What is the best way to find big fish manually?

Advanced methods and approaches for solving Sudoku puzzles

What is the best way to find big fish manually?

Postby 999_Springs » Sat Mar 22, 2008 9:22 pm

I usually try to find strong links and see if they turn into X-wings, swordfish, etc. This seems to work well with X-wings and 2x2x2 or 2x2x3 swordfish. But for the bigger ones I don't have a method of finding them manually which works well and just have to stare at the puzzle and see if any pop out before my eyes. I recently attempted this puzzle:
Code: Select all
4.6|..2|...
...|..4|...
.5.|3..|1..
---+---+---
.8.|1..|93.
...|...|.2.
.2.|9..|85.
---+---+---
.3.|8..|5..
...|..7|...
7.1|..9|...

which needs two 3x3x3 swordfish and a jellyfish and 4 hours of frustration to solve, and if I were to see any of these in the future, I would need a method of finding big fish.
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Postby Bigtone53 » Sat Mar 22, 2008 10:17 pm

999_Springs,

I believe that Arcilla's method works in principle with bigger fish in the same way as it easily does for x-wings and 3x3x3 swordfish. Arcilla's method can be found here
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Re: What is the best way to find big fish manually?

Postby denis_berthier » Mon Mar 24, 2008 7:41 am

999_Springs wrote:I usually try to find strong links and see if they turn into X-wings, swordfish, etc. This seems to work well with X-wings and 2x2x2 or 2x2x3 swordfish. But for the bigger ones I don't have a method of finding them manually which works well and just have to stare at the puzzle and see if any pop out before my eyes.

Arcilla introduced a new view of fish here: http://forum.enjoysudoku.com/viewtopic.php?t=5017&start=0&postdays=0&postorder=asc&highlight
I wasn't aware of her post when I introduced the rn- and cn- spaces in my book and later in a few posts in connection with hidden chains (e.g. here http://forum.enjoysudoku.com/viewtopic.php?t=5555).
In the proper rn- or cn- space, a fish looks like a naked Subset.

The rn- and cn- spaces can be considered as a formalisation and a generalisation of Arcilla's view.
They are defined formally in my book and less formally in these threads:
http://www.sudoku.org.uk/SudokuThread.asp?fid=4&sid=9235&p1=2&p2=10
http://forum.enjoysudoku.com/viewtopic.php?t=5555
In my book and on my web pages, you can find an extended Sudoku board including these spaces. You can also find a method for using them systematically. This can be helpful for finding fish and other patterns.
rn and cn spaces are implemented in Ruud's Sudocue program, so that you don't have to compute them manually.

As the rn- and cn- spaces are the representation of generalised logical symmetries, they can be used for finding much more than fish, e.g. hidden xy, xyt and xyzt chains.
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