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]