets the three eliminations in one fell swoop ... plus six more in c3 and c5.

A similar row\col sashimi jellyfish is theoretically possible. Does that motivate you to write a frankenfish solver

BTW, I guess tarek never got around to updating the head post.

I'm hoping it's not because he's waiting on me for something. What's missing

[daj95376]

Yes ronk, I'm going to have to add frankenfish to my new solver. You sure have been patient on helping me with them. I stare at a puzzle, and come up empty ... and you show me where there's a simple frankenfish.

Okay, I see how a similar jellyfish pattern would work. Thanks!

BTW, on May 07 you posted some Exemplar updates. On May 14, tarek said that he'd update the head post in 10 days or so. The head post has not been updated since May 14.

[Pat]

the (unfinned) franken swordfish r289\c35b9 gets the three eliminations in one fell swoop

The list of types of fish in the first post
has the finned (basic) fish before the (un-finned) Franken

whereas my own personal preference is for
any (un-finned) fish before any finned

tarek has been silent these past few weeks

~ Pat

[ronk]

The list of types of fish in the first post
has the finned (basic) fish before the (un-finned) Franken

whereas my own personal preference is for
any (un-finned) fish before any finned

Same here ... when it comes to basic fish and franken fish. However, mutant fish are quite a bit more difficult for me to see, so I notice finned and sashimi basic fish before any variety of mutant fish.

Tarek's sequence very closely, if not exactly, follows the chronological identification of fish ... and IMO is thus the proper introductory sequence for newcomers.

[tarek]

BTW, I guess tarek never got around to updating the head post.

I'm hoping it's not because he's waiting on me for something. What's missing

BTW, on May 07 you posted some Exemplar updates. On May 14, tarek said that he'd update the head post in 10 days or so. The head post has not been updated since May 14.

tarek has been silent these past few weeks

Tarek's sequence very closely, if not exactly, follows the chronological identification of fish ... and IMO is thus the proper introductory sequence for newcomers.

I do apologise for the delay...... I will be updating the head post today. I need also to refresh myself with all the posts from the start because I'm suire a few definitions need to be added also....

& I haven't forgot about your comments mike which will be adressed along with the last few posts here....

tarek

[Pat]

Since I'm not familiar with all of the fish,
how should I select from the few that I do know?

The list of types of fish in the first post is also a difficulty ranking

choose the one with lowest ranking 1st (easiest)

i'd say the difficulty ranking is somewhat of a personal preference,
and cannot be stated absolutely.

~Pat

[tarek]

I have to stay away from absolute statements

I guess that a franken x-wing can be spotted easier than a finned jellyfish (after all it is a finned swordfish).

This also should go probably for the size of fish........I remeber somewhere that spotting a naked quad is easier than a naked double for non PM solvers.

however, the reason for listing types & sizes in their current fashion is aimed to facilitate the transition from what was commonly used before to what are considered tobe "difficult to spot techniques". with time, I'm sure that the finless varieties would stand out as easier (absolute )

I myself still find it easier to spot the finned x-wing than spotting a swordfish (maybe because I look for it first )

tarek