What if the following constraint is added to the vanilla Sudoku rules:

In the final solution (not just the initial clues), each digit's opposite counterpart must appear in the opposite location. That is, if the digit D appears in row R, column C, then the digit 10-D must appear in row 10-R, column 10-C. For example, if there is a 4 in r2c3, there must be a 6 in r8c7.

Can anybody come up with an interesting puzzle along these lines?

What about minimality of the initial clues? Obviously, each clue will automatically generate its counterpart, so I'm inclined to believe that a minimal clue set could contain as few as 8 clues. (Note that the digit in r5c5 must always be 5, so it is never necessary to provide that as a clue.)

Of course, a minimal clue set cannot also be symmetric. In fact, it must be anti-symmetric, in the sense that if there is an initial clue in row R, column C, then there cannot also be an initial clue in row 10-R, column 10-C. Thus, a minimal symmetric clue set (minimal among symmetric clue sets) will have exactly twice as many clues as its minimal non-symmetric counterparts.

Any thoughts?

Bill Smythe