No.

Arminius:

Perfect Logicians.

Players A and B both have got the number 12 written on her forehead. Everyone sees the number on the front of the other but does not know the own number. The game master tells them that the sum of their numbers is either 24 or 27 and that this numbers are positive integers (thus also no zero).

Then the game master asks repeatedly A and B alternately, if they can determine the number on her forehead.

`A: "No". B: "No". A: "No". B: "No". A: "No". ....`

After how many "no"s does the game end, if at all?

So I wrote in the said riddle: “this numbers are positive integers (thus also no zero)”.

It seems that you have not read the said riddle.