In chess we have one-dimensional variants. In sudoku we haven't (at least I'm not aware of any).
I'm would be suprised if you have some nice ideas.
Saying it more formally:
Find an intersting sudoku variant with only a row and so much fields as you like.
Of course odd-even/sum/product/consecutive constraints ... are allowed.
I hope for tough variants.
I know making this single row to a circle, to a moebius strip or some of such rows to a plus-sign, a letter or a dollar-symbol would be the next steps. But lets begin with one-dimensional sudoku before we go into almost one-dimensional variants.
Pyrrhon