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,

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@preshtalwakar If you like this video,

please check out my books. There are links

in the video description.

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. http://www.hcs.harvard.edu/~hrp/issues/1996/Boolos.pdf

TED-Ed did a video about "the hardest logic puzzle ever" they called "the three gods riddle." https://youtu.be/LKvjIsyYng8

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

know*

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?

Whoopee! I got this one!

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

anyquestion 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 (+/-)

How do you know that door A doesn’t lead to freedom

Oh sorry

good logic

Would you lie to me?

I will just take out my shotgun and kill the warden in an American way.

you can do better than that no logic in this

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.

Doesn't "how old are you?" work too?

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

Keep asking if 1+1 is 3

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.

we can write the yes , no in two door and remain the other. then we can ask tell me the name of the right door. 🙂

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.

No loopholes, no fun.

at least born in the same month are 2 studends

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?

What is 2+2.

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

“will you tell me the truth when i point at that door”, good o’le absurdity

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.

If he is an evil warden, all the doors would lead to imprisonment and the whole ordeal would have been a cruel joke.

I thought you are only allowed to ask Yes or No and not to chat with the worden…

What happens if you ask “are you lying?” Would that confuse the warden with enough time to find a way to escape?

Just ask the question "what's 3×3" if he says 9 its a freedom door, if he says yes or no it's the imprisonment door

Lol easy

Okay same logic, but I thought of asking the question does door A lead the same place as door B

I like turtles,,,

Just ask him to go in door that his favorite then lock him bcus no evil warden set ur freedom dude..

That took me WAY longer to work through than I'd thought it would. 🙁

Pointing to a door and asking a question about another door doesn’t quite compute.

I didn't catch you please

1:06 jumpscare!!!!

or you could ask if 9+10=21 lol

This doesn't work when we realize that freedom doesn't exist.

Sorry, but you explained the problem pretty badly.

points to bdoes door b lead to freedom?-Yes

Aha!

walks in and diesWhat if the warden is blind? Ha!

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.

it is not Nice. I don't like it. chiiiiiiiiii

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.

A said ask if the door was brown

This isn’t even correct

I dont rly get it he may be lying saying yes or no at imprisonment so you didnt prove it at all

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?

What color is the door?

Yes

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..

Lies he says yes or no RANDOMLY

Ask a question that isn't applicable.

Reminds on %s and prices after inflation or any %al change in price.

Will this work for a black person?

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.

I'll just wait to be killed

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.

Why don't you just ask a question you know the answer to so you know if they're lyingd

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.

My mind didn't work so I randomly chose C

C.

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.

Wonderful problem. Didn’t think of it at all.

What if you ask about the door that leads to imprisonment and he says "yes" by chance?

Could you do the Monty Hall problem?

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.

I love how I thought only 1 of them lead to freedom*face slap*

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

I found a creative way:

Point Door C and ask Does door A lead to freedom?

Yes = Door A and No = Door B

That warden is getting fired. No matter how evil he is, you're probably in there for a reason.

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.

I got this

ask a question without a yes-no answer

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

It's the Monty-Hall problem 😀

I’m so angry at myself for not getting this!!

You do not which

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

Or you can say answer the opposite answer to the door that leads to inprisonment therefor by passing the quiz

So simple but I did not get it before becoming bored and giving up 🤤

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.