The New Sudoku Players' Forum

[ronk]

Is not a "school of Turbots" an illegal pattern -- an illegal jellyfish? Doesn't that make exposing the school more like elimination-by-contradiction (EBC) than logic

[udosuk]

Doesn't that make exposing the school more like elimination-by-contradiction (EBC) than logic

I think EBC is a type of logic, perhaps a better way to phrase your question is "Doesn't that make exposing the school more like elimination-by-contradiction (EBC) than direct deduction?"

Just ask Carcul or rep'nA, who frequently post moves in the line "if cell A is x, then a deadly pattern occurs, therefore x is eliminated from cell A"... What do we call this logic? EBCAU (elimination-by-contradiction-assuming-uniqueness)?

[daj95376]

I think of DanG's approach as being akin to Uniqueness arguments.

In Uniqueness, the argument is that a deadly pattern will exist if ...

In DanG's approach, the argument is that a School of Turbots (or Invalid Jellyfish/Coloring) will exist if ...

Here's the exemplar for NoFish20 based on DanG's approach.

Code: Select all

# NoFish20
*-----------------------------*
| /  /  . | /  /  / | .  .  . |
| /  X  . | /  X  / | .  .  . |
| X  /  . | /  /  X | .  .  . |
|---------+---------+---------|
| /  /  . | /  /  / | .  .  . |
| X  /  . | /  X  / | .  .  . |
| /  X  . | /  /  X | .  .  . |
|---------+---------+---------|
| .  .  * | .  /  / | .  .  . |
| .  .  * | .  /  / | .  .  . |
| .  .  * | .  /  / | .  .  . |
*-----------------------------*


[tarek]

No, DanG's eliminations are based on the fact theat a pattern is identified if a certain elimination is made.......

The argument should be at what stage did he identify the pattern
a. just by looking at the grid
b. or after a conscious (what if this was true/false)

the answer would then lead to another argument...........


tarek

[ravel]

The argument should be at what stage did he identify the pattern
a. just by looking at the grid
b. or after a conscious (what if this was true/false)

Thats the point, why i liked it so. You can spot it just like a finned x-wing, once you have the pattern in mind.

[ronk]

You can spot it just like a finned x-wing, once you have the pattern in mind.

I agree but unless I missed it, we're ignoring the fact that we don't have an associated explanation -- a direct deduction as someone said -- for why the pattern yields the exclusions that it does.

Well, actually we do have Rod Hagglund's broken wing as Obi-Wahn illustrated, but we don't seem to be using that anymore.

[daj95376]

Below is a templates pattern that I created based on my investigation into DanG's remarks on tilted pairs. I was searching for the minimal number of (/) cells needed to support the tilted pairs. I hope that my results come close. I (also) believe that grouped coloring based on any conjugate (X) pair might produce the same results.

Note: I deliberately did not reduce the Locked Candidate (1) in [b2].

Code: Select all

^-----------------------------------^
|  /  X  /  |  /  /  /  |  /  /  X  |
|  X  /  /  |  /  /  /  |  X  /  /  |
|  *  *  *  |  .  .  .  |  *  *  *  |
|-----------+-----------+-----------|
|  X  /  /  |  .  .  .  |  /  /  X  |
|  /  X  /  |  .  .  .  |  X  /  /  |
|  .  .  .  |  *  *  *  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
^-----------------------------------^


If you add a fin cell at [r2c5], then [r6c5] is the only remaining elimination. This is a finned tilted pairs representation of the <5> pattern in NoFish6.

Code: Select all

^-----------------------------------^
|  /  X  /  |  /  /  /  |  /  /  X  |
|  X  /  /  |  /  #  /  |  X  /  /  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|-----------+-----------+-----------|
|  X  /  /  |  .  .  .  |  /  /  X  |
|  /  X  /  |  .  .  .  |  X  /  /  |
|  .  .  .  |  .  *  .  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
^-----------------------------------^


[Edit: changed 'will' to 'might' to better present my belief.]

[Myth Jellies]

You can spot it just like a finned x-wing, once you have the pattern in mind.

I agree but unless I missed it, we're ignoring the fact that we don't have an associated explanation -- a direct deduction as someone said -- for why the pattern yields the exclusions that it does.

Well, actually we do have Rod Hagglund's broken wing as Obi-Wahn illustrated, but we don't seem to be using that anymore.

Ron and I actually had a discussion about impossible swordfish here. Impossible jellyfish, such as the one represented by this pattern, should not represent a very large leap either.

[ronk]

Below is a templates pattern that I created based on my investigation into DanG's remarks on tilted pairs. I was searching for the minimal number of (/) cells needed to support the tilted pairs. I hope that my results come close.
[...]
Note: I deliberately did not reduce the Locked Candidate (1) in [b2].

Code: Select all

^-----------------------------------^
|  /  X  /  |  /  /  /  |  /  /  X  |
|  X  /  /  |  /  /  /  |  X  /  /  |
|  *  *  *  |  .  .  .  |  *  *  *  |
|-----------+-----------+-----------|
|  X  /  /  |  .  .  .  |  /  /  X  |
|  /  X  /  |  .  .  .  |  X  /  /  |
|  .  .  .  |  *  *  *  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
^-----------------------------------^


Based on the empty cells, your exclusion cells are correct AFAICT. But you are using Locked Candidates (1) to provide six empty cells, so IMO the proper templar for exclusions r6c456<>X is ...

Code: Select all

^-----------------------------------^
|  /  X  /  |  /  /  /  |  /  /  X  |
|  X  /  /  |  /  /  /  |  X  /  /  |
|  /  /  /  |  .  .  .  |  /  /  /  |
|-----------+-----------+-----------|
|  X  /  /  |  .  .  .  |  /  /  X  |
|  /  X  /  |  .  .  .  |  X  /  /  |
|  .  .  .  |  *  *  *  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
^-----------------------------------^


... which has a total of 28 empty cells. Now, using that templar, how do you describe the direct deduction that yields those exclusions

[daj95376]

Based on the empty cells, your exclusion cells are correct AFAICT. But you are using Locked Candidates (1) to provide six empty cells, so IMO the proper templar for exclusions r6c456<>X is ...

Now, using that templar, how do you describe the direct deduction that yields those exclusions

Q1: If you revisit your Exemplars for fish, you'll see that there are several examples where you don't perform the Locked Candidates eliminations because it restricts the pattern excessively when fin cells are included. That was my reasoning as well. In order to properly include the fin cell in my example for NoFish6, I needed to flag the eliminations in [r3] for the unfinned pattern, but I also needed to allow occupied cells for the finned pattern.

Q2: I'm not sure, but I thought that some of my other posts using tilted pairs was followed by posts where someone used grouped coloring to perform the same eliminations. That's why I said that I believe that grouped coloring might also work with the general pattern I produced. My belief could easily be wrong!!!

Unlike fish patterns, the tilted pairs pattern can perform eliminations in cells that are not directly seen by the X cells. Maybe that's why I've been able to get some of the NoFish puzzles to work with it.

I still don't know if the tilted pairs pattern is just some variant of Broken Wings. If someone who understands Broken Wings has time to check, I'd appreciate knowing. TIA!!!

[daj95376]

I don't know if this qualifies as a direct deduction explanation for the unfinned tilted pairs pattern, but it is an explanation.

Code: Select all

# Locked Candidate (1) in [b2r3] => ![r3c123789] (followed by)
# Either [r2c1]=X -or- [r1c2]=X
^-----------------------------------^
|  /  X  /  |  /  /  /  |  /  /  X  |
|  X  /  /  |  /  /  /  |  X  /  /  |
|  /  /  /  |  .  .  .  |  /  /  /  |
|-----------+-----------+-----------|
|  X  /  /  |  .  .  .  |  /  /  X  |
|  /  X  /  |  .  .  .  |  X  /  /  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  .  |
^-----------------------------------^


If [r2c1]=X is true, then the grid reduces to:

Code: Select all

#  ([r6c3] or [r6c8]) => ![r6c456]
# !([r6c3] or [r6c8]) => LCs (2) in [b7c3]+[b9c8] => X-Wing c27/r56 => ![r56c456]
^-----------------------------------^
|  /  /  /  |  /  /  /  |  /  /  @  |
|  @  /  /  |  /  /  /  |  /  /  /  |
|  /  /  /  |  .  .  .  |  /  /  /  |
|-----------+-----------+-----------|
|  /  /  /  |  .  .  .  |  /  /  /  |
|  /  .  /  |  .  .  .  |  .  /  /  |
|  /  .  .  |  *  *  *  |  .  .  /  |
|-----------+-----------+-----------|
|  /  .  .  |  .  .  .  |  .  .  /  |
|  /  .  .  |  .  .  .  |  .  .  /  |
|  /  .  .  |  .  .  .  |  .  .  /  |
|  /  .  .  |  .  .  .  |  .  .  /  |
^-----------------------------------^


If [r1c2]=X is true, then the grid reduces to:

Code: Select all

#  ([r6c3] or [r6c8]) => ![r6c456]
# !([r6c3] or [r6c8]) => LCs (2) in [b7c3]+[b9c8] => X-Wing c19/r46 => ![r46c456]
^-----------------------------------^
|  /  @  /  |  /  /  /  |  /  /  /  |
|  /  /  /  |  /  /  /  |  @  /  /  |
|  /  /  /  |  .  .  .  |  /  /  /  |
|-----------+-----------+-----------|
|  .  /  /  |  .  .  .  |  /  /  .  |
|  /  /  /  |  .  .  .  |  /  /  /  |
|  .  /  .  |  *  *  *  |  /  .  .  |
|-----------+-----------+-----------|
|  .  /  .  |  .  .  .  |  /  .  .  |
|  .  /  .  |  .  .  .  |  /  .  .  |
|  .  /  .  |  .  .  .  |  /  .  .  |
|  .  /  .  |  .  .  .  |  /  .  .  |
^-----------------------------------^


ronk: Didn't you just know that I'd work overlapping X-Wings into the explanation!!!

[DanG]

Sorry guys but there is no sense in finding templates.
School of Turbots come in different patterns and sizes, even in the same grid!
I looked over Obi-Wahn's first 5 NoFish grids and here is what I found;

NoFish1 contains the pattern, but couldn't spot any elimination.
Then:

Code: Select all

NoFish2
....1.85.87.....32..............7......82...7..96.4..8..59...7.4.....1.6....8.52.
After SS eliminations:

 3 -3  3 |  .  .  3 |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 3  3  3 | T3 T3  . |  .  .  .
---------+----------+---------
T3  3  . |  . T3  . |  3  .  .
 .  . T3 |  .  . T3 |  3  .  .
 .  3  . |  .  . .  | +3  .  .
---------+----------+---------
 .  .  . |  .  .  . |  .  .  .
 .  . T3 | T3  .  . |  .  .  .
T3  3  . |  .  . T3 |  .  .  .
 
 if r1c2=3 clears r1;c2;b1, r6c7=3 clears c7
 then b24578 = School of Burbots (size 5x7)
 therefore r1c2<>3
=================================================================================

NoFish3
..5....7.1......6..43...2....6..2..53...7...........2..5.8...9....9.48....7.26.3.
After SS eliminations:

 .  .  . |  .  9  9 | -9  .  9
 .  . T9 |  . T9  . |  9  .  9
T9  .  . |  .  . T9 |  .  .  9
---------+----------+---------
 . T9  . |  . T9  . |  9  .  .
 .  . T9 |  .  . T9 |  9  .  .
 .  9  9 |  .  9  9 |  .  . +9
---------+----------+---------
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
T9 T9  . |  .  .  . |  .  .  .

 if r1c7=9 clears r1;c7;b3 => r6c9=9 clears r6
 then b12457 = School of Burbots (size 5x7)
 therefore r1c7<>9
=================================================================================

NoFish4
..72....62...4..758.....1..1.4.6.8...2.8....3.....9....3...4..14..6..2.....7.....
After SS eliminations:

T9  .  . |  . T9  . |  .  .  .
 . T9  9 |  .  .  . | T9  .  .
 .  .  9 | T9  .  . |  .  9 T9
---------+----------+---------
 . T9  . |  .  .  . |  .  9 T9
T9  .  9 |  .  .  . | T9  .  .
 .  .  . |  .  .  . |  .  .  .
---------+----------+---------
 .  .  . | T9  .  . |  . T9  .
 .  .  9 |  . T9  . |  . T9  .
 9  9 -9 |  .  9  . |  9  9  .

 if r9c3=9 clears r9;c3 => r78c8= locked => clears c8
 then b1234689 = School of Burbots (size 5x11)
 therefore r9c3<>9
=================================================================================

NoFish5
..4..8......2..1.....5.134.9.....8.64.8...71.751.....383...4........6..75.7......
After SS eliminations:

 .  9  . |  9 T9  . | T9  .  .
 .  9  . |  .  . T9 |  .  . T9
 .  9 +9 |  .  9  . |  .  .  9
---------+----------+---------
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  9 T9  . |  .  . T9
 .  .  . |  .  . T9 |  . T9  .
---------+----------+---------
 .  .  . |  9  9  . | T9 T9  .
 .  .  9 | -9  9  . |  9  .  .
 . +9  . |  9  9  9 |  .  .  .

 if r8c4=9 clears r8;c4;b8 => r9c2=9 =>r3c3=9 clears r3;b1
 then b23569 = School of Burbots (size 5x7)
 therefore r8c4<>9


Dan

[RW]

Code: Select all

NoFish2
....1.85.87.....32..............7......82...7..96.4..8..59...7.4.....1.6....8.52.
After SS eliminations:

 3 -3  3 |  .  .  3 |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 3  3  3 | T3 T3  . |  .  .  .
---------+----------+---------
T3  3  . |  . T3  . |  3  .  .
 .  . T3 |  .  . T3 |  3  .  .
 .  3  . |  .  . .  | +3  .  .
---------+----------+---------
 .  .  . |  .  .  . |  .  .  .
 .  . T3 | T3  .  . |  .  .  .
T3  3  . |  .  . T3 |  .  .  .
 
 if r1c2=3 clears r1;c2;b1, r6c7=3 clears c7
 then b24578 = School of Burbots (size 5x7)
 therefore r1c2<>3

Why do you need to clear column 7 and box 1? Isn't it enough to say if r1c3=3 clears r1c6; r469c2?

Code: Select all

NoFish4
..72....62...4..758.....1..1.4.6.8...2.8....3.....9....3...4..14..6..2.....7.....
After SS eliminations:

...

 if r9c3=9 clears r9;c3 => r78c8= locked => clears c8
 then b1234689 = School of Burbots (size 5x11)
 therefore r9c3<>9

You don't need box 8 and 9 for that elimination. These cells alone make up an impossible pattern:

Code: Select all

T9  .  . |  . T9  . |  .  .  .
 . T9  9 |  .  .  . | T9  .  .
 .  .  9 | T9  .  . |  .  9 T9
---------+----------+---------
 . T9  . |  .  .  . |  .  9 T9
T9  .  9 |  .  .  . | T9  .  .
 .  .  . |  .  .  . |  .  .  .
---------+----------+---------
 .  .  . |  9  .  . |  .  9  .
 .  .  9 |  .  9  . |  .  9  .
 9  9 -9 |  .  9  . |  9 -9  .

which also gives an elimination in r9c8.

Even this would be an impossible pattern:

Code: Select all

T9  .  . | T9 T9 T9 |  .  .  .
 . T9  . |  .  .  . | T9  .  .
 .  .  . | T9 T9 T9 |  .  . T9
---------+----------+---------
 . T9  . |  .  .  . |  .  . T9
T9  .  . |  .  .  . | T9  .  .
 .  .  . |  .  .  . |  .  .  .
---------+----------+---------
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .

RW

[ronk]

You don't need box 8 and 9 for that elimination. These cells alone make up an impossible pattern:

Code: Select all

T9  .  . |  . T9  . |  .  .  .
 . T9  9 |  .  .  . | T9  .  .
 .  .  9 | T9  .  . |  .  9 T9
---------+----------+---------
 . T9  . |  .  .  . |  .  9 T9
T9  .  9 |  .  .  . | T9  .  .
 .  .  . |  .  .  . |  .  .  .
---------+----------+---------
 .  .  . |  9  .  . |  .  9  .
 .  .  9 |  .  9  . |  .  9  .
 9  9 -9 |  .  9  . |  9 -9  .

which also gives an elimination in r9c8.

What's your reasoning for r9c8?

[RW]

What's your reasoning for r9c8?

Same as DanG's reasoning for r9c3 but with a hidden single instead of the locked candidates (if r9c8=9 clears r9;c8 => r8c3=9 => clears c3).