## Turbo Fish ....revisited

Advanced methods and approaches for solving Sudoku puzzles

### Turbo Fish ....revisited

I have seen where turbo's can be solved having four strong sides and one weak side. My question is that I have found a way to solving turbo's that works, about 80% of the time.with 1 strong side and 4 weak sides. This, of course, is not satisfactory.

Below is an example of a turbo with with just that.

The turbo is in (4's) at: r1c2, r1c9, r7c2, r8c3 and r8c9

Is there a way to sove turbo's with just one strong and four weak sides with 100% accuracy?

Thanks.

| *-----------*
|..9|8.7|2..|
|...|4.5|.6.|
|.6.|...|...|
|---+---+---|
|6.8|...|..3|
|.7.|...|.4.|
|4..|...|7.2|
|---+---+---|
|7..|...|.1.|
|.1.|7.9|...|
|..3|5.1|9..|
*-----------*

*-----------*
|..9|8.7|2..|
|...|4.5|.6.|
|.6.|...|...|
|---+---+---|
|6.8|...|..3|
|.7.|...|.4.|
|4..|...|7.2|
|---+---+---|
|7..|...|.1.|
|.1.|7.9|...|
|..3|5.1|9..|
*-----------*

*--------------------------------------------------------------------------------------*
| 35 345 9 | 8 136 7 | 2 35 145 |
| 128 238 127 | 4 1239 5 | 138 6 1789 |
| 1258 6 12457 | 1239 1239 23 | 13458 35789 145789 |
|----------------------------+----------------------------+----------------------------|
| 6 259 8 | 129 124579 24 | 15 59 3 |
| 12359 7 125 | 12369 1235689 2368 | 1568 4 15689 |
| 4 359 15 | 1369 5689 68 | 7 589 2 |
|----------------------------+----------------------------+----------------------------|
| 7 24589 2456 | 236 23468 23468 | 34568 1 4568 |
| 258 1 2456 | 7 23468 9 | 34568 2358 4568 |
| 28 248 3 | 5 2468 1 | 9 278 4678 |
*--------------------------------------------------------------------------------------*
Gee

Posts: 50
Joined: 18 March 2007

### Re: Turbo Fish ....revisited

Gee wrote:Is there a way to sove turbo's with just one strong and four weak sides with 100% accuracy?

No. There must be a minimum of 2 two strong sides ... and these sides may not be adjacent. See Nick70's seminal post here.

BTW, as we've discussed before, you should be asking for help on the Help with particular puzzles forum. In that forum, you will also find a "Sticky topic: How to ask for help", recommending a way to post puzzles, both with and without pencilmarks.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Turbo Fish ....revisited

ronk wrote:
Gee wrote:Is there a way to sove turbo's with just one strong and four weak sides with 100% accuracy?

No. There must be a minimum of 2 two strong sides ... and these sides may not be adjacent. See Nick70's seminal post here.

ronk, I don't know whether I am agreeing with you, because of terminology.

There is, in my eyes, a finned 2 string kite which is the same as what Mike Barker, et alia, decided was a grouped Turbot.

http://forum.enjoysudoku.com/viewtopic.php?t=2971

My unsureness is what you (ronk) mean by a strong side, and whether that matches what Gee is getting at. (Which I made no sense of.)
wintder

Posts: 297
Joined: 24 April 2007

### Re: Turbo Fish ....revisited

wintder wrote:There is, in my eyes, a finned 2 string kite which is the same as what Mike Barker, et alia, decided was a grouped Turbot.

I see no such thing. Since it's rather difficult to post what one doesn't see , perhaps you should post what you do see.

My unsureness is what you (ronk) mean by a strong side, and whether that matches what Gee is getting at

I'm taking Gee's strong side to mean conjugate link.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Turbo Fish ....revisited

ronk wrote:I'm taking Gee's strong side to mean conjugate link.

So.
wintder

Posts: 297
Joined: 24 April 2007

### Re: Turbo Fish ....revisited

wintder wrote:
ronk wrote:I'm taking Gee's strong side to mean conjugate link.

So.

Since you apparently wish to be flippant, I'm dropping out of this pseudo-discussion.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Code: Select all
`. . . | . . . | . x .x . . | . . . | x . x. . . | . . . | . x .---------------------. . . | . . . | . . .. . . | . . . | . . .. . . | . . . | . . .---------------------. . . | . . . | . . .# . . | . . . | . x .. . . | . . . | . . .`

For those unwilling to read linked threads this is the general pattern of a grouped Turbot, or finned 2 string kite.

It does not have conjugate links and may be what Gee is hinting at?
wintder

Posts: 297
Joined: 24 April 2007

### Torbo Fish ...revisited.

First let me apologize for posting this is the wrong forum. I have been shown the error of my ways and it won't happen again.

I used "Strong" side to mean a conjugate pair. I didn't mean to create any ambiguity as to the intrepretation.

My questioned was prefaced by this URL.

http://www,sudoku.com/boards/viewtopic.php?php?t=833

Nick70, stated that it was possible to have four "strong" sides and one "weak" side in a Torbo to find two candidates. Hence, my original inquiry.

Thank you for your indulgence.
Gee

Posts: 50
Joined: 18 March 2007

### Re: Turbo Fish ....revisited

wintder wrote:There is, in my eyes, a finned 2 string kite which is the same as what Mike Barker, et alia, decided was a grouped Turbot.

Gee’s unresolved 4’s grid is shown below. Could you point out the grouped Turbot?
Code: Select all
`. 4 . | . . . | . . 4. . . | . . . | . . .. . 4 | . . . | 4 . 4------+-------+-------. . . | . 4 4 | . . .. . . | . . . | . . .. . . | . . . | . . .------+-------+-------. 4 4 | . 4 4 | 4 . 4. . 4 | . 4 . | 4 . 4. 4 . | . 4 . | . . 4`
Sudtyro

Posts: 68
Joined: 21 December 2006

### Re: Turbo Fish ....revisited

Gee wrote:The turbo is in (4's) at: r1c2, r1c9, r7c2, r8c3 and r8c9

Code: Select all
`.  4A . | . . . | . . 4E.  .  . | . . . | . . ..  .  4 | . . . | 4 . 4--------+-------+-------.  .  . | . 4 4 | . . ..  .  . | . . . | . . ..  .  . | . . . | . . .--------+-------+-------.  4B 4 | . 4 4 | 4 . 4.  .  4C| . 4 . | 4 . 4D.  4  . | . 4 . | . . 4`

The unresolved 4’s grid is shown above, with your five Turbot candidates marked with letters A-E.

A Turbot fish is actually just a simple Alternating Inference Chain (AIC) of four candidates that starts and ends with a strong link (side). Any (fifth) candidate that can “see” (weakly link to) both ends of the chain can be eliminated. As Ronk pointed out, you must have at least two strong links (sides) to form the chain.

Your five candidates have only the one strong link between A and E. Hypothetically, however, if you were to omit the 4’s in r8c5 and r8c7, you would then also have a strong link between digits C and D, and could then form the following AIC in Eureka notation:
C = D – E = A =>(implies) B <> 4, since candidate B can see both C and A.

You may be more comfortable with the equivalent closed AIC or (discontinuous) loop, which would be:
B - C = D – E = A – B => B <> 4.
There are now five “sides” showing, comprising two strongs and three weaks.

If we go a step further and also omit the 4’s in r7c3 and r9c2, we’d then have the hypothetical case you mentioned of four strong sides and one weak. The same AIC applies, but we now get a second elimination, E <> 4, because A must now be a 4, due to the conjugate link between A and B.

Using the fact that the hypothetical conjugate link (between B and C) is also a weak link, one can easily write down a suitable AIC for the second elimination:
A = B – C = D => E <> 4.
The full 5-sided loop would be:
E - A = B – C = D – E => E <> 4.

The key point of all this is that five candidates having only one strong link cannot form a Turbot fish. You might want to use an AIC to check on that 80% figure you mentioned.
Sudtyro

Posts: 68
Joined: 21 December 2006

### Re: Turbo Fish ....revisited

Sudtyro wrote:
wintder wrote:There is, in my eyes, a finned 2 string kite which is the same as what Mike Barker, et alia, decided was a grouped Turbot.

Gee’s unresolved 4’s grid is shown below. Could you point out the grouped Turbot?
Code: Select all
`. 4 . | . . . | . . 4. . . | . . . | . . .. . 4 | . . . | 4 . 4------+-------+-------. . . | . 4 4 | . . .. . . | . . . | . . .. . . | . . . | . . .------+-------+-------. 4 4 | . 4 4 | 4 . 4. . 4 | . 4 . | 4 . 4. 4 . | . 4 . | . . 4`

There isn't one.

Here is what I said.

My unsureness is what you (ronk) mean by a strong side, and whether that matches what Gee is getting at. (Which I made no sense of.)

ronk added that a strong side is a conjugate link.

I still don't find a place that defines that.

Edited to change "grouped link" to conjugate link.
Last edited by wintder on Wed Oct 24, 2007 6:26 pm, edited 1 time in total.
wintder

Posts: 297
Joined: 24 April 2007

### Re: Torbo Fish ...revisited.

Gee wrote:First let me apologize for posting this is the wrong forum. I have been shown the error of my ways and it won't happen again.

I used "Strong" side to mean a conjugate pair. I didn't mean to create any ambiguity as to the intrepretation.

My questioned was prefaced by this URL.

http://www,sudoku.com/boards/viewtopic.php?php?t=833

Nick70, stated that it was possible to have four "strong" sides and one "weak" side in a Torbo to find two candidates. Hence, my original inquiry.

Thank you for your indulgence.

http://forum.enjoysudoku.com/viewtopic.php?t=833
wintder

Posts: 297
Joined: 24 April 2007

Here's some definitions I've saved. However, I doubt if they'll help in this discussion.

Code: Select all
`===== ===== ===== ===== Definitions:Strong Link  <==>  Conjugate Pair  <==>  Connected Pair for a CandidateWeak      Link - At most  one element is trueStrong    Link - At least one element is trueConjugate Link - Exactly  one element is true`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Thanks daj, it does clear it all up for me.

nick70, referenced above several times, has a strong side as a conjugate pair.

There need not be any strong sides, using that definition.

Using conjugate links to be strong sides adds fins to the pattern and 2 strong sides are required.
wintder

Posts: 297
Joined: 24 April 2007