dobrichev wrote:Your formalism sounds reasonable to me, but let see what others will say.

I am waiting for replies too, because I feel my proof is too simple, so I can be wrong.

dobrichev wrote:There are examples with puzzles that cover entire UA with givens. Permuting the givens within the UA always results in a valid puzzle, but minimality could change. So I have in mind that UA are partially isolated subgrids, being prepared for surprises of any kind in this area.

If I undersood you correctly, you say about twin puzzles. Please, clarify - in what way puzzle's minimality could be changed by permuting UA set formed by givens (clues)? I'd say UA is fully isolated subgrids. I think UA set can be fully explored without solution grid knowlege. (Maybe I am wrong.)

dobrichev wrote:Serg wrote:Let's consider sample n-digit n-valent strongly minimal UA set.

What about extension of your proof to n+m digits in n-valent strongly minimal UA set? For n=2 we know such exist.

It would be nice to get proof of m-digit n-valent (m > n) strongly minimal UA sets non-existence. In that case we would know all strongly minimal UA sets are bivalent. But I cannot extend my proof yet to this case .

Serg