Cenoman wrote:eleven wrote:You would have to show, that r1c3=3. But i think, that's almost as hard as solving the puzzle in a conventional way.

Well, as the sticks symmetry is a uniqueness technique, couldn't we say: I add 3r1c3 as extra clue, and if the new puzzle has a solution, it is necessary the same as the unique solution of the original one ?

As soon as you accept uniqueness, this guessing technique is logically valid. Guessing has always been considered as still worse than T&E (although many real players use it). In the present situation, it's not arbitrary guessing, it's educated guessing - so, it may not be worse than T&E, after all.

Cenoman wrote: My question: is it possible to build a non symmetric minimal puzzle (having a symmetric solution) ?

Almost obviously yes, by starting from a symmetric full grid. What might be interesting in the context of symmetry is a notion of symmetrically minimal puzzle (not necessarily minimal in the general sense).