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You are a hit-man undercover at a dinner party. You are in a conversation with three people. One of them is your target. You get to ask two questions before they get tired and leave. You know that one person always says yes because he is mute, the other almost always no, and the other says a relative answer according to his outlook. You also know that your target's favorite color is cyan and that the person who almost always says no only says yes when you ask someone (him or someone else) if he likes dogs. How do you find your target and finish your job?

Hint: Read each persons characteristics again carefully.

ULTIMATE HINT:

Don't ask questions about themselves.
Ask questions about people other than themselves.

SECOND ULTIMATE HINT:

The person who is mute is not the target. What would you want with a deaf person?

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    $\begingroup$ How can the first one say anything if he is mute? Do you mean deaf? Also, do I need to direct my question at any of the people, or can I ask a question for all three to answer? Also, is the target necessarily the one whose answer is relative? $\endgroup$
    – Franklin Pezzuti Dyer
    Commented Jun 13, 2017 at 23:00
  • $\begingroup$ no the target may be any of the three $\endgroup$
    – Ethan Yun
    Commented Jun 13, 2017 at 23:04
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    $\begingroup$ hmmmm, is the target the ONLY one who likes the color cyan? $\endgroup$
    – stack reader
    Commented Jun 14, 2017 at 0:08
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    $\begingroup$ The last hint makes it much easier, but you should have written in the question that everyone is all knowing about everyone else. $\endgroup$
    – stack reader
    Commented Jun 14, 2017 at 0:25
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    $\begingroup$ "the person who almost always says no only says yes when you ask someone (him or someone else) if he likes dogs." Does this mean that 2 people will answer in the case where Im asking someone other than that person. A = Deaf guy B = Dog guy ask A if he likes dogs , he says yes, will B also answer yes ? $\endgroup$
    – user3660570
    Commented Jun 14, 2017 at 6:56

3 Answers 3

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I'm not entirely sure that it is possible if the target is allowed to act completely arbitrarily, and you cannot make any additional assumptions about the behaviour of the no-man.

Reason: Due to the nature of the other two people, questions you ask will never actually give you any direct information about other people. The yes-man will answer yes regardless of whatever you say, while the no-man(because almost-always-no-man is too long...) will answer no except for any question of the form "Does X love dogs?", and even then the actual identity of X is irrelevant. Given this, the target could randomly pick one of these two, and answer questions exactly as if he were them. I'm not sure if this is what the question means when it says "He answers according to his outlook."

I'll take a crack at it anyway, and see what the minimal assumptions might be to solve it. I'll use some basic information theory to explain my approach. Let's call the 3 people A, B and C.

Now, at the start, there are six possible configurations of A, B, and C(Y = yes-man, N = no-man, T = target): YNT, YTN, TYN, TNY, NYT, NTY. Assuming they are all equally likely, this would mean that the entire "system" has an entropy of $log_2$(6) ~ 2.6 bits. You can only get 2 bits of info at most by asking 2 questions, so clearly finding the exact configuration is impossible.

Information theoretically, the location of T should be given by an entropy of $log_3$(3) ~ 1.58 < 2 bits, so the right approach would be to isolate T from the others. This requires a way to generate a question that T would answer differently from Y and N, which is impossible without somehow banning the "arbitrary answers" strategy. So, given all this, under the assumption that "based on his outlook" represents a greedy strategy from T(where without indulging in meta-think he just tries to directly answer questions as if somebody else is T/he is not T)...

Question 1

Ask A: "If I asked B if he likes dogs, what would he say?". If the answer is yes, A is either N(since he was asked about liking dogs) or Y(he always answers yes). If the answer is no, A is T(since from a greedy POV, making B look like he is not N seemingly reduces an outsider's view of the probability of A being T from 1/3 to 1/4).

If question 2 is needed,

Ask B: "If I asked C if he likes dogs, what would he say?". By a similar line of reasoning, if the answer is yes, B is Y/N, and C is T, else B is T.

This is the first time I'm actually trying to solve a puzzle here, so any pointers/corrections would be welcome!

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    $\begingroup$ I agree that without some kind of cheating it is unsolvable. $\endgroup$
    – Jan Ivan
    Commented Jun 14, 2017 at 6:46
  • $\begingroup$ I like the information theoretic approach! $\endgroup$
    – justhalf
    Commented Jun 14, 2017 at 9:03
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    $\begingroup$ Why do neither of your questions ask about preferring the color cyan? Isn't that the only definitive indicator of the target's identity? $\endgroup$
    – MikeQ
    Commented Jun 15, 2017 at 18:34
  • $\begingroup$ If A were T, they would answer yes in the first question, since it would effectively make the question useless. $\endgroup$
    – Rob
    Commented Jun 16, 2017 at 2:54
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    $\begingroup$ I dont understand the YNT, YTN e.t.c. classification. I assume you assume you don't know which person is which, but then your configurations also seem to assume that the target is not yes-man or no-man? $\endgroup$
    – Adam
    Commented Jun 20, 2017 at 10:31
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I see a lateral thinking tag, so I'm going to say that your target is the one wearing the cyan tie, pocket square, or other visible piece of cyan apparel.

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  • $\begingroup$ I guess that would be correct $\endgroup$
    – Ethan Yun
    Commented Jun 17, 2017 at 18:41
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There are two question to ask to three people. The first person always says yes. The second person will always say yes to a question about dogs, otherwise no. The target, based on comments, will always say no to a question regarding their appreciation of cyan (because they know the hitman knows that they like cyan).

The questions can be phrased in such a way so that only the target will say no.

First Question:

If you had a dog, would you like your friend give you a cyan collar as a gift?

Second Question:

Alternate question: "Would you like a cartoon about a cyan colored dog?"

Say to:

Say this question to two of the people.

Explanation:

If one of those people says no, that's the target. If both say yes, the other is the target.

Of course, this assumes that the deaf person and the dog enthusiast cannot be the target.

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    $\begingroup$ Please hide the content of your post that contains your solution. You can do this by editing your answer and adding >! in front of the lines. $\endgroup$
    – Sensoray
    Commented Mar 26, 2018 at 20:04
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    $\begingroup$ Why can we assume that the dog enthusiast cannot be the target? $\endgroup$
    – puzzledPig
    Commented Mar 26, 2018 at 20:11

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