logical deduction - Engineers logic test for a job

Two engineers go to a job interview. They are introduced and told they are looking for people with team working skills. Without time to talk or get to know each other, they are guided to two different rooms with a window from which they see a wind turbine park.

Engineer A can see 22 turbines.
Engineer B can see 4 turbines.

They are told that in the park there are 24 or 26 turbines, none of them are seen by both engineers at the same time, and between the two they can see all the turbines in the park.

During the next hours, an interviewer will ask them a question per round, always being the same question. He will ask first to engineer A, and, if he does not answer, will then ask to engineer B. The question is: "Are there 24, or 26 turbines in the park?".

If one of the engineers answer correctly, both are hired.
If one answer incorrectly, none will be hired.
If there's no answer, the interviewer will go ask the next engineer, starting a round of "question to engineer A - question to engineer B", always starting by engineer A.

Knowing that both consider they are very logic people and really want the job: In how many rounds will they manage to answer correctly, without any doubt, if possible?

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EDIT: Oras found this puzzle asked 2 years ago (with a different story) here, however since the numbers differ and it's rather old I will keep the post. By the way, this is my first post here, glad to be part of the community!

Answer

Answer

$A$ will know how many there are in the third round of questions.

Consider some simpler versions of the problem first

Case 1

There are $26$ turbines.
$A$ can see $24$ and $B$ can see $2$ and they are both told that there are either $24$ or $26$.

First round
$A$ doesn't know but does know that $B$ either sees $0$ or $2$ turbines.
If $B$ sees $0$, then, by the fact that $A$ doesn't know, $B$ would know that $A$ cannot see $26$ (otherwise $A$ would know there are not $24$).
Because $B$ sees $2$, they say that they don't know.

Second round

$A$ now knows that $B$ does not see $0$ turbines and must see $2$ so $A$ knows that there are $26$ turbines.

Now consider a slightly different set-up

Case 2

There are $24$ turbines.
$A$ can see $22$ turbines and $B$ can see $2$ turbines and they are both told that there are either $24$ or $26$ turbines.
Notice that the situation, from $B$'s perspective, is exactly the same as in Case 1 and $B$ will suppose that $A$ sees either $22$ or $24$ turbines. Thus, we get the following

First Round
$A$ doesn't know. $B$ doesn't know.

Second Round
$A$ says they don't know.

$B$ now realises that $A$ does not have $24$ turbines, otherwise we would be in Case 1 and $A$ would know how many turbines there are. Hence, $A$ must see $22$ turbines and $B$ knows the overall number to be $24$.

Case 3 (the current case)

There are $26$ turbines
$A$ sees $22$ and $B$ sees $4$. Notice that, from $A$'s perspective the scenario is the same as in Case 2 and $A$ knows that $B$ can see either $2$ or $4$ turbines. The questioning proceeds as follows

First Round
$A$ doesn't know., $B$ doesn't know.

Second Round
$A$ doesn't know., $B$ doesn't know.

Third Round
Because $B$ doesn't know in the second round, $A$ knows that $B$ does not see $2$ turbines (otherwise we are in Case 2). Hence, $A$ knows there must be $26$ turbines.