Ajò Dimonios wrote:

Having an extra clue cannot make the scheme more difficult because it is in contradiction with the fact that it is always possible to adopt a method of solving the difficulty identical to that of the scheme with a clue in less (always with single solution) simply using the elimination of the candidate as the first resolution move.

Eleven wrote:

No.

If you remove a clue from a unique puzzle, you cannot know, if it still has a single solution. You would have to prove it, before you use the UR. But to prove it, you must solve it without uniqueness techniques.

So the puzzle with the extra clue is definitely harder.

I show you with a simple chain that what you say is not correct. We start from the fact that both schemes allow only one solution (it is an essential feature to be able to use the methods of uniqueness. Consequently, nobody forbids me to write the following chain on puzzle n2: 9r3c6 = {UR Type 3 (43 + 36) r35c46} => - 3 r7c4 => 9r3c6; stte. If 9r3c6 is false it implies that the UR type3 is true and consequently that r7c4 = 3 is false and that r3c6 = 9 is true which leads to the solution. Therefore the two schemes they have the same difficulty.

Paolo