An old challenge

[Zaevod]

This is a challenge I posted in some places before. There are infinite solutions, but they aren't really trivial.

You are in a locked chamber with 3 identical doors. You have a single key, which is disintegrated immediately after you unlock any of the three doors. The doors are indestructible, and it's impossible to figure out what's behind them without opening them first or asking a magical computer.

One door leads to an awesome place, while the other 2 lead to an incredibly boring place.

In this chamber, there is also a magical computer which possesses all the information that can be obtained about existence. It has a few peculiarities:

1- When you input an answerable statement, it only answers with either "true" or "false";

2- It only has enough energy left for one answer;

3- It has a bug that causes the answers to be inverted (true becomes false, and vice-versa) 50% of the time. It can also predict exactly when this bug will occur, but can't avoid it. The bug inverts only the final answers, without affecting the values used to calculate the answers.

4 (EDIT)- The computer cannot receive orders to give answers in specific situations (the input has to be a statement, not an order or a question). Statements MUST include actual things (concepts, objects) with verifiable values, but these things cannot be hypothetical things with values directly attributed by the person, they must depend on the thing itself.

5- You can attribute labels and concepts to each door and use these labels in your final statement, but you must specify which label refers to which door (e.g. 'labeling the left, center and right doors with x,y and z, respectively, statement about x, y and z and the doors they represent.');

6- The computer is very smart and can understand any statement exactly as you intend it to (but you need to have an actually meaningful statement that you can understand). This just means that words will be interpreted in the correct context and language;

7- The computer cannot be hacked through any means.

How can you figure out the door that takes you to the good place, with 100% certainty?

I have a possible solution I'll post if nobody finds an answer.

Edit: someone already found a solution here: http://www.flashflashrevolution.com/...1&postcount=55

[TheSaxRunner05]

Make it like "the cube" movie where 1 room is safe and the other two kill you painfully.

[Zaevod]

Could be that, too. The point is that you need to discover which door is the good one, either way.

[Doug31]

Can you ask it if it would say about something? Since then it knows if it will invert it or not, so you know it's inverted twice or not at all, so you can know for sure it's telling the truth?

[Dynam0]

Not sure what the bug has to do with anything since the computer is capable of answering only once and the answer, so far as I can guess, doesn't tell you if the bug has occurred or not.


1) "Door 'x' leads to the awesome place." You have a 1 in 3 chance to have the computer answer 'true'. If the computer says 'false' you'd be left with a 50:50 chance of guessing the right door. Obviously not a good choice.

2) "Doors 'x' and 'y' lead to the same place." Same thing here, the computer would have to say 'true' implying that door 'z' leads to the awesome place in order for you to be 100% certain. If it says 'false' (which there are two out of three instances in which this statement can be false) you're left with a 50:50 chance to guess 'x' or 'y'. Still no good and just as bad as option 1.


This bug thing really gets me confused though..not sure how it helps the situation.

There's probably a dumb philosophical loop-hole in this whole thing lol

[Doug31]

My way defeats the possibility of its 50% error if it's allowed. But as Dynam0 suggested, it seems there isn't really a way to get past the other part. If true is 1 and false is 0, it's taking all the information you give it through a black box to a functional that outputs only 1 of 2 things, and there are 3 possibilities so that if you only get 1 of 2 things there's no way to distinguish between at least 2 of them. So there must be some way to "cheat" the system.

I have some ideas of how to "cheat", but I doubt any of them are allowed. For instance, turning the computer off after the first letter of its output, and saying it has only used 0.2 to 0.25 answers, so it still has enough energy to do another 0.75 to 0.8, and then ask it another question and deduce the answer based on the first letter of it.

Edit: I think I might have solved it:
Label the doors x, y, and z, from left to right.
Give x the value 0, y 1, and z 2.
I have a computer that overflows and explodes if the value its given is at least 3.
Now have my computer add 1 to the value of the door that leads to the good place.
Now ask, would this computer say that my computer would say the value for y is 2?

If yes, then y leads the good way. If no, then x leads the good way. If no response, z leads the good way.

[Zaevod]

Originally Posted by Doug31

Can you ask it if it would say about something? Since then it knows if it will invert it or not, so you know it's inverted twice or not at all, so you can know for sure it's telling the truth?

Yes (I'm glad people here didn't take an eternity to figure this out like others, lol).

Originally Posted by Dynam0

Not sure what the bug has to do with anything since the computer is capable of answering only once and the answer, so far as I can guess, doesn't tell you if the bug has occurred or not.

...
There's probably a dumb philosophical loop-hole in this whole thing lol

You can work around the bug with logic.

Originally Posted by Doug31

My way defeats the possibility of its 50% error if it's allowed. But as Dynam0 suggested, it seems there isn't really a way to get past the other part. If true is 1 and false is 0, it's taking all the information you give it through a black box to a functional that outputs only 1 of 2 things, and there are 3 possibilities so that if you only get 1 of 2 things there's no way to distinguish between at least 2 of them. So there must be some way to "cheat" the system.

I have some ideas of how to "cheat", but I doubt any of them are allowed. For instance, turning the computer off after the first letter of its output, and saying it has only used 0.2 to 0.25 answers, so it still has enough energy to do another 0.75 to 0.8, and then ask it another question and deduce the answer based on the first letter of it.

Edit: I think I might have solved it:
Label the doors x, y, and z, from left to right.
Give x the value 0, y 1, and z 2.
I have a computer that overflows and explodes if the value its given is at least 3.
Now have my computer add 1 to the value of the door that leads to the good place.
Now ask, would this computer say that my computer would say the value for y is 2?

If yes, then y leads the good way. If no, then x leads the good way. If no response, z leads the good way.

You can't make the computer overflow like that. It's far simpler than that, really (in some aspects. The statement will ultimately be a little complicated, anyway). Read the first post carefully.

[Spenner]

That's an interesting idea that it will remain answerless as a 3rd option, but what if it HAS to output something?

What about a question like, "Output True if and only if the awesome door is the one I am touching with my hand, and not until I have placed it on the correct one" or is that out of the means of the machine?

[Doug31]

Thing is, the computer isn't overflowing. The computer I have made up is, which means that it just sees it as not even a statement and thus doesn't respond. So no computer actually blows up.

[Zaevod]

1- When you input an answerable statement, it only answers with either "true" or "false";

Which implies...

(I'm giving too many hints) XP

But the bug messes up that, too, and you must find a way to circumvent both problems simultaneously.

[Spenner]

Can you put in an unanswerable statement though?

Or how about a more detailed question like this:

"The door on the left is A, then B, then C. Only answers with A and B are a theorum of this system, and therefore they are the only answerable results of this formal system. Is door A the desired awesome door? If yes, then A = true"

I mighta worded that bad I'm horrible with mathspeak : < but anyhow, there's no need to include the notion of the third door. It doesn't answer if it's not an answerable part of the question, therefore it's implied to be C

[Zaevod]

Originally Posted by Spenner

That's an interesting idea that it will remain answerless as a 3rd option, but what if it HAS to output something?

What about a question like, "Output True if and only if the awesome door is the one I am touching with my hand, and not until I have placed it on the correct one" or is that out of the means of the machine?

The computer cannot attribute "true" or "false" to things that are neither, and those are the two possible output messages. So...

And your statement doesn't work because it isn't a statement, it's an order (read rule number 4)

In short, you need to find actual, non-hypothetical things to use in your statement.

Originally Posted by Spenner

"The door on the left is A, then B, then C. Only answers with A and B are a theorum of this system, and therefore they are the only answerable results of this formal system. Is door A the desired awesome door? If yes, then A = true"

Doesn't work, sorry.

[Spenner]

But it can just not output anything to imply that it is C, couldn't it?

I guess I could word it more like this then also: "The door I am touching is true after I touch the awesome one" or is that not applicable?

[Zaevod]

Originally Posted by Spenner

But it can just not output anything to imply that it is C, couldn't it?

I guess I could word it more like this then also: "The door I am touching is true after I touch the awesome one" or is that not applicable?

Your statement needs to be something of the type "X exists", "X or Y are Z", etc., which means it must be a phrase that can be answered with true or false.

If I say "My username is Zaevod" the computer will answer true.

You can't say "say true if I do X", because that's an order, not a statement.

"The door I am touching is true after I touch the awesome one" actually will always answer as true if you mean "true" as in "a true door", because they are true doors, before or after you touched the awesome door.

I'm going to sleep now, but I'll put more hints tomorrow if necessary.

[Doug31]

Let the statement be ??

Where ?? means you implied, which it perfectly understands, This computer says the good door is the first door gives a response of true, this computer says the good door is the second door gives a response of false, and not a statement otherwise. The implication is a solution to this problem which exists so even though you don't necessarily know what it is, since the computer can perfectly tell what you mean, it gives you the solution anyway. And since I used the either not inverted or doubly inverted "this computer says" clause, it must tell the truth.

[Zaevod]

Originally Posted by Doug31

Let the statement be ??

Where ?? means you implied, which it perfectly understands, This computer says the good door is the first door gives a response of true, this computer says the good door is the second door gives a response of false, and not a statement otherwise. The implication is a solution to this problem which exists so even though you don't necessarily know what it is, since the computer can perfectly tell what you mean, it gives you the solution anyway. And since I used the either not inverted or doubly inverted "this computer says" clause, it must tell the truth.

The computer can't tell what you mean if you don't know what you mean XD (how can you mean something without knowing it???)

But that was actually pretty cool.

There must be an actual statement. It's just that the computer will always interpret whatever words you used correctly, in the context you meant him to understand them.

You've got the main issues figured out, now just make a statement that includes everything XD

[Dynam0]

You're giving an order to the computer again Doug...you can't do that.

Let "True" mean yes.
Let "False" mean that the bug has occurred so the answer is actually true, and thus yes.

The awesome door is the one in the middle.

Answer: It doesn't matter since the computer will agree with this statement either way. Any door will be the awesome door then!!!!

I'm going to bed xD

[Doug31]

Then use the computer says door 1 is the good door, and if not, then I didn't mean this as a statement. Either you get a yes or a no response, and then repeat for each door.

[One Winged Angel]

I'm heavily leaning towards 'or' being a necessary conjunction in my statement but I'm having trouble coming up with the exact statement I need.

Quick question, if I ask something along the lines of 'You will answer 'true' in response to this question and A leads to the awesome place or you will answer 'no' in response to this question and B leads to the awesome place', is it possible to receive no response from the computer? (I know this isn't the correct statement, just as an example)

I have a feeling I'm somewhere in the right ball park but I'm tired right now and can't figure out how to isolate the door without a third response from compy (no response works)

[xThai]

ill attempt this tomorrow morning since im tired. i gotta look over my logic textbook. i have something in mind but i forgot some of the predicate logic i learned.