The HARDEST Logic Puzzle Ever (Simpler Version): Two Doors To Freedom Riddle
Video Overview & Insights
An evil warden holds you prisoner, but offers you a chance to escape. There are 3 doors A, B, and C. Two of the doors lead to freedom and the third door leads to lifetime imprisonment, but you do not 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?
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
My blog post for this video: https://wp.me/p6aMk-55e
Source
I read it as 1 door leads to freedom instead of 2 and I was so confused
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
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This is easy and not the hardest riddle. I'm answering before seeing the solution. Point to the middle door and ask "Does the door on the right lead to freedom?" If yes, then go in the right door. If no, then go in the left door.
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All the inmates at a maximum security prison are now asking the same question the warden. 😮
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The question is confusing because it implies that if you point to a door, you would ask a question about that door.
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The simplified version of the HARDEST logic puzzle ever deserves the simplified version of the HARDEST answer ever:
Point to door A. Ask: "If I were pointing at door B, would your answer to 'does door C lead to freedom?' be random?"
Suppose the answer is "yes":
If door A is the door of doom, then we got "yes" by random chance, but doors B and C are safe.
If door B is the door of doom, then we got "yes" because we are told the truth about door B, so door C is safe.
If door C is the door of doom, then we cannot get "yes" as the answer will necessarily be "no".
Conclusion: If "yes", then door C is safe.
Suppose the answer is "no":
If door A is the door of doom, then we got "no" by random chance, but doors B and C are safe.
If door B is the door of doom, then we cannot get "no" as the answer will necessarily be "yes".
If door C is the door of doom, then we got "no" because we are told the truth about door B, so door B is safe.
Conclusion: If "no", then door B is safe.
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There is no description what you are pointing , so warden can ignore that
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Great Puzzle..although if we point to A, an imprisonment door (another both doors, B&C are freedom doors) we still follow the same pocedure: if warden say "yes" we will chose the door wich we have questioned, the answer "no" we will chose the third doore..just because we never know which door we point to..in the beginning process
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Great puzzle
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"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.8/5 stars on 31 reviews)
ffs. I thought it was 1 door that leads to freedom and 2 doors that keep you trapped. no wonder I got stuck 😠
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"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.6/5 stars on 3 reviews)
My solution:
Point to a door and ask him a paradoxical question like, "will you answer this question with a No?"
In case of the imprisonment door, I will get an answer randomly since it doesn't depend on the question, but in case of the freedom doors the warden needs to answer the door truthfully which cannot happen for this question so he will remain quite
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"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews.
I point to qny door and ask "Is your answer to my question 'no'?" There's no way to answer truthfully so he won't answer if it's one of the right doors but if it's te bad door he will give an answer cuz he doesnt care about correctness. That's what I'd do
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"Math Puzzles Volume 2" is a sequel book with more great problems. (rated 4.3/5 stars on 4 reviews)
Point to any door and ask "will you answer this question with a "no"?"
If the warden answers I go through a different door.
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"Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 5 reviews)
Easy solution. Your question is, "May I look behind that door?"
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"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews)
Solution I came up with was point at a door and ask "will you let me escape if I go through this door?" If it's one of the freedom doors, the answer will be yes. If it's the life imprisonment door, and the warden says no, then you know to pick one of the other doors. If it's the life imprisonment door and the warden says yes, then they've now promised to let you escape, so even though that door led to life imprisonment BEFORE, they're gonna have to let you escape anyway.
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"The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews)
Ask a 'yes/no' question that cannot be answered truthfully (for example, because it is paradoxical). If the warden gives a clear yes or no answer then do not go through that door.
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"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews)
Basically, you are eliminating the door you point to, so if you get a lie answer, it doesn't matter which other door you choose, since both are safe. And if you're pointing to a safe door, you can trust the answer to tell you which of the other two are also safe.
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More User Perspectives
Id ask if his mother was a whore
@JUSTINBODHII did not realize that the warden only answered yes or no tothe questions so i just answered "ask what 2+2 is because the warden will be found out regardless ifthey said yes or no"
@lavenderly_I did not realize that the warden only answered yes or no tothe questions so i just answered "ask what 2+2 is because the warden will be found out regardless ifthey said yes or no"
@lavenderly_What color is the door? If he lies, then you will know what door it is, if he tells the truth, wellll, your screwed.
@The0negam3rboiA similar but different version is this.
Two doors, one leads to death, the other to freedom.
Two wardens, one in front of each door. One warden always speaks the truth, the other one always lie.
Ask one question, to one warden, that make you 100% choose the door to freedom.
Answer: Ask any of the warden, "If I ask the other warden, what door he stands in front of, what will he answer?"
Then always choose the answer that is the "death" door, this will get you to always get you the freedom door.
that sounded really hard until i notice theres 2 freedom doors and not 1
@icaro8264So basically: if the warden is telling the truth, Door B is a door, to freedom and if he is being random then Door A is not a door to freedom. Cool.
@undercoveragent9889Solved in 5 minutes
@michaellautermilch9185My answer was "Will you let me leave if I go through this door?" If no, go through another door. If yes, then no matter what the state of the door is, the warden just said you could leave through that door.
@tottgwnIf door A leads to freedom, the random answer can be the door B lead to freedom but can be imprisoning door, and your logic is fail.
@fanimazakura7662After solving the ozo riddle from Ted this one is a cakewalk
@demonslimeThe diagram could reflect the fact that in the "Freedom Warden truthful" scenario Door A leads to freedom, in both the Yes and No cases.
@taotoo2Translation table (each symbol represents the statement):
p: Door A leads to freedom
q: Door B leads to freedom
r: Door C leads to freedom
Truth Table:
p | q | r |
T | T | F
T | F | T
F | T | T
Notice there are missing truth values there should be 8 permutations (2^3). These have been omitted as only one of p, q, r can be false (remember the axioms of the question stating two doors lead to freedom and one leads to imprisonment).Here are the omitted permutations.
T | F | F
F | T | F
F | F | T
F | F | F
T | T | T
Remember that the warden knows which each door leads to.
Remember if p is true and you point to p and ask the question to the warden "Does Door B lead to freedom" then the warden will reveal the truth; which is that q is true if r is false. Thus pick Door B if false pick Door C.
Now if p is false and you point to p and ask the question to the warden "Does Door B lead to freedom" the warden gives a random answer either true or false. Thus how can we ensure we open the correct door in this case? Well remember if p is false then q and r are true. Thus both Door B and Door C
lead to freedom.
So opening Door B when the warden answers 'yes' or opening Door C when the warden answers 'no' ensures that you open a door leading to freedom in both cases of when p is true and when p is false.
Easy solution: Ask warden if I'm going to punch the first door, if he says yes, don't punch it, if he says no, do punch it. That automatically makes it the door leading to imprisonment (As it is the only one that can lie) and therefore, the other 2 lead to freedom.
Of course this is assuming the doors all exhibit macro-quantum-like behaviors, and the the warden is the "observer"
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.
@richarddow8967a 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
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)
The answer is to vote Trump and He will hand out freedom. I win
@ThemhealsThe 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.
@Kounomura(Pointing door A)
You: Does door B lead to freedom?
Warden: (laugh)
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.
@RealElevenTimesThe 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...
@LucaBerg22Is 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.
Have you had intimate relations with your grandmother?
@MrSoggyjocksMy 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😁
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.
@johnhudson1965I don't understand this. If the warden is evil, why would he give you a 66 2/3 % chance of escaping.
@grizzkid795Why am I still doing time? I know the answer.
@TroyGainer01So, when do I get my free goat?
@M0r9h3usI’m proud my myself that I figured out a solution in about 2 minutes.
@Ravie3Ask 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 :)
@klavesinThe 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.