## Superior Variants

For fans of Killer Sudoku, Samurai Sudoku and other variants
evert I think you may find this useful The Ultimate FISH Guide. Only vanilla are considered there but the concepts of base and cover sets is illustrated.
Glyn

Posts: 357
Joined: 26 April 2007

As Glyn mentioned, the definitions in the guide (which need some updates) are versatile enough to cover all variants.

To catch all possible fish, you need to consider constriant groups in your base and/or your cover groups ...

You have alos to look at the overlapping puzzles as 1 huge puzzle with overlaping constriant groups.

tarek

tarek

Posts: 3759
Joined: 05 January 2006

evert wrote:I think a definition of Fish could be as follows:

1. There are n different groups g(i) (i = 1..n).
2. A certain digit k has n different possible placements in each of the groups g(i).
3. None of these cells occur in more then one of the groups g(i).
4. There are also n different groups h(j) (j = 1..n).
5. Each group h(j) contains exactly one of the cells from each group g(i) where digit k can be placed.
6. Each placement for k in one of the groups g(i) occurs in exactly one of the groups h(j).

In this situation: k can be excluded from every cell in a group h(j), that does not occur in any of the groups g(i).

I wonder if this definition is both minimal and sufficient.
Sufficient in the sense that the exclusion of k is justified.
Minimal in the sense that all conditions 1 to 6 are necessary - otherwise the exclusion of k is not justified.

hi evert

see the fish definition (2007.Oct.2, on page 22 of "The Ultimate FISH Guide")
it does allow for possible overlap within the "base",
also for possible overlap within the "cover"

Pat

Posts: 3964
Joined: 18 July 2005

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