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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?


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!

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  • $\begingroup$ Is it possible for the engineers to come up with a strategy before the interviewer starts asking them questions, or not? $\endgroup$ – Excited Raichu Oct 4 '18 at 10:30
  • $\begingroup$ wait never mind didn’t read close enough $\endgroup$ – Excited Raichu Oct 4 '18 at 10:30
  • $\begingroup$ Is it possible, that one of them does not see any turbines? $\endgroup$ – Torsten Link Oct 4 '18 at 11:03
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    $\begingroup$ this is duplicate of a question asked before, cant find it yet :) $\endgroup$ – Oray Oct 4 '18 at 11:24
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    $\begingroup$ @Oray Good catch! I had not seen this one but it doesn't surprise me that it's already there. It has the feeling of a Green-Eyed Dragons problem. $\endgroup$ – hexomino Oct 4 '18 at 11:46
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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.

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  • $\begingroup$ This is correct :) $\endgroup$ – Evaldor Oct 4 '18 at 11:42
  • $\begingroup$ @hexomino I don't quite get it. Why does A know what B sees just from the answer "i don't know" $\endgroup$ – user52327 Oct 4 '18 at 14:27
  • $\begingroup$ @Jannis Which part are you referring to? $\endgroup$ – hexomino Oct 4 '18 at 14:28
  • $\begingroup$ @hexomino literally all: B doesn't know what a sees. In the first example he sees either 0 or 2 from A perspective, but he doesn't know what a sees, so he says 'idk'. How does A figure out B's view? $\endgroup$ – user52327 Oct 4 '18 at 14:32
  • $\begingroup$ @Jannis Does Case 1 make sense? A figures it out purely because B passes. If B doesn't pass, then B must see 0. If B does pass, then B must see 2. A knows this because if B had 0 then B would think A had 24 or 26 and would only pass with 24. $\endgroup$ – hexomino Oct 4 '18 at 14:53
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I will try:

  1. A knows that B has 2 or 4 and B knows that A sees 20 or 22

But lets forget about that for a moment.

2. A does not say anything, so B knows, that he did not see 25 or 26 turbines as then 24 would not be possible anymore and he could instantly answer.

So then

3. B himself does not say something, so A knows: He doesn't have 0 or 1, because otherwise he would have known from 2. that it must be 24.

After that

4. A still doesn't know, if B has 2 oder 4, so he says nothing.

Next step:

5. B knows: If A had 24, then he would have known, there are 26 turbines (as 3. states, that B cannot have seen 0 turbines) and would have answered: A does NOT have 24... B still does not answer

And finally

6. A knows: If B had 2, then he knew from 5. that it cannot be 26 and would answer 24. So finally A knows: B saw 4 and can answer correctly.

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  • $\begingroup$ "1. A knows that B has 2 or 4 and B knows that A sees 22 or 24". Are you sure? Check those numbers :) $\endgroup$ – Evaldor Oct 4 '18 at 11:40
  • $\begingroup$ you are right.... argh $\endgroup$ – Torsten Link Oct 4 '18 at 11:43
  • $\begingroup$ fixed it... one more step necessary $\endgroup$ – Torsten Link Oct 4 '18 at 11:48
  • $\begingroup$ Now it's correct! $\endgroup$ – Evaldor Oct 4 '18 at 11:55
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So, let’s start with what each engineer knows about the other:

Engineer A knows that

engineer B sees either 2 or 4 turbines.

In addition, Engineer B knows that

engineer A sees either 20 or 22 turbines.

So, round 1 begins,

and A has no way to know how many turbines B saw (2 or 4), so they pass.

Then it’s B’s turn, and

they now know some new information. B knows that A thinks that B has either 2, 4, or 6 turbines. If B had 6 turbines, he/she would be able to guess 26 on this turn, because B knows that either A has 20 or 22 turbines, and A must have 20 (because 28 is too many.) B now knows that A thinks that B has either 2 or 4 turbines (because A can use this logic as well). If A had 20 turbines, A could guess 24 using this logic (because 22 is too few). So, B knows that A has 22 turbines,

and therefore,

B guesses 26, turn 1.

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  • $\begingroup$ If A sees 20 turbines then A would suppose that B sees 4 or 6 (not 2 or 4) so they would not be able to guess 24 as you say in the last line of the 4th paragraph. Consider the scenario where A sees 20 turbines instead of 22. What changes from Bs perspective? $\endgroup$ – hexomino Oct 4 '18 at 11:38

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