7b53 wrote: .... can this be true for the 12 coins puzzle ?? ....
I'm sure it is. This problem barely has a solution at all. If you look at all the internet stuff, you'll see that a mighty struggle is required just to identify the false coin in three weighings. To also find whether it is ligher or heavier, in all scenarios, would surely require a fourth weighing.
.... if a coin never touches the scale, does it consider to be an "outcome from the scale"? ....
Oh, I don't know. The original problem never used the phrase "outcome from the scale". As long as you identify the false coin, you have satisfied the conditions stated in the puzzle, even if you still don't know whether it is lighter or heavier.
.... from your 4 coins example, if i would change the limit to 3 weighings, do i have to include "please say at the end whether it is lighter or heavier"? ....
In my opinion. yes. If you don't include that phrase, you don't have a good puzzle, because a solution exists with just 2 weighings.
When you invent a puzzle, you should be careful to say exactly what you mean.
When you try to solve a puzzle, you should be careful to figure out exactly what is being asked for.
That's what makes a good puzzle. The statement in the problem can be technically correct, but easily misinterpreted by a solver who doesn't read the problem carefully. That's what the 12 coins puzzle is all about.