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

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Source

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.

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Sounds the Christian God….free choice. Don't choose wrong lmao

if you know their gender just ask what their gender is and if they lie thats the imprisonment and if theyre honest go in the door. that was my opinion but this one works too

points to a door"Would you say both the other doors lead to freedom?"

If he answers either yes or no, the pointed door is prison one.

If he says yes and no, or does not answer, the pointed door leads to freedom.

how about this for a question "Will this door help me not escape?"

I would point to a random door then ask the warden, "You want to hear the most annoying sound in the world?" then proceed to demonstrate it non stop until he got tired of it and let me go free.

Point at door A and ask "Is this statement false?" If he says yes or no, you picked the bad door

My guess: point to any door, and ask if one of the other doors you're not pointing to is the imprisonment door. For example I point to A, and ask if B is the imprisonment door. If he says yes, just go through door C; if he says no, go through door B. This works even if the door I point to is the imprisonment door because I just need to ensure the door I pick to go through is NOT the imprisonment door by not going through the door I point to and going through one of the other doors based on the warden's answer.

Edit: Yep, got it right 🙂 to be fair, I got the idea from a Ted-Ed riddle that has the three alien overlords if you guys know about that.

I'm proud of myself for solving this one.

Just ask which door leads to freedom duh

My solution is more complicated. Point at A and ask "does door A leads to same thing?". If the answer is yes – go to B, is the answer is no, go to C. Same outcome

If A is a good door and A=B then go to B. If A is good and A!=B then go to C. And if A is a bad door – then you can go into any of two doors

I point to any door asking if the one to the x side leads to freedom

1) the answer is "yes" : I open that next door.

2) the answer is "no" : I open the (3rd) remaining door

Plus, this must be one the of easiest oness (since i never find a solution)

Nahhhh what if he say yes randomly?

Couldn't you just point to door A and ask him if he is the Warden? If he answers Yes then just leave through door A. If he answers No then go through door B or C.

0:19 “…but you do not which door….” is a typo. It should read “…but you do not

knowwhich door…”why point to door A?

What is freedom?

Point to door 1 and ask "is the middle door the door to imprisonment?" If the answer is no, and you pointed to the freedom door, then you're safe to walk through the middle door. If the answer is no, and you pointed to the imprisonment door, then you're still safe to walk through the middle door.

If the answer is yes, and you pointed to the freedom door, then you're safe to go through the right door. If the answer is yes, and you pointed to the imprisonment door, you're still safe to go through the right door.

No = use the middle door

Yes = use right door

Little Help? So, I stopped the video, not wanting to hear the answer…so PLEASE PLEASE PLEASE do not give me the answer. I just want to check with someone who does to see if my strategy is correct.

Given the wording of the puzzle, my strategy would be to point at a door and then ask a yes/no question that doesn't have a yes/no answer. If the warden says yes or no, then I must have pointed to the door that leads to lifetime imprisonment.

The question that first comes to mind (and no, I did not originate this question) is: "Is the set of all non-recursive sets non-recursive?" It is clearly a yes/no question, but it does not have a yes/no answer. For those wondering, a non-recursive set is any set that does not contain itself. So the set of all sets is clearly recursive while the set of all digits from 1 to 10 is clearly non-recursive.

"hey warden, what's up?"

In Soviet Russia, evil warden is YOU!👇

Okay, so it really took me a while to understand this. Broke it down, tried to explain. Hope this is helpful and not more confusing.

In the case of A = freedom, then:

B = yes is a true statement because A is good, so B and A are the good doors.

If B = no and is a true statement because A is good, then C and A are the good doors.

In the case of A = prison, then:

If B = yes, this is still a true statement, because A is the bad door, so B and C have to be good.

“B = yes,” can not be a false statement because if A is good, then, “B = yes,” is true, and if A is not good, and you’re told, “B = yes,” then it has to still has be true because A is the only door that is bad.

If A = prison, then:

If B = no, in this case, this is not a true statement, because A is the bad door, but because you do not know whether A is good or bad, you don’t know if this is a true or false statement. Since it is possible for, “B = no,” to be a true statement, C is the definite choice. ("A," could be good or bad. "B = no," could be good or bad. C is definite if you're told, "B = no").

And to summarize the conclusion in the video:

If B = yes, this is a true statement and can not be false, so pick B.

If B = no, this could be true or false, but if you're told this, it can be deduced that C is the definite choice, so pick C.

Here was my conundrum. I wanted to do a variation of "what would the other person say…". So point to A and ask "what would you say if I pointed to B and asked if it leads to freedom". How does the warden answer if B is the imprisonment door?

Couldn’t you just ask him any non yes or no question? Like if I point to door A and ask, what color is this door and he says “No” then that seems like a dead giveaway.

I solved it differently but there are multiple correct answers as long as you:

Ask any question that tells you a clear answer on any door you are not pointing at.

Do NOT go through whatever door you are pointing at.

Trust the answer as truthful. (If isn't, then either door you aren't pointing at is safe.)

Why not just ask "are you going to answer my question randomly?"

points to door A, ask which one door that leads to imprisonment. if they answer it truthfully then just goes which not. if they either answer "yes" or "no" then goes any other than A

Thank you for making these videos. Perhaps I need more practice. I don't understand even after your explanation 😅

I answered it as I point to door 1 and ask “would you have answered randomly had I picked door 2?” If he says yes I go through door 3 if no then door 2.

I did the opposite but I'm not sure if it would work. Could someone check my work? I picked a random door, let's say door A, and asked "Does Door B lead to imprisonment?" If yes, pick C, if no, pick B.

"Will you walk through that door with me?"

If the answer is truthful, and the warden isn't insane or suicidal…

The random "yes" could also mean that DoorB leads to imprisonment..

If the warden says yes randomly (because the answer to your question is no) and you open DoorB.. you just got set up for life time imprisonment..

This logic may increase your chances but I don't see how it's guaranteed.

Ask him "I'm lying to you, am I?" If he is not able to hive any answer – the door is "good" one. If any answer is given then the door is bad. I know the correct answer is different because the number of doors (2+1) must be important somehow, but anyway 🙂

I’m proud my myself that I figured out a solution in about 2 minutes.

So, when do I get my free goat?

Why am I still doing time? I know the answer.

I don't understand this. If the warden is evil, why would he give you a 66 2/3 % chance of escaping.

Easy. Poinjt to a door, ask " does this door lead to imprisonment?". If the door does lead to freedom, he's forced to say " i cant answer the question ", then choose that door. If he lies then he'll say "yes/no", then choose one of the other doors. Similar to other games.

My solution (before watching the answer):

1. I have to point to a door, and all of them look the same, so for simplicity I’ll always point to A.

2. I will always get a “yes” or “no” and absolutely no other information, so every strategy will have to look like:

If “yes” -> choose door X

If “no” -> choose door Y

3. If A leads to imprisonment, then no matter what I ask, the answer is random. So the X and Y must not include A itself, otherwise there is a chance I will lose.

4. So in my strategy, X and Y have to be B and C, but I’m not sure in what order.

5. If A leads to imprisonment, then I always win with my strategy. Because both B and C must lead to freedom.

6. Otherwise, A leads to freedom and any question I ask will be answered truthfully.

7. Either B or C (or both) lead to freedom. So the question is as follows: “Does B lead to freedom?”.

8. I know that if A leads to imprisonment, I can choose either B or C and win, so I can trust the answer. And if A leads to freedom, I can also trust the answer.

I win😁

Have you had intimate relations with your grandmother?

Is schrödingers cat alive?

If he say nothing youre good to go. If he say's yes ore no you know it is the door to imprisonment.

The pointing to a door and asking about other is bs… Like, then beat the sh** out of the warden and open the three doors could be a valid answer too…

I ask if god is real and then walk through that door. If it's true then I've answered one of lifes greatest mysteries.

(Pointing door A)

You: Does door B lead to freedom?

Warden: (laugh)

The range of possible questions must be limited, because if we find out whether the jailer is telling the truth or lying, then the solution is trivial. It cannot be a question that reveals this.

The answer is to vote Trump and He will hand out freedom. I win

The good old "will you [the warden] answer to this question with 'no'?" ought to work as well. If the warden says yes, take door B. If the warden says no, take door C. If he doesn't answer, take door A.

It's in this case superior over the objective form. Funny thing is, if he stands in front of a good door, he cannot answer, but he can trivially answer if he stands in front of the bad door. Everybody else however would be incapable of answering it if he stands in front of the bad door (it's random, how would they know?) but would find it trivial if he stands before a good door (obviously no: he won't answer it at all)

a simular one:

2 doors…..1 is freedom and 1 is jail

2 guards…..1 lies and 1 truthful

1 question leads to 100% freedom.

Answer: “What would the other guard say if i ask him if THIS door is the door to freedom?“

Any 'yes' answer is jail and any 'no' answer is freedom

you violate your assumption. In the situation where Door A is not the escape, the warden answers randomly per the rules. He doesn't have to answer truthfully that B is the escape. Your rules are "if you point to the door that leads…' So his decision to be truthful isn't based on if B is true or not.

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