## Finned Turbot Fish

Advanced methods and approaches for solving Sudoku puzzles

### Finned Turbot Fish

OK, we have Finned X-Wing and Turbot Fish. We can also mix the 2 and have Finned Turbot Fish, where the strong and weak links may be in any kind of constraint. Probably more common on highly constrained puzzles like the the "Argyle" layout by Pyrrhon. In this layout, no number may be repeated in the "partial" diagonals drawn with gray lines.

Here is a Finned Turbot Fish, the '#' is the fin, the '*' are strong links (in rows), the '+' are cells where we can remove the candidate.

The logic is :
Either one of the cells in R4C13 (fin) is true
Or Else all the cells in R4C13 are false -> R4C8 = true -> R3C7 = false -> R3C3 = true
Thus one of the cells in R4C13+R3C3 must be true -> all the cells marked with '+' must be false.

This look very much like a Finned XWing, the differences are :
The weak link between R3C7 and R4C8 goes through a diagonal, instead of a column. It can be any other link.
We may remove the candidate on more cells. A Finned XWing would only allow to remove the candidate in R45C3, but not in R24C1.

And now a Twice Finned Turbot Fish !

Here we have two fins : R3C13 and R4C13. Here goes :

Either one of the cells in R4C13 (bottom fin) is true
Or Else all the cells in R4C13 are false -> R4C8 = true -> R3C7 = false -> one of the cells in R3C13 (top fin) must be true
Thus one of the cells in R4C13+R3C13 must be true -> all the cells marked with '+' must be false.

Eating fish is said to improve your brain performance
Jean-Christophe

Posts: 149
Joined: 22 January 2006

I think what you are referring to as a finned Turbot fish as also been called a grouped Turbot Fish. Here is one reference: http://forum.enjoysudoku.com/viewtopic.php?p=24396
Mike Barker

Posts: 458
Joined: 22 January 2006

I knew this was probably aready discovered. Thanks for pointing me this. So I'll use the name already adpoted by others
Jean-Christophe

Posts: 149
Joined: 22 January 2006