No, spider. We are alone here. Show your weapons! 
Carleas is observing the precesses in this thread from outside anyway, but currently he has no chance to get in.
[tab]Okay, I will give you the next step.
Next step:
A: “No” => b < 21.
B: “No” => a > 6.
And so on.
By this I have given you almost the whole solution. [size=85](Now, hurry up, because the others are coming soon.)[/size]
Good luck![/tab]
No I don’t want to play with a recursive solution until you acknowledge that my inductive solution is sound.
It isn’t “sound” because
…that isn’t true.
The entire game is figuring out what the other person must know. That is why it is in the category of “Perfect Logicians”, else one couldn’t be certain of what the other might deduce.
If anything, that’ll add a couple of nos.
Then just count them.
Like at the first no I know I don’t have a 9, then at the second no you know you don’t have a 9 and I know that you know.
Exactly.
They both know that they don’t have a 9 from the start. But neither knows that the other knows that because one might have a 15 and thus the other would have a 12 or a 9. Each can see a 12, but they can’t know they don’t have a 15 and thus the other person thinking that he might have a 9 or a 12.
If the person saying “no” suspects that he might have a 9, the reasoning that he said “no” because he realizes that he must have either 12 or 15, doesn’t hold. When the 15 is discounted, he would still wonder if he had 12 or 9.
Any of them would immediately say yes if they could see a 9. This is obvious to both.
If both of them say no on the 1st round, then none have 9.
This is evident.
?? How so?
If you see a 9, how do you know whether you have a 18 (for 27) or a 15 (for 24)?
Even after the first round, 9 is still an option.
[tab]
Next step:
A: “No” => b < 18.
B: “No” => a > 9.
And so on.[/tab]
The whole solution (with the solution process):
[tab]In the beginning A knows that (1) a = 12 or a = 15, and (2) B knows that b = 12 or b = 15.
Okay. But A does not know that B (2) knows, and B does not know that A (1) knows. So the statement above is not suited for the recursive conclusion.
But both A and B know all of the following statements and that each of them knows that the other one knows them:
(3) a = 24 - b or a = 27 - b and (4) b = 24 - a or b = 27 - a.
Now, from the first “No” of A and from (4) follows (5) b < 24, because if b >= 24, then A would be able to conclude a. This is the motor for the recursive conclusion.
Now, from the first “No” of B and from (3) and (5) follows (6) a > 3.
And so on.
A: “No” => b < 21.
B: “No” => a > 6.
A: “No” => b < 18.
B: “No” => a > 9.
A: “No” => b < 15.
B: “Yes”. Because together with the information of (2) there remains only one possibility.
Now add the „No“s!
The game ends after 7 „no“s.[/tab]
I remind you of the riddle I posted on 14 January 2016:
Who is depicted here?
Incorrect (for several reasons).
Sorry, try again.
My solution is absolutely correct.
Your “there-is-no-solution-solution” is incorrect.
That is incorrect. Sorry. Try again.
“Famous last words.”
You should know me well enough to at least accept a tiny bit of doubt if I am telling you that you are incorrect.
Would I say it without a reason?
My actual words were:
First correction:
You must disqualify zero and all negative numbers when you word the riddle, else your count will be different.
Agreed?
No.
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.
Oops … your right, I missed that (silly me). My apologies. One must VERIFY anything I say (age n all). 
… so on to the next issue:
Second correction:
This is the issue with all such “perfect logician”, “recursive” riddles.
Being so perfect, they both already know that the other knows this sort of game. Even without being perfect, both you and I know of this algorithmic method. And the whole issue is to be able to realize what the other person knows so that each member can depend upon the answers being given by the others.
As with the “Blued eyed puzzle” and all such similar algorithms, there must be a number with which to begin. You chose “24”, as most people would. But perfect logicians are not “most people”. They know to choose, from the many options, the starting point that would lead to the least number of rounds. The question is “how many no’s are required?” They could have begun their count at 48 or at 100. That would be silly. Why would they? But then again, why would they start at 24?
In all of these scenarios, the place a more perfect logician would begin is the number that is the closest that both parties would necessarily not be able to resolve the puzzle by knowing. They both want for the first “no” to be informative, telling them of something they didn’t already know. They both see a “12” and thus both know that the other knows that the only options for any party is either:
[list]9
12
15[/list:u]
It is a waist to begin at 100 and count your way down when you already know that nothing is going to be resolved until you get close to those numbers. It is also silly to begin with 24 for the same reason. Both parties know that they could begin at any number higher than 15, but can’t choose which number unless they privately begin the known algorithm at 24 (the lowest known sum) and simply count to themselves down to “18” (or merely add the difference of the sums to the 15). They both can deduce from the beginning that neither would be able to say “yes” if they began from the number 18. Thus that is where to begin.
a) They both already know that both already know that their number is <18.
b) And that means that after the first “no”, they both know that their number is >9, eliminating one of the possibles.
c) Second “no”, their number must be <15, eliminating a second possible, leaving only one possible number.
Puzzle resolved with more perfect logicians with only 2 "no"s.
But that isn’t my last objection/“correction”.