Mad Hatter question

[bonanova]

With a nod to itsmee's 999 puzzle.

You fall down Alice's rabbit hole and are faced with three doors, each labeled This Way Out.

But you've been around this block before. You know only one door will get you home,

And you don't even want to imagine what's behind the other two.

Mad Hatter volunteers to help.

edit He will answer one yes/no question truthfully, if he can.

If he cannot, he will disappear without uttering a word.

Let's say the doors are A B C and you've got tickets for the Grateful Dead.

What's the question that will get you to the show?

Edited March 27, 2013 by bonanova
Clarify yes/no question

[witzar]

I would assign values -1, 0, 1 to the doors, then I would agree with Mad Hatter to call value assigned to the correct door by X, and finally I would ask him, "Is 1/X > 0?"

[BobbyGo]

Would it not be easiest just to ask, "Which door is the correct door to lead me home?"

Unless he can only respond with 'Yes' or 'No', but I didn't see that stipulation.

[bonanova]

Would it not be easiest just to ask, "Which door is the correct door to lead me home?"

Unless he can only respond with 'Yes' or 'No', but I didn't see that stipulation.

Good point.

It must be a yes/no question.

Thanks.

[Yoruichi-san]

I'd ask, like, "If there is at least one door to the left of the correct door, is there more than one door to the left of the correct door?"

Or any question that is posed: IF [something that is not true for one of the doors] is true, THEN is [something that is true for only one of the remaining doors] true?

[ThunderCloud]

I would re-label the doors 1, 2, and 3, and then ask, "What answer can you give that has as many letters as the number on the correct door?". If the Hatter says "Yes" I choose door 3 / C; if he says "No" I choose door 2 / B, if he vanishes I choose door 1 / A.

[bonanova]

I would re-label the doors 1, 2, and 3, and then ask, "What answer can you give that has as many letters as the number on the correct door?". If the Hatter says "Yes" I choose door 3 / C; if he says "No" I choose door 2 / B, if he vanishes I choose door 1 / A.

That will work.

I will leave the puzzle open for other approaches if there are any.

[BMAD]

I would stand halfway between the middle door and the right door frame and ask if the correct door is to the left of me. if it is, he will say yes and then i know which door to enter. If it is the right door, he would say no, and i know which door. If it is the door in the middle he would disappear as the door is neither to the left or right of me in which case i know which door it is.

Edited March 28, 2013 by BMAD

[bonanova]

I would stand halfway between the middle door and the right door frame and ask if the correct door is to the left of me. if it is, he will say yes and then i know which door to enter. If it is the right door, he would say no, and i know which door. If it is the door in the middle he would disappear as the door is neither to the left or right of me in which case i know which door it is.

How will you choose between the center and left doors?

By standing halfway between the middle and right doors, both the left and middle doors are on your left.

[bonanova]

[spoiler='The answer I was looking for]

[spoiler='If you are through looking for it']Would you agree that either the way home is the right door, or its the left door and you will answer no?

If the right door leads home Hatter will say yes; if it's the middle door he'll say no, and he will disappear if it's the left door.

[bonanova]

I would assign values -1, 0, 1 to the doors, then I would agree with Mad Hatter to call value assigned to the correct door by X, and finally I would ask him, "Is 1/X > 0?"

A new approach. Works for me.

[Yoruichi-san]

*Clears throat*

The responses to my approach:

YES->rightmost door

NO->middle door

*poof*->leftmost door

It's similar to bon-chan's approach of setting up a logical question that cannot be answered by a simple yes/no for one of the doors.

[bonanova]

*Clears throat*

The responses to my approach:

YES->rightmost door

NO->middle door

*poof*->leftmost door

It's similar to bon-chan's approach of setting up a logical question that cannot be answered by a simple yes/no for one of the doors.

I'm not sure he poofs for the left door.

In your logic does F -> anything?

I was not sure that he could not say Yes or No, with equal validity if it were the leftmost door.

That is, A -> B can be taken to be ^A v B: F implies anything, and anything implies T.

So for the leftmost door and A = "there is at least one door to the left of the correct door"

your question is If A then are there 2 doors left of the correct door.

A being false, can't the answer be Yes or No instead of "I can't answer because the premise is false"?

The only approach is to force a Yes/No/Can't answer response, agreed.

Explanation for F -> T to be legit:

If 2+2=5 then New York is a small city.

In every case where 2+2=5 New York is a small city.

But there are no cases where 2+2=5.

Thus: In no case is New York a small City.

The only prohibited conditional is T -> F. the other three are OK. No?

[Yoruichi-san]

Okay, he might not poof, but he can't answer either, and a non-answer is an answer ;P. My logical setup was not F->T, it was F->no longer a simple yes/no question. Your example is a case where the premise is always false, in which case the statement itself has no inherent meaning and therefore you can manipulate it as you will. The question I used I posed is either true or false, in the case it is true, it is a yes/no question, but if the first part is false, then it is not a yes/no question.

I.e. if I asked you:

If you are going on vacation this month, are you going leaving for more than a week?

If the first part is true, then it is a simple yes/no question. If it is not, you would answer with, like, "I'm not going on vacation this month" or sth. If you answered yes or no, it would indicate you are going on vacation this month.

[bonanova]

Okay, he might not poof, but he can't answer either, and a non-answer is an answer ;P. My logical setup was not F->T, it was F->no longer a simple yes/no question. Your example is a case where the premise is always false, in which case the statement itself has no inherent meaning and therefore you can manipulate it as you will. The question I used I posed is either true or false, in the case it is true, it is a yes/no question, but if the first part is false, then it is not a yes/no question.

I.e. if I asked you:

If you are going on vacation this month, are you going leaving for more than a week?

If the first part is true, then it is a simple yes/no question. If it is not, you would answer with, like, "I'm not going on vacation this month" or sth. If you answered yes or no, it would indicate you are going on vacation this month.

But if he could answer anything, he could answer yes; and you might not get home.