I believe almost everyone has heard this riddle before.

There are three people in front of you. One always tells the truth, one always lies, and one answers randomly between truth and lies. You can ask 3 yes-or-no questions to any of the people. How can you figure out which person tells the truth, which person lies, and which person speaks randomly?

There are several variations on this riddle, including an infamous version where you can't tell if what they are saying means yes or no.

Here's one I came up with.

There are three people in front of you. One always tells the truth, one always lies, and one answers randomly between truth and lies. THE THREE PEOPLE DO NOT KNOW THE IDENTITY OF ANYONE BESIDES THEMSELF. You can ask 3 yes-or-no questions to any of the people. How can you figure out which person tells the truth, which person lies, and which person speaks randomly?

Good luck!

  • 1
    Can you clarify how the random person works? If they don't know the answer, will they say "I don't know" or respond with either yes or no randomly? – Zimonze Nov 16 at 18:29
  • @Zimonze they will say a random thing of yes or no, regardless of they know or not. – Excited Raichu Nov 16 at 18:32
  • 1
    What about the truthteller and liar? Will they say that they don't know? – Zimonze Nov 16 at 18:35
  • @Zimonze yes, they will – Excited Raichu Nov 16 at 18:36
  • Wait, so when you ask a question, can it only be to one person or to the whole group of three? I guess I'm not finding "to any of the people" to be clear enough. – Dorrulf Nov 16 at 18:44
up vote 3 down vote accepted

Alright, let's try this I guess...

I have 2 questions, one I will ask once, and one I will ask twice.
1st question: Ask the person if my underwear is blue (they can't see it). If they answer "I don't know", they're either a truth teller or liar. If they answer yes or no, then we know they are the random one.
2nd question: Ask the person if my eyes are brown (let's say they're actually blue). If they answer no, they are the truth teller or the random, and if they answer yes then they are the liar or the random.
I will ask person 1 the first question. If I find them to be the random, I will ask the 2nd question to each of the next people. If I find them to be either the truth teller or liar, then I will ask the same person the second question and one of the remaining to people the first question again.
Possible outcomes: (in Q-P:A format, 1 - 3)
1-1:Random 2-2:T/F no need for 3rd question, person 3 must be remaining T/F
1-1:T/F 2-1:T/F 3-2:Random remaining 3rd person is remaining T/F
1-1:T/F 2-1:T/F 3-2:T/F remaining 3rd person is Random

  • This gets the check for being the first- my solution used the same exact first question with rot13(Vf gjb cyhf gjb svir?) as the second question. – Excited Raichu Nov 16 at 19:00
  • Wow, well that really would've been something if they had both been the same. – Dorrulf Nov 16 at 19:11

I can think of one question to start with:

"Do you know whether you tell the truth, lies, or both?"
This question should weed out one of the three rather quickly since the truth-teller will always answer 'yes' and the liar will always answer 'no', but the intermittent answerer will do either and 'pair up' with one of the two people, leaving the other's identity clear without a doubt.

However, I cannot think of a way to weed out the intermittent answerer just yet, since there is a 1/4 chance that they mimic the other person exactly (first answer doesn't matter - either the truth-teller or the liar gets separated from the other two. Then, assuming equal probabilities of either a truth or a lie from this person, there is the one-in-four chance that they answer identically to the one person that they were paired up with initially. Perhaps the same question could be asked again twice and we could rely on the 3-in-4 chance of the intermittent answerer changing their answer.

Question 1:

Ask someone "If I were to flip a coin, will it land on heads?"

Result:

If the answer to Question 1 is "yes" or "no", they are the random-teller.

Skip to Question 3.

If the answer to Question 1 is "I don't know", they are not the random-teller.

Ask someone else Question 2.

Question 2:

Same as Question 1.

Result:

If the answer to Question 2 is "yes" or "no", they are the random-teller.

If the answer to Question 2 is "I don't know", the person you did not interrogate yet is the random-teller.

Question 3:

Ask one non-random-teller "Is 2+2=4?" This identifies the truth teller or liar, and by process of elimination identifies the last person as well.

Result:

Success!

  • rot13(Jul jbhyq gur enaqbz gryyre fnl lrf be ab? Nyfb, jul jbhyqa'g gur yvne yvr nobhg abg xabjvat naq fnl lrf be ab?) – kanoo Nov 16 at 21:15
  • @kanoo look at op's comments on the post. – Zimonze Nov 16 at 23:03

Approach one of them,

point to one of the other two, and ask "Does this person tell the truth?"

Approach a different individual

point to one of the other two and ask the same question. Since none of them know the others' identities, both the truthteller and the liar will answer that they do not know, while the third person will answer randomly between "yes" and "no"

Your third question is

"Do you know your own identity?",

with the caveat that

you should ask this question of an individual who has responded "I don't know" to a previous question. "Yes" means this is the truthteller, "no" means this is the liar

  • rot13(Jul jbhyq gur enaqbz gryyre fnl lrf be ab? Nyfb, jul jbhyqa'g gur yvne yvr nobhg abg xabjvat naq fnl lrf be ab?) – kanoo Nov 16 at 21:16

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