The New Sudoku Players' Forum

[Sudtyro]

The following 3’s candidate grid was derived from puzzle #239 in “SuDoku for Dummies” (2005) after running through the basics. The candidate in r6c7, if true, would eliminate all three candidates in r1 via interactions through boxes 2,3,5 and 6. So, short of trial & error, is there a single-digit rule (fish, coloring, hinge, etc) that traps r6c7? Can’t seem to find one...still learning!

Code: Select all

. . . | . 3 . | 3 3 .
. . 3 | 3 . 3 | . 3 3
. . 3 | 3 . 3 | 3 . .
------+-------+------
. . . | . . . | . . .
. . . | . 3 . | 3 . 3
. . . | . . 3 | 3 . 3
------+-------+------
. . . | . . 3 | 3 3 .
. . . | 3 . 3 | 3 . .
. . . | . . . | . . .


[Pat]

Code: Select all

. . . | . 3 . | 3 3 .
. . 3 | 3 . 3 | . 3 3
. . 3 | 3 . 3 | 3 . .
------+-------+------
. . . | . . . | . . .
. . . | . 3 . | 3 . 3
. . . | . . 3 | 3 . 3
------+-------+------
. . . | . . 3 | 3 3 .
. . . | 3 . 3 | 3 . .
. . . | . . . | . . .



r6c7 is indeed a good place to start the loop,
it sets the c9 3 in box3,
thus the r1 3 is in box2
and the box5 3 in r6 - conflict

but Nishio's method may be considered trial-and-error
- not what you asked for

[udosuk]

Sudtyro, I'm no fishing expert... But I'm pretty sure your pattern should have already been discussed by our "marine biologists" inthis thread...

From what I see it's at least a "Kraken X-wing with 2 fins" (seethis link):

Code: Select all

  .  .  .  |  . *3  .  | *3 #3  .
  .  .  3  |  3  .  3  |  .  3  3
  .  .  3  |  3  .  3  |  3  .  .
-----------+-----------+-----------
  .  .  .  |  .  .  .  |  .  .  .
  .  .  .  |  . *3  .  | *3  . #3
  .  .  .  |  .  .  3  | -3  .  3
-----------+-----------+-----------
  .  .  .  |  .  .  3  | @3 $3  .
  .  .  .  |  3  .  3  | @3  .  .
  .  .  .  |  .  .  .  |  .  .  .

Potential X-wing: r15c57
Potential fins: r1c8, r5c9
Elimination links/chains: r6c7-[3]-r5c9, r6c7-[3]-r78c7=[3]=r7c8-[3]-r1c8
Thus r6c7=3 will cause the fins in r1c8+r5c9 to disappear and form the X-wing in r15c57 => r6c7<>3

However, I think there could be other ways to classify this fish, perhaps a "Mutant-Sashimi-Finned-Franken-Swordfish" or some other fancy names... But that's up to the experts...

[ronk]

So, short of trial & error, is there a single-digit rule (fish, coloring, hinge, etc) that traps r6c7?

r6c7 is indeed a good place to start the loop,
it sets the c9 3 in box3,
thus the r1 3 is in box2
and the box5 3 in r6 - conflict[list]

That suggests "grouped multi-coloring" as a logical technique.

Code: Select all

 .  .  . |  .  B  . |  b  b  . 
 .  .  3 |  3  .  3 |  .  3  A 
 .  .  3 |  3  .  3 |  3  .  . 
---------+----------+---------- 
 .  .  . |  .  .  . |  .  .  . 
 .  .  . |  .  c  . |  3  .  a 
 .  .  . |  .  .  C | -3  .  a 
---------+----------+---------- 
 .  .  . |  .  .  3 |  3  3  . 
 .  .  . |  3  .  3 |  3  .  . 
 .  .  . |  .  .  . |  .  .  . 

Grouped strong links, grouped x-cycle, constraint subsets, and mutant fish all apply. See Mike Barker's list of techniques with links here.

[Pat]

-- and mutant fish all apply

thanks! i thought it should - and managed to miss it anyway.

finned Mutant Swordfish

rcb\rcb

"base" = r1,c9,b5
"cover" = r6,c5,b3
fin at r5c9

Code: Select all

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



~ Pat

[daj95376]

Is a single-digit Double Implication Chain (sd-DIC) considered T&E?

Code: Select all

[r6c6]=3                                                    => [r6c7]<>3
[r5c5]=3 => [r1c5]<>3 => [r1c78]=3 => [r2c9]<>3 => [r6c9]=3 => [r6c7]<>3


Is there an equivalent bi-directional chain?

[Edit: corrected typo where <1> should have been a <3>]

[ronk]

Code: Select all

[r6c6]=3                                                    => [r6c7]<>3
[r5c5]=3 => [r1c5]<>3 => [r1c78]=1 => [r2c9]<>3 => [r6c9]=3 => [r6c7]<>3


Is there an equivalent bi-directional chain?

You've got it right there. As a nice loop expression ...

r6c7-3-r6c6=3=r5c5-3-r1c5=3=r1c78-r2c9=3=r56c9-3-r6c7, implies r6c7<>3

You can start at any node and get one implication stream reading left-to-right ... and the other right to left.

[Sudtyro]

You guys are amazing!! A "finned mutant swordfish"...definitely got a lot of reading to do!!

Thanks to all for your inputs!

Sudtyro (mostly tyro)