dailysudoku.com

[Marty R.]

I had a 6-fish yesterday and was researching to see if it had a name. The Wikipedia entry indicated there's no point in giving it a name in a 9x9 puzzle. Could someone explain that to me? Why would my 6-fish be paired with a swordfish? I just don't get it.

"# 5-fish : squirmbag - For 9×9 Sudoku, there's no in point naming higher-order (>4) fish, since every N-fish comes paired with a 9-N fish whose effect is the same (thus any 5-fish is paired with a jellyfish; any 6-fish with a swordfish; any 7-fish with an x-wing; any 8-fish with a hidden or naked single). Nevertheless, a 5-fish is occasionally called a squirmbag.
# 6+ fish : 6-gronk, 7-gronk.. [23] - these patterns are only useful for Sudoku larger than 9×9."

[Steve R]

Marty, if you still have your 6-fish, it should be easy enough to find its dual.

The general scheme is this. Suppose, in an n x n puzzle, you have an m x m fish for X based on rows. The nature of the fish is that it also identifies m columns. These columns are the target columns in the sense that X can be eliminated from the target columns except where they intersect the base rows.

Now think about the other n – m columns, those which are not targets. Where can X be placed? Only outside the base rows. So now we have n – m columns in which X can be placed only in the n – m rows which are not base rows. That is, we have an (n – m) x (n – m) fish based on columns. This is the dual fish. If your 6-fish was based on rows, there would be another fish based on the non-target columns.

This may be a little abstract. Bear in mind that fish are nothing to do with boxes (unless thy have fins); they otherwise relate entirely to columns and rows. So you can permute the columns and rows until a 5-fish based on rows looks like this:

[Marty R.]

Steve, thank you very much for taking the time and effort for that explanation.

I don't still have the 6-fish. All my puzzles are done with pencil and paper and there's no trail.