## Fishy ER

Advanced methods and approaches for solving Sudoku puzzles

### Fishy ER

This may have already been noticed and the examples I have seen can be solved by coloring but I think it is easier for a person to see it in terms of empty rectangles:

Code: Select all
`*-----------------------------------------------------------------------------*| 1245    6       1257    | 8       35      345     | 1457    457     9       || 459     489     589     | 7       6       1       | 2       3458    3458    || 145    B1478    3       | 9       2       45      | 14567   4578   X145678  ||-------------------------+-------------------------+-------------------------|| 6       5       4       | 3       8       2       | 179     79      17      || 8      B379     79      | 6       1      A57      | 45      345     2       || 123     123     127     | 4       57      9       | 8       6       35      ||-------------------------+-------------------------+-------------------------|| 259     289     2589    | 1       4      A67      | 3      *5789   *5678    || 134     134     6       | 5       379     8       | 49      2      *47      || 7       34      589     | 2       39      36      | 4569    1       4568    |*-----------------------------------------------------------------------------*`

*=marks the "hinge" or "ER complement"
A=conjugate 7's
B=conjugate 7's
X= 7 can be eliminated

Or it can be looked at as a partial swordfish which the ER has the possibility of making the elimination or turning the partial swordfish into an x-wing(sashimi?) which makes the elimnation. This same rule would work with higher fish or grouped strong links

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`Multiple strong links:*-----------* |...|o..|.x.| |.o.|...|..x| |.o.|.o.|..x| |---+---+---| |...|o..|.+a| |...|.o.|.a+| |...|...|...| |---+---+---| |...|...|...| |...|...|...| |...|...|...| *-----------*`

o= candidates
a=candidates forming ER
+=possible ERI's
x=eliminations

Where there can be(must be) other candidates present as long as they don't destroy the strong links or empty rectangle.

Code: Select all
`Grouped strong link:*-----------* |..o|...|..x| |...|...|...| |oo.|.o.|..x| |---+---+---| |...|...|..a| |...|.o.|.a+| |...|...|..a| |---+---+---| |...|...|...| |...|...|...| |...|...|...| *-----------*`

o= candidates
a=candidates forming ER
+=possible ERI's
x=eliminations

Where there can be(must be) other candidates present as long as they don't destroy the strong links or empty rectangle.

Code: Select all
`Partial Jellyfish:*-----------* |o..|o..|.oo| |o.o|o..|oo.| |.b.|.b.|..x| |---+---+---| |..o|o..|..a| |..o|.bb|.a+| |o..|...|..a| |---+---+---| |.b.|o..|o.x| |.b.|o.b|.ox| |o..|o..|.o.| *-----------*`

a=candidates that form the ER
+=ERI
b=candidates making a partial jellyfish
o=other candidates(no other candidates are present)
x=eliminations

There is a finned fish that makes one of the eliminations, and I suppose that people may find mistakes in this post and all eliminations given could be done by other finned fish or another technique, but I think ER's are easy to spot so are probably useful.

The reason it works is that the candidates either make the eliminations directly, or eliminate a "rib" of the partial fish making it a legitimate lower fish which in turn makes the eliminations.

I refer to the "rib" of the fish as being the line that the eliminations occur on.

Hopefully people can find examples where this is useful. It seems that any elimination done by this technique could potentially be done another way, but I think this may be easier to spot because you just spot the ER and then check for strong links or partial fish to make any eliminations.

So the summary is... " An ERI that is on the rib of a partial fish makes eliminations along the other ribs of the partial fish".

Any thoughts?
doduff

Posts: 32
Joined: 29 May 2006