ultimate fish and nishio

Advanced methods and approaches for solving Sudoku puzzles

Postby Mike Barker » Sat Mar 31, 2007 12:12 am

Here's the PM for the puzzle. In general I know I'd appreciate it if they were posted along with or in place of the digit placements for a fish. Like Glenn, I don't have an option to emulate SS.
Code: Select all
| 1   56  3  | 8   9   7  | 4   2   56 |
| 25  7   8  | 4   235 6  | 59  39  1  |
| 9   256 4  | 1   235 25 | 8   7   356|
:------------+------------+------------:
| 258 4   6  | 25  7   9  | 1   38  35 |
| 3   25  7  | 6   1   258| 259 89  4  |
| 258 1   9  | 3   58  4  | 25  6   7  |
:------------+------------+------------:
| 6   9   2  | 7   4   1  | 3   5   8  |
| 4   8   5  | 9   6   3  | 7   1   2  |
| 7   3   1  | 25  258 258| 6   4   9  |
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Re: Invalid Jelly

Postby daj95376 » Sat Mar 31, 2007 12:23 am

gsf wrote:do we have the ss technique/method order anywhere?

Code: Select all
===== ===== ===== ===== Simple Sudoku

- 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
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Re: Invalid Jelly

Postby ronk » Sat Mar 31, 2007 12:33 am

gsf wrote:the constraint options to emulate simple sudoku is a good idea
but the sequence didn't jump out from angus' site
do we have the ss technique/method order anywhere?

daj95376's list of SS techniques agrees with angusj's 1-year old post here. Changes since then have been minor I suspect ... and most of us could modify on our own -- from any starter options you provide.

I doubt emulation would be perfect because of Colors and Multi-Colors (x-cycle). Both are single-digit coloring with Colors using one chain of conjugate links. Multi-Colors uses two chains and deductions using three or more chains is not supported AFAIK. The xy-wing might be problematic as well.

[edit: eliminated technique list which daj95376 had already posted]
Last edited by ronk on Sat Mar 31, 2007 8:33 am, edited 1 time in total.
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Re: Invalid Jelly

Postby daj95376 » Sat Mar 31, 2007 12:46 am

DanG wrote:
Code: Select all
+-----------+-----------+
|  .  .  .  |  .  .  .  |
|  .  X  .  |  .  X  .  |
|  .  .  X  |  X  .  .  |
+-----------+-----------+
|  .  X  .  |  X  .  .  |
|  .  .  X  |  .  X  .  |
|  .  .  .  |  .  .  .  |
+-----------+-----------+

But when the slope in one box is different from the other 3 ones, we get the invalid pattern.
I would rather call it "School of (perfect) Turbots". See how many they are?
Of cause since they are turbots, there should be some guardians somewhere there.

Your 'slope' example matches how I get Kraken fish to decompose -- basic/finned/Sashimi X-Wings and Skyscrapers -- into an error state.

Code: Select all
# Skyscraper in rows 'ab' => (-) => (+) => column 'c' empty
+-----------+-----------+
|  .  .  .  |  .  .  .  |
|  . +X  .  |  .  X  .  | a
|  .  . -X  |  X  .  .  |
+-----------+-----------+
|  . -X  .  |  X  .  .  |
|  .  . +X  |  .  X  .  | b
|  .  .  .  |  .  .  .  |
+-----------+-----------+
                  c

Skyscraper eliminations turn on it through strong links.
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Re: Invalid Jelly

Postby gsf » Sat Mar 31, 2007 12:50 am

daj95376 wrote:
Code: Select all
===== ===== ===== ===== Simple Sudoku

- 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

thanks Danny (and Ron)
then this option in my solver will come close to ss
Code: Select all
-qT1H1T2BT3T4H2W2W3XYH3H4

the differences will be in { colors multi-colors } vs. { X-cycle (single candidate) Y-cycle (bivalue candidates) }
I believe (but don't have proof) that my { X Y } covers ss { colors multi-colors XY-wing }

and thanks Mike
I was commenting on my solver not being able to read in "fishy" grids with only one value
(like the 5's only grids to illustrate fish application in the previous posts)
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Postby daj95376 » Sat Mar 31, 2007 1:34 am

I apologize for not including the PM for NoFish6. Here's what I do when I encounter a fishy grid without a PM.

Code: Select all
# original
*-----------------------------------*
|  .  5  .  |  .  .  .  |  .  .  5  |
|  5  .  .  |  .  5  .  |  5  .  .  |
|  .  5  .  |  .  5  5  |  .  .  5  |
|-----------+-----------+-----------|
|  5  .  .  |  5  .  .  |  .  .  5  |
|  .  5  .  |  .  .  5  |  5  .  .  |
|  5  .  .  |  .  5  .  |  5  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  .  5  .  |
|  .  .  5  |  .  .  .  |  .  .  .  |
|  .  .  .  |  5  5  5  |  .  .  .  |
*-----------------------------------*

Code: Select all
# set cells with period (.) to 12346789
# set cells with five   (5) to 123467895
*-----------------------------------------------------------------------------------------------*
| 12346789  123467895 12346789  | 12346789  12346789  12346789  | 12346789  12346789  123467895 |
| 123467895 12346789  12346789  | 12346789  123467895 12346789  | 123467895 12346789  12346789  |
| 12346789  123467895 12346789  | 12346789  123467895 123467895 | 12346789  12346789  123467895 |
|-------------------------------+-------------------------------+-------------------------------|
| 123467895 12346789  12346789  | 123467895 12346789  12346789  | 12346789  12346789  123467895 |
| 12346789  123467895 12346789  | 12346789  12346789  123467895 | 123467895 12346789  12346789  |
| 123467895 12346789  12346789  | 12346789  123467895 12346789  | 123467895 12346789  12346789  |
|-------------------------------+-------------------------------+-------------------------------|
| 12346789  12346789  12346789  | 12346789  12346789  12346789  | 12346789  123467895 12346789  |
| 12346789  12346789  123467895 | 12346789  12346789  12346789  | 12346789  12346789  12346789  |
| 12346789  12346789  12346789  | 123467895 123467895 123467895 | 12346789  12346789  12346789  |
*-----------------------------------------------------------------------------------------------*

Feeding this PM into a solver will only produce eliminations associated with <5>. However, validation checking must be disabled.
Last edited by daj95376 on Fri Mar 30, 2007 10:08 pm, edited 2 times in total.
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Postby gsf » Sat Mar 31, 2007 1:59 am

daj95376 wrote:[code]# set cells with period (.) to 12346789
# set cells with five (5) to 123467895

Feeding this PM into a solver will only produce eliminations associated with <5>. However, validation checking must be a feature and disabled.

thanks, a nice addition to the bag of tricks
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School of Turbots

Postby DanG » Thu Apr 05, 2007 3:45 am

Thanks ronk for spotting the correct number of Turbots in the school (my previous post)!

We may have to find a name for a tilted pair of cells contained in a box. I will call it ramp or sloper till somebody else come up with a better name.

The topic here is about finding invalid patterns in a grid. AFAIK Rod Hagglund 1st found such a pattern and called it "broken wing" here: http://www.sudoku.org.uk/discus/messages/29/385.html?1158390877 . Later some other guys rediscovered the same pattern and name it Turbot Fish just to keep it on the marine (lol).

Now a hint how to spot a Turbot:
1. Highlight a candidate number.
2. Find the possible slopers, one in each box, preferably of max. 3 cells which may resemble a "hinge".
3. Focus only on those boxes which form a loop for the given candidate. Ignore the joint of the hinges if any. That may form a closed loop of slopers which may look like conjugate pairs.
4. Start from one cell of a sloper and follow the assumed conjugate pairs only along the lines/columns till you return to the same box you started from. If the return path leads to the other cell of the sloper and the link count is 4,6,8, the pattern is a Turbot(size 5,7,9).

Code: Select all
..2.1765..8.......7..2....99....4......58..2...1..67...5...2.....7.9.28...64...3.

This is not a minimal puzzle and was generates for the sake of current topic.
How many Turbots in the school are there for candidates 8 and 9?
Any Turbots for 5 and 6?

Dan
P.S. Seems like the rule I stated previously about the odd number of slopers does not always hold! Mea culpa.
Last edited by DanG on Fri Apr 13, 2007 10:00 pm, edited 2 times in total.
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Re: School of Turbots

Postby ronk » Thu Apr 05, 2007 10:53 am

DanG wrote:The topic here is about finding invalid patterns in a grid. AFAIK Rod Hagglund 1st found such a pattern and called it "broken wing" here: http://www.sudoku.org.uk/discus/messages/29/385.html?1158390877 . Later some other guys rediscovered the same pattern and name it Turbot Fish just to keep it on the marine (lol).

Nick70's turbot fish predates Rod Hagglund's broken wing.
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Postby DanG » Thu Apr 05, 2007 3:30 pm

Thanks ronk again, I was not aware of that post.
My full credit for Turbots goes to Nick70, unless somebody else find a previous post..:D
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Postby Obi-Wahn » Wed Apr 11, 2007 11:23 am

In my point of view Turbot Fish and Broken Wings, while used on similar patterns, are different techniques. While Nick70 mentions that a loop of five strong links is impossible in a valid puzzle, he didn't draw the conclusion that one of the excess candidates that prevent this pattern must be true.
Every exclusion candidate of the Turbot Fish technique lies within the pattern, i.e. is one of the five candidates forming the pattern. The Broken Wing technique on the other hand may deliver an exclusion candidate totally unconnected to the Turbot Fish pattern.
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Postby daj95376 » Wed Apr 11, 2007 2:37 pm

DanG mentioned tilted links. Using X-Colors, I've found that they can appear where least expected. (I hope this isn't a repeat of an explanation elsewhere! Just my luck this is the Broken Wing pattern, of which I'm still not familiar.)

Code: Select all
My X-Colors Notation:

B --     Blue
b -- not Blue
G --     Green
g -- not Green

In NoFish20, tilted links appear in [b245~1]. The important thing is how [c12] affect [b7].

Code: Select all
NoFish20:

....97.5.1.......9....2.1.4..34.8....8...2...9...7..2.....4.7......6..48.29..36..

*--------------------------------------------------------------------*
|  38     34     248   |  1      9      7     |  23     5      6     |
|  1     ~357    2567  |  368   *35     4     |  23     78     9     |
| ~3567   9      567   |  368    2     *56    |  1      78     4     |
|----------------------+----------------------+----------------------|
|  2      6      3     |  4      1      8     |  5      9      7     |
| *57     8      157   |  9     *35     2     |  4      6      13    |
|  9     *45     145   |  36     7     *56    |  8      2      13    |
|----------------------+----------------------+----------------------|
|  68     1      68    |  5      4      9     |  7      3      2     |
|  357    357    57    |  2      6      1     |  9      4      8     |
|  4      2      9     |  7      8      3     |  6      1      5     |
*--------------------------------------------------------------------*

# X-Colors [b1245] => [r8c12] => ![r8c3]
*-----------------------------------*
|  .  .  .  |  .  .  .  |  .  5  .  |
|  . b5 b5  |  . B5  .  |  .  .  .  |
| g5  . g5  |  .  . G5  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  5  .  .  |
| g5  . g5  |  . G5  .  |  .  .  .  |
|  . b5 b5  |  .  . B5  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  5  .  .  |  .  .  .  |
| G5 B5 -5  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  5  |
*-----------------------------------*

In NoFish19, tilted links appear in [b458~7]. The important thing is how [r79] affect [b9].

Code: Select all
NoFish19:

.2....65.....3......6.29..88.......5...4...62.79..3.....831..7..........3...78.4.

*-----------------------------------------------------------------------------*
|  79      2       3      |  8       4       1      |  6       5       79     |
|  1579    8       157    |  567     3       56     |  24      29      479    |
|  457     45      6      |  57      2       9      |  3       1       8      |
|-------------------------+-------------------------+-------------------------|
|  8       46     *24     |  1       9      *26     |  7       3       5      |
|  15      3       15     |  4       8       7      |  9       6       2      |
| *26      7       9      | *256     56      3      |  14      8       14     |
|-------------------------+-------------------------+-------------------------|
| ~2456    4569    8      |  3       1      *2456   |  25      7       69     |
|  24567   1       2457   |  2569    56      2456   |  8       29      3      |
|  3       569    ~25     | *2569    7       8      |  125     4       169    |
*-----------------------------------------------------------------------------*

# X-Colors [b4578] => [r79c7] => !([r2c7],[r8c8])
*-----------------------------------*
|  .  2  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  | -2  2  .  |
|  .  .  .  |  .  2  .  |  .  .  .  |
|-----------+-----------+-----------|
|  .  . G2  |  .  . B2  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  2  |
| B2  .  .  | G2  .  .  |  .  .  .  |
|-----------+-----------+-----------|
| b2  .  .  |  .  . b2  | B2  .  .  |
| b2  . g2  | g2  . b2  |  . -2  .  |
|  .  . g2  | g2  .  .  | G2  .  .  |
*-----------------------------------*

In NoFish15, after extending the concept to include a fifth box [b2] through a strong link in [c5], tilted links appear in [b2578~4]. The important thing is how [r46] affect [b6].

Code: Select all
NoFish15:

...8.7....1.3..6.....45...89.4.....7.............4.1...2.....7.453......7....2.39

*--------------------------------------------------------------------*
|  25     4      256   |  8     *16     7     |  3      9      12    |
|  8      1      7     |  3      2      9     |  6      5      4     |
|  3      9      26    |  4      5     *16    |  7      12     8     |
|----------------------+----------------------+----------------------|
|  9     ~36     4     | *126    8      13    |  5      26     7     |
|  1256   368    18    |  26     7      356   |  9      4      236   |
| ~256    7      25    |  9      4     *356   |  1      8      236   |
|----------------------+----------------------+----------------------|
| *16     2      9     | *16     3      4     |  8      7      5     |
|  4      5      3     |  7      9      8     |  2      16     16    |
|  7     *68     18    |  5     *16     2     |  4      3      9     |
*--------------------------------------------------------------------*

# X-Colors [b4578] => [r46c89] => [r5c9]
*-----------------------------------*
|  .  .  6  |  . G6  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  6  .  .  |
|  .  .  6  |  .  . B6  |  .  .  .  |
|-----------+-----------+-----------|
|  . g6  .  | g6  .  .  |  . G6  .  |
| b6 g6  .  | g6  . b6  |  .  . -6  |
| b6  .  .  |  .  . b6  |  .  . B6  |
|-----------+-----------+-----------|
| B6  .  .  | G6  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  6  6  |
|  . G6  .  |  . B6  .  |  .  .  .  |
*-----------------------------------*

Yes, this is very similar to explanations that I've offered elsewhere for these puzzles. However, I find X-Colors combined with tilted links to be the simplest approach so far; so that's why I included it.
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Postby Myth Jellies » Fri Apr 13, 2007 5:18 am

No X-Coloring/Nishio, or its associated assumptions are needed if you combine fish groups with simple coloring. These are equivalently simple.
Code: Select all
NoFish 20:
*-----------------------------------*
|  .  .  .  |  .  .  .  |  .  5  .  |
|  . a5 a5  |  . A5  .  |  .  .  .  |
| A5  . A5  |  .  . a5  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  5  .  .  |
| A5  . A5  |  . a5  .  |  .  .  .  |
|  . a5 a5  |  .  . A5  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  5  .  .  |  .  .  .  |
|  5  5 -5  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  5  |
*-----------------------------------*

(5)r8c3 sees both conjugate fish groups in r26/c23 and r35/c13

Code: Select all
NoFish19:
*-----------------------------------*
|  .  2  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  | -2  2  .  |
|  .  .  .  |  .  2  .  |  .  .  .  |
|-----------+-----------+-----------|
|  .  . a2  |  .  . A2  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  2  |
| A2  .  .  | a2  .  .  |  .  .  .  |
|-----------+-----------+-----------|
| a2  .  .  |  .  . a2  |  2  .  .  |
| a2  . A2  | A2  . a2  |  . -2  .  |
|  .  . A2  | A2  .  .  |  2  .  .  |
*-----------------------------------*

(2)r8c8 sees both conjugate fish groups in r78/c16 and r89/c34

Code: Select all
NoFish15:
*-----------------------------------*
|  .  . a6  |  . A6  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  6  .  .  |
|  .  . A6  |  .  . a6  |  .  .  .  |
|-----------+-----------+-----------|
|  . a6  .  | a6  .  .  |  .  6  .  |
| A6 a6  .  | a6  . A6  |  .  . -6  |
| A6  .  .  |  .  . A6  |  .  .  6  |
|-----------+-----------+-----------|
| a6  .  .  | A6  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  6  6  |
|  . A6  .  |  . a6  .  |  .  .  .  |
*-----------------------------------*
(6)r5c9 sees both conjugate fish groups in r45/c24 and r56/c16
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School of Turbots

Postby DanG » Sat Apr 14, 2007 1:23 am

I figure out a faster way for the above eliminations: patern recognition:idea:
Code: Select all
NoFish20:
....97.5.1.......9....2.1.4..34.8....8...2...9...7..2.....4.7......6..48.29..36..
*-----------------------------------*
|  .  .  .  |  .  .  .  |  .  5  .  |
|  .  5  5  |  .  5  .  |  .  .  .  |
|  5  .  5  |  .  .  5  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  5  .  .  |
|  5  .  5  |  .  5  .  |  .  .  .  |
|  .  5  5  |  .  .  5  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  5  .  .  |  .  .  .  |
|  5  5 -5  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  5  |
*-----------------------------------*
if r8c3=5, the rest of c3<>5
then r2356/c1256=School of Turbots,
therefore r8c3<>5
================================================================================

NoFish19:
.2....65.....3......6.29..88.......5...4...62.79..3.....831..7..........3...78.4.
*-----------------------------------*
|  .  2  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  | -2  2  .  |
|  .  .  .  |  .  2  .  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  2  |  .  .  2  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  2  |
|  2  .  .  |  2  .  .  |  .  .  .  |
|-----------+-----------+-----------|
|  2  .  .  |  .  .  2  |  2  .  .  |
|  2  .  2  |  2  .  2  |  . -2  .  |
|  .  .  2  |  2  .  .  |  2  .  .  |
*-----------------------------------*
if r8c8=2, the rest of r8<>2
then tower12=School of Turbots,
therefore r8c8<>2

================================================================================
NoFish15:
...8.7....1.3..6.....45...89.4.....7.............4.1...2.....7.453......7....2.39
*-----------------------------------*
|  .  .  6  |  .  6  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  6  .  .  |
|  .  .  6  |  .  .  6  |  .  .  .  |
|-----------+-----------+-----------|
|  .  6  .  |  6  .  .  |  .  6  .  |
|  6  6  .  |  6  .  6  |  .  . -6  |
|  6  .  .  |  .  .  6  |  .  .  6  |
|-----------+-----------+-----------|
|  6  .  .  |  6  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  6  6  |
|  .  6  .  |  .  6  .  |  .  .  .  |
*-----------------------------------*
if r5c9=6, the rest of r5<>6
then tower12=School of Turbots,
therefore r5c9<>6

How cool is that!:D
DanG
 
Posts: 20
Joined: 28 March 2007

Postby ravel » Sun Apr 15, 2007 10:30 am

Very nice!
I seldom followed the fish threads, cause i preferred to make the eliminations with grouped coloring. But this way these eliminations are really easy to spot.
ravel
 
Posts: 998
Joined: 21 February 2006

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