The HARDEST Logic Puzzle Ever (Simpler Version): Two Doors To Freedom Riddle

Hey, this is Presh Talwalkar. An evil warden holds you prisoner, but offers you a chance
to escape. There are three doors A, B, and C. Two of the doors lead to freedom and the third door
leads to lifetime imprisonment, but you do not know
which door is what type. You are allowed to point
to a door and ask a single yes/no question
to the warden. If you point to a door
that leads to freedom, the warden does answer
your question truthfully, but if you point to the door
that leads to imprisonment, the warden answers
your question randomly, either saying yes or no
by chance. Can you think of a question and figure out a way to escape for sure? Give this problem a try,
and when you’re ready, keep watching the video
for the solution. So here’s a way that you
can escape for sure. Point to door A
and ask the question, “Does Door B lead to freedom?” If the warden answers “Yes,”
then pick door B. If the warden answers “No,”
then pick door C. This strategy is guaranteed to work regardless of the door type
of A. So why does it work? Let’s work through the logic. Door A can either have
two different types. It can either lead to freedom, in which case the
warden is truthful, or it can lead to imprisonment, in which case the warden
answers randomly. Let’s consider the first case,
that the door leads to freedom. In this case, if the warden
answers “Yes” to your question, then that means the warden is
answering truthfully, and Door B does lead
to freedom. Similarly, if the warden says Door B
does not lead to freedom, the warden is answering truthfully, which means door B
leads to imprisonment. That means the other door,
door C, leads to freedom. So you can see that
if the warden answers “Yes,” you should pick door B, and if the warden answers “No,”
then you should pick door C. But what about the case
where door A leads to imprisonment, and the warden answers randomly? Well, in this case, if door A
leads to imprisonment, that means the other two doors,
B and C, lead to freedom. So you can always pick doors
B and C in these cases no matter what the warden answers. So if you pick door B
when the warden answers “Yes,” that will lead to freedom, and you pick door C when the
warden answers “No,” that once again
will lead to freedom. So this shows that logically, if you pick door B when the
warden answers “Yes,” and if you pick door C
when the warden answers “No,” you are guaranteed to find a door that leads you to freedom. Did you figure it out? Thanks for watching this video.
Please subscribe to my channel. I make videos on math and game theory. You can catch me on my blog,
“Mind Your Decisions,” which you can follow on
Facebook, Google+ and Patreon. You can catch me on social media:
@preshtalwakar If you like this video,
please check out my books. There are links
in the video description.

100 thoughts on “The HARDEST Logic Puzzle Ever (Simpler Version): Two Doors To Freedom Riddle

  • I forgot to put the source in the video description originally. This puzzle is a variation of the ace and jacks problem, a preliminary problem in the paper about “the hardest logic puzzle ever.” Boolos, George (1996). “The hardest logic puzzle ever”. The Harvard Review of Philosophy. 6: 62–65.

    TED-Ed did a video about "the hardest logic puzzle ever" they called "the three gods riddle."

  • The solution is so simple that I kind of feel I should have managed to find it by thinking about it calmly, which I honestly didn't even try. It's also conceivable to find this solution through brainstorming.
    The puzzle of the three gods is incredibly harder, so I'd say if anything, that's the one that takes the prize for the hardest ever.

  • Would have been the most difficult, if the warden had responded with "Ozo" and "Ulu", so you wouldn't know which is "yes" and which is "no"…

    In this case my question would have been:
    " If I asked you: "the door A leads to freedom?", you would say "Ozo"? "
    So if he responds "Ozo", the door A leads to freedom 100%, otherwise if he says "Ulu" one of the other leads to.

  • The question I came up with is if you point at a door and ask if it is one of the 2 doors that will lead to imprisonment. But the question that the video came up with is probably better. But it doesn't say you can't ask a yes-no question with flawed logic so idk

  • This is true but it doesn't tell me the POV of the prisoner. "If door A leads to freedom, than you are guaranteed to go to freedom" but the prisoner doesn't know door A leads to imprisonment. So how does that make sense?

  • You should ask: are the two door leading to freedom adjacent? If yes, pick the middle door. If no, pick one of the door on the right of left.

  • You can ask any question that is yes/no. Simply point to a door and ask if you are the warden. We all know you are the prisoner. The warden's response gives away the answer.

  • Yes, I figured this out
    Actually there are many puzzles which uses this feedback technique, like a + × -=- and -×+=-
    So the key is multiply, in this feed one result to the other, then the result does not depend on true/false (+/-)

  • You can just ask a non yes no question and if the warden answers yes or no pick another door, of he answers your question go through the door you pointed at.

  • Before I see answer u pick middle and ask if to left is the life sentence if yes u switch to right if no u pick left

  • What if you ask a yes-no question whose answer would be paradoxical and therefore the warden cannot answer truthfully. If he answers at all, go to a door he is not pointing to. If he does not answer, enter the door you're pointing to.

  • This is easy. Point to any door, then ask the question: do all three doors lead to freedom? If the warden answers no, then the door you are pointing at leads to freedom. If the warden answers yes, then the door you are pointing at leads to eternal imprisonment.

  • Point at door B and ask: "If I pointed at the door to the left of this one and asked 'Does this door lead to imprisonment?', is there a chance you would tell me 'yes'?".
    If door A is imprisonment: warden answers 'yes', as there would be a 50/50 chance to say yes in that case and he is giving a truthful answer.
    If door B is imprisonment: warden answers either 'yes' or 'no'.
    If door C is imprisonment: warden answers 'no', as pointing at a door leading to freedom would never cause him to say 'yes' in the hypothetical question.
    Therefore, if the answer to your question is 'yes', door C is safe. If the answer is 'no', door A is safe.

  • Point to Door A and ask "does Door B lead to freedom?"

    If he answers "yes" then choose Door B. If Door A also leads to freedom and he is telling the truth, then of course Door B is safe. If he is randomly responding, then Door A is the imprisonment door and Door B is thus safe. No matter which one Door A is, Door B will be safe if he answers yes.

    If he answers "no" then choose Door C. If Door A leads to freedom and he is telling the truth, then Door B is the imprisonment door and so Door C is safe. If he is randomly responding, then Door A is the imprisonment door and Door C is thus safe. No matter which one Door A is, Door C will be safe if he answers no.

  • I honestly don't think the warden is going to free you if he's evil to start with. Name a time when any political prisoner was given this logic puzzle?

  • So wait there ? If you point at door A and question door B there is 4 ways it can work ? Telling the truth with yes and no and telling lies with yes and no.

  • I diddnt get it but I got a solution that’s pretty likely to work
    Pick a random door…since two of the three are good and one is bad that’s a 2/3 chance that the answer is truthful so ask the question does this door lead to imprisonment if he answers yes go to one of the other two of he answers no choose that one and this may be only 2/3 chance however since the answer is random not always the opposite that means that even if that door is the bad door it’s a 50/50 whether the answer is truthful and since you already lost a 2/3 chance of good and went into the 1/3 you’d have to be having a really unlucky day to lose the 50/50 chance right after that and lose both so just hope choose that door if no it’s not bad and choose different if yes It is bad

  • You could just ask if you are wearing a blue shirt. If you are and he says no, choose a different door. If you are and he says yes, choose that door.

  • Hey ! there is a text error; in the video , in question.

    But you do not " know " which door is of what type.

    Know is missing.

  • I give him a paradox so if it is freedom he will struggle to answer, but if it was inprisonment, he would answer easily

  • I didn't figure it out, but I knew that the answer would involve multiple doors. I might have been able to figure it out if I thought about it for longer though.

  • My solution (not as good as OP's): Point to any door and ask "Will I get out of prison?"* If it's a freedom door he will have to truthfully say "I don't know." or not reply. If it's the prison door, he will definitely say "yes" or "no". If he says "I don't know" or nothing take that door. If he says "yes" or "no" take one of the other doors.

    * You could also just ask any unknown question about the future like "Will I live to be 100?"

  • Extend the 12 inch line outside the square and connect the 3 inch line from the upper right hand corner of the square.
    You now have the square of the diagonal equal to the sum (12+9) squared plus 3 squared.
    The 12 and 9 inch lines are parallel so you can 'slide' the 3 inch line along those lines. It is only the sum 12 + 9 that matters.

  • But his answer doesn't determine the door. So if he answers randomly and says door B leads to freedom, that could be a lie. Therefore you have imprisoned yourself.

  • My answer:
    Ask a yes-no question which does not have a proper answer, if he says either yes or no, then it is the door that leads to imprisonment
    If he does not answer, then it is the door to freedom

  • if u find urself in this situation, ask him something of true meaning and pick some door. if the door leads to freedom, u got some deep insight into our world and can use it. if u get imprisoned, u had no real way in life to know more than u can see/discover. so why be free then after all?

  • Point to door C and ask 'are you going to respond with "no" instead of "yes"?', if he answers "yes" or "no" don't take door C, if he can't answer, pick door "A" or "B".

    ^ Is that cheating? probably..

  • Me kicks all of the doors open looks asks is this one to freedom even tho I know it is and the second one is this one prison no even tho it is is this one freedom yes I go out the last door technically I did not go in it or knock the. Warden out and get him to open it he he he and I can ask him and make the noise out of his mouth ha

  • Point to the center door and say “does this door and the one to its left lead to the same result? If he says yes pick A; if he says no pick C

  • I pointed to door A and asked the warden if I could have some paper and a pencil to work this out on and he said "No".

  • I might have been on the right track. I thought about pointing to door A and asking if both door B and C lead to freedom. If he said yes he wouldn't be being truthful, one of them would have to be bad for him to tell the truth, B and C are good to go. If he said no then go through door A. I shouldn't have looked at the answer, I would have got it in a month or so.

  • Could you point to door a and ask ‘If I could ask you 100 times if this door leads to freedom would your answer be the same each time?’ If he answers yes the answer is the same, then the door leads to freedom so choose it. If the answer is no, the answer will change choose either of the others.

  • OK, so the interesting question for me is what is a general strategy for framing the appropriate question. A useful place to start is to assume that we're going to have to break it down into cases. There are only six cases: all combinations of yes/no and A/B/C being the door leading to imprisonment. Just drawing out the 2 x 3 grid and staring at it suggested to me that the question has to maximize the information being collected by asking something about a door other than the one being pointed to. Then start guessing questions and examining all the cases. The most obvious question is, "does that door lead to freedom?" With that question, an examination of the cases reveals that two of them are impossible, leading to the answer.

  • It is not a contentious point.
    It is related.

    Doors B and C are to the left and right of Door A.

    Point to Door A and ask if the door to its left will lead to your freedom. 🙂

  • I thought – Pick any door and ask: 'Are the other two doors prison doors?' If he answers 'yes' he is lying because there cannot be two prison doors and thus the door you chose is the prison door and you can pick any of the others two doors. If he says 'no' he is telling the truth (both doors are not prison doors) and thus your door is a prison door and thus you can pick any of the other two doors. But this is probably wrong since it is not the answer he got but hey I tried.

  • Ask him a hard maths question like does 75436 squared equal 5690590096, if he thinks about it and says yes then go through the door, if he immediately says yes or no, go through one of the other doors.

  • But let’s make it spicier
    There are 3 wardens and one lies one tells the truth and one answers randomly. You can only ask 1 question to each warden specifically. However there isn’t s yes or no, it’s ozo, or ulu. But if you don’t answer in 2 minutes, a trolley will come hurdling toward you, killing you. You have to either push a fat man in the way, pull a lever and kill someone else. Or die, or solve it in 2 minutes.

  • My first thought was to ask a paradox question (something like "will you say no?") so he'll be stumped if he tries to tell the truth

  • Still haven't watched the answer, but I set this up similat to a K-Map(Karnaugh map) under the premise that I was pointing at A and asking "Does door C lead to freedom?".

    With that my diagram looked like this:
    ABC| 00 | 01 | 10 | 11
    0 | X | X | X | Yes/No
    1 | X | Yes | No | X

    0 Indicates the door is unsafe.
    1 Indicates the door is sasfe.
    X means the scenario is not possible (i.e. 0 or 2 unsafe doors).
    Other entries (e.g. Yes, No, and Yes/No) are all of the answer(s) I can receive in that scenario.

    From the diagram it became obvious that when A is safe I will learn the truth about C and thus if the answer is "No" I should go out door B and when it is "Yes" I should go out door C. When A is unsafe both doors B and C are safe so the random answer makes no difference and thus I can safely act as I would if door A were a safe door.

  • ANSWER: point to door A n ask warden "door B leads to life time imprisonment right?"
    if he says "NO" -open door B
    if he says "YES"- open door C

  • Point to a door, ask if a different door is door to freedom.
    If warden answers yes, the original door is either the one to imprisonment or freedom. If it is freedom, we know the other one is also freedom. If it is the imprisonment one, the other two are good. Go through the door you asked about.

    If warden answers no: either the door you’re pointing to is freedom, in which case we know that the door you asked about is imprisonment, which rules out the door you asked about, but since the door you pointed to could also be imprisonment and that could give the same answer, you need to go in the door that you neither pointed to nor asked about

  • I don't get it.. perhaps someone can explain it to me: what about door A? You're saying it's always B or C but what how come it's never door A?
    Cheers 🙂

  • Quotation: "Point to door A and ask the question, "Does door B lead to freedom?"

    When you point at Door A but ask a question about Door B, how do you know the Warden is answering the question about Door A or Door B? He could ignore your pointing and answer the question about the actual Door B, because you said Door B, or he could answer the question about Door A, because you're pointing at Door A. Or you could confuse him and he thinks the door you're pointing at, Door A, is Door B. You don't know.

    And the warden can't be that evil if he gives you a 66% chance to escape and a revealing question to ask.

Leave a Reply

Your email address will not be published. Required fields are marked *