Saturday 23-Jan-2010
... by: John Francis
John White observes:You can extend all of these in the following ways:
A. You are not restricted to rows and colums.
B. As with X-Wing and Swordfish, you can 'Fin' Jellyfish.
C. Why stop at 4......
The reason for stopping at 4 is because of the symmetry between possible candidates in a cell and potential sites for a given digit.
It's best explained by considering Naked and Hidden n-tuples.
Consider a Naked heptuple. This is a set of seven cells in one set (row, col or box) which between them only have seven different candidates. This means that these seven cells will contain those seven values in some order.
Now describe that situation it another way. The cells *not* in the n-tuple are the only ones which can include numbers not in those n candidates.
This is the description of a hidden (9-n)-tuple (hidden pair, in this case).
This means there's no need to go beyond 4 in describing a strategy; Naked quints are the same as hidden quads, and so on. For a strategy described using numbers greater than four there is an equivalent description using smaller numbers (and interchanging the roles of candidates in a cell and positions for a digit).

