You are in a prison. There are 3 doors, and a ghost standing in the middle of the prison. He says one of the doors is the way to freedom while the other two lead to death. You get to ask only one question. He will only answer with YES or NO. All he says is truth. What do you ask to find the door to freedom?
The puzzle lays a restriction on the ghost's answers, but not on your question (i.e., your question doesn't have to be a yes/no question). I think it's a bit of misdirection.
Give the doors names: "Door 1 I name 'Yes', Door 2 I name 'No', and Door 3 I give no name. Behind the door of which name lies freedom?"
The ghost can answer "Yes," "No," or nothing, and by his answer he designates the name you gave that door.
This is very similar to GOTO 0's answer, but this doesn't involve asking two questions for the price of one.
I will try to be in the spirit of the riddle: Ask only one question and get a real YES/NO aka true/false response:
If I take the first door and my brother takes one of the first two doors, will at least one of us get to freedom ?
- If the first door leads to freedom, the answer is yes.
- If the third door leads to freedom, the answer is no.
- If the second door leads to freedom, the answer would be maybe/don't know, so the ghost cannot answer with yes/no.
Keeping in mind that the ghost will only answer if the answer is yes or no, a way to find the door to freedom is to formulate a question such that the answer would be yes, no, or anything else respectively for each of the three doors. In the latter case, the ghost will not answer at all.
There are several possibilities, one of them is this one.
If the door to freedom is not the third one, then is it the first one? Otherwise, what was the name of Napoleon Bonaparte?
- If the door to freedom is the first one, the ghost will answer yes.
- If the door to freedom is the second one, the ghost will answer no.
- If the door to freedom is the third one, the ghost will not answer.
My first thought: It is a trick question. Pay attention to your environment. If there are only 3 doors, one of them must be the one through which you entered. And since you are in prison, you know that this door does not lead to freedom, you can just ask the ghost "Is this the door leading to freedom?" while pointing on one of the other two doors in the room. If he says "Yes" you pick that door, if he says "No" you pick the other one. It is kind of an prove through exclusion attempt.
If it is not a trick question, and you actually entered the room which has 3 doors on top of the one through which you entered, the best you can do is try to act based on the Mounty-Hall-Problem. You might only be able to increase your chances to a chance of 5/6 chance, but not to a 100%.
You cannot get 3 informations out of 1 bit. You can combine 2 infos into 1 bit, but not 3. (Bit operations all have only 2 input and 1 output channels).
You could ask the ghost for example "If I picked the left door and somebody would show me one of the remaining doors leading to death, could he show me the middle door?" If the answer would be "Yes", you could switch to the right door, as it would have a 2/3 chance to be the freedom door. (See Mounty-Hall-Problem) If the answer would be "No", you definitly know the mid door is the freedom door. A 100% chance and a 2/3 chance combine to (6/6+4/6)/2, which is 5/6.
my question would be:
Among the propositions 1. "You are a liar", 2. "You will reply negatively" and 3. "This door leads to freedom", is there an odd number of true propositions?
I stole this answer (without shame) from: https://puzzling.stackexchange.com/a/2310/9835 It is for an other version of your question where there are 2 guards (one truth full and one lying). But can perfectly be used here
There are 2 possibilities here:
The number of truths is odd, 1. is false, 2. is false, so 3. must be true.
The number of truths is even, 1. is false, 2. is true, so 3. must be true.
Either way you created a paradox if the door you are pointing to is not the one to freedom, so what ever happens the door you are pointing to leads to freedom :)
All credits to Florian F.
Although the Ghost only has a two word vocabulary (Yes or No are its possible responses), I would ask a question that makes full use of its vocabulary;
If you were to walk past each of these doors from left to right, and say 'yes' when you passed a 'door of life' and 'no' when you encountered a door leading to death, what would you say?
In this manner I've extracted all the information I need with one question.
I will ask him,"response me "Yes" if the 1st door has the way to freedom, or response me "No" if the 2nd door has the way to freedom."
If He response, "Yes"
I'll go through 1st door.
If He response, "No"
I'll go through 2nd door.
If He didn't response,
I'll go through 3rd door.
I have a question inspired from another puzzle that i found here that could work.
Is it simultaneously true that the second door is bad and either the third door is bad or your answer to this question is "no"?
For the sake of simplicity I labeled the door that leads to freedom as good and the other ones as bad.
I am gonna divide my question in 3 sentences
A = The second door is bad
B = The third door is bad
C = The answer is "no"
So the question can be wrote like this:
A AND (B OR C)
Assuming the 3 cases:
1. First door is the good one => A=True, B=True
true AND (true OR whatever) = true
2. The second door is the good one => A=False
false AND (whatever) = false
3. The third door is the good one => A=True, B=False, C=?
true AND (false and C) = R (R=answer)
If R = true, then it is required that C is also true, but a C that is true implies that R is false (contradiction)
If R = false, then C is also false, but that means that R is true (again contradiction)
So, if the ghost answers with yes we take the first door, if the answer is no we take the second door, and if there is no answer we take the third.
This is a big supposition, but just maybe it happens that the ghost has a quirk where it doesn't wait for you to finish asking the question if it has heard enough of it to be 100% confident of the answer.
In this case, I'd ask, very slowly: "Is the door to freedom one of these two doors: this red door right here, or..." and after a long pause, pace slowly between the other doors, indecisively, finally finishing the question "...this blue door?"
If the ghost is an impatient sort of ghost, or an optimized-algorithm ghost, and the red door is the one to freedom, it will answer "yes" right away.
Otherwise, you'll get a "yes" or "no" only after naming the second door, and there's your answer.
I would chose any two doors(X,Y) and ask the following question:
If X,Y does not lead to the same place, does X lead to freedom ?
If he Says "YES"
If he says "NO"
If he keeps quite, it means that my first condition was false. Thus,
Chose Z (the left out door)
Figured i'd add my answer here, since it's slightly different from the other approaches, and you can never have enough answers to strange ghosts in impossible situations
If you'd completely and utterly forget about the middle door, and you'd draw a cross on the right door, would THE door leading to death have a cross on it?
This works because
If the middle door (was) the life one, the ghost would have 2 doors leading to death, with no way to determine which one i meant by 'THE door'. However, if door 2 was death, then he now only knows of a single door that leads to death, and can answer without a problem. Resulting in Yes to right, No to left, Silence to middle.
Note that you can't ask
Would the door leading to life have a cross on it? Because as many a logic professor will tell you, quantifying over an empty set is always true.