An old challenge

[PaperclipGames]

Originally Posted by Dynam0

Only one "answerable" statement, yes.

I can make as many unanswerable statements as I want; read the rules again.

Ahhh! I see! Yeah, but it depends on whether you can define False to mean True.

[Zaevod]

EDIT: I kinda forgot to post this earlier. I guess it's because it was very similar to the idea behind PaperclipGames' solution, but the shortest solution I know is something like "((Left door is awesome)OR((Right door is awesome)AND(Statement X is false)))XOR(You are bugged)", where X = 'Statement X is false'.

I was looking for a solution I posted in another forum, because it already had a lengthy explanation, but couldn't find it. Well, anyway:

My original approach was to solve the problem without taking the bug into account first, and then adding things to the resulting statement to deal with the bug. The solution I originally came up with to deal with the bug wasn't quite as elegant as "XOR you are bugged", though, but it still works.

Unbugged solution:

The purpose of the statement in this case is to simply force a true answer for one door, a false for another and no answer for the remaining door. There are endless different labels that can be used for this, for example:

Left door: A zebra.

Center door: A dog.

Right door: A mammal.

Why a mammal? In this case, I decided to create an unanswerable statement through vagueness instead of a paradox.

The statement "considering that the left, center and right doors are respectively labeled with a zebra, a dog and a mammal, the animal which represents the door that leads to the awesome place is a zebra" works.

If the left door is awesome: True, naturally.

If the center door is awesome: False, because dogs aren't zebras.

If the right door is awesome: There is no answer, because a mammal can definitely be a zebra, but it can also be a dog, a cow, etc. "Mammal" is a valid, existing concept which can be used as a label, but there are many specific types of mammals and the computer can't determine the specific species in this case. It also isn't stating that "all mammals are zebras", because that would be false. It is referring to a single but unspecified mammal. Therefore, no answer.

Bugged solution:

Simply "XOR you are bugged" would work, but what I did instead was something in the lines of "If I said X in the exact condition you are in relation to whether the bug is happening, you would say true".

So, let's analyze:

"Considering that the left, center and right doors are respectively labeled with a zebra, a dog and a mammal, if I said 'the animal which represents the door that leads to the awesome place is a zebra' in the exact condition you are in relation to whether the bug is happening, you would say true"

6 possible outcomes:

1 - Bug isn't happening, left door is the good one: the original statement for the unbugged solution is true. The computer knows it's not bugged, so it knows it would say true. Therefore, the answer is true.

2 - Bug isn't happening, center door is the good one: the original statement for the unbugged solution is false. The computer knows it's not bugged, so it knows it would say false. Therefore, the answer is false.

3 - Bug isn't happening, right door is the good one: the original statement for the unbugged solution has no answer. The computer knows it's not bugged, but it knows it wouldn't give an answer. Therefore, the final answer is false (because the statement "you would say true" is false). (yes, this is a problem which will be dealt with)

4 - Bug is happening, left door is the good one: the original statement for the unbugged solution is true. The computer knows it's bugged, so it knows it would say false instead. Therefore, the answer is false (it wouldn't say "true") which the bug then inverts to true.

5 - Bug is happening, center door is the good one: the original statement for the unbugged solution is false. The computer knows it's bugged, so it knows it would say true instead. Therefore, the answer is true which the bug then inverts to false.

6 - Bug is happening, right door is the good one: the original statement for the unbugged solution has no answer. The computer knows it's bugged, but it knows it wouldn't give an answer as there is nothing to invert. Therefore, the answer is false which the bug then inverts to true.

We have a pretty messed up situation: With the current statement it would say (true, false, false) if unbugged and (true, false, true) if bugged. That means that the statement only works for the left and center doors. This can be corrected, however, if we append something like this to the current statement:

"OR the animal which represents the door that leads to the awesome place is a cow"

The final statement would be:

"Considering that the left, center and right doors are respectively labeled with a zebra, a dog and a mammal, if I said 'the animal which represents the door that leads to the awesome place is a zebra' in the exact condition you are in relation to whether the bug is happening, you would say true OR the animal which represents the door that leads to the awesome place is a cow"

This new isolated addition would have the following outcomes:

1- No bug, left: false.
2- No bug, center: false.
3- No bug, right: undefined.
4- Bug, left: true (originally false).
5- Bug, center: true (originally false).
6- Bug, right: undefined.

How can this help?

Before giving the final answer, the computer considers only the non-inverted values for the answers when calculating the final answer, regardless of whether the bug is happening or not. In this case, this would be the outcome:

1- No bug, left: (true OR false) = true
2- No bug, center: (false OR false) = false
3- No bug, right: (false OR undefined) = undefined
4- Bug, left: (false OR false) = false (inverted to true)
5- Bug, center: (true OR false) = true (inverted to false)
6- Bug, right: (false OR undefined) = undefined

Which proves that this final statement works.

Of course, the "XOR you are bugged" solution for the bug is much better, but at least the solution for the unbugged problem was pretty simple in the end.

[Doug31]

Wow, so the solution is just a reworded version of what some people were trying to say earlier. Also I thought you said it was short and we were thinking too hard with our answers that were A LOT shorter than this?

[Zaevod]

Originally Posted by Doug31

Wow, so the solution is just a reworded version of what some people were trying to say earlier. Also I thought you said it was short and we were thinking too hard with our answers that were A LOT shorter than this?

It's not "the" solution, just a possible solution. Paperclip also solved it (the others had the idea to solve it, but didn't come up with a definitive statement), that's why I posted (check his answer, it's better anyway). Your answers were short, but they didn't fully work. I didn't really say it was short, did I? I said it wasn't trivial.

[Nullifidian]

Going by what dynam0 said that you can make as much unanswerable statements as you want given that it can only answer once it receives an answerable statement, can't you just combine three statements into one, two about the doors and one about the bug, and get an answer from that? If it fails to answer it means at least one of the three things in your statement is conflicting with the others and you can then revise your statement.

You are currently not experiencing a bug and door one and two are not correct.
You are currently not experiencing a bug and door two and three are not correct.
You are currently not experiencing a bug and door one and three are not correct.
Repeat each statement twice and when it does answer, you'll know what door to take.

Correct me if I'm wrong or if this was already said in some way because I haven't read/made sense of any of the other posts yet lol.

edit: or even easier:
Door one and two are not correct, door three is correct.
Door one and three are not correct, door two is correct.
Door two and three are not correct, door one is correct.
This way you bypass the entire bug alltogether because it'll only answer when the statement is true, regardless of the true or false response of the computer.

[Zaevod]

Originally Posted by _.Spitfire._

edit: or even easier:
Door one and two are not correct, door three is correct.
Door one and three are not correct, door two is correct.
Door two and three are not correct, door one is correct.
This way you bypass the entire bug alltogether because it'll only answer when the statement is true, regardless of the true or false response of the computer.

The statements themselves are redundant ("door three is correct" means the same as "door one and two are not correct"), but, anyway, let's see...

I didn't originally consider the possibility of many unanswerable statements input separately, but let's consider this anyway: What's unanswerable about these statements? They seem to be either true or false 100% of the time, so I'm not sure what you're getting into :/

[One Winged Angel]

edit: nvm, it made sense until I typed it out lol

[Zaevod]

Btw, the first problem with Dynam0's solution is that it instructs the computer to assign different meanings for "true" and "false" than what is originally intended by default, which also contradicts rule 4.

[Reincarnate]

[Zaevod]

For those who missed it: PaperclipGames already solved it in the previous page.

[Dynam0]

Originally Posted by Zaevod

Btw, the first problem with Dynam0's solution is that it instructs the computer to assign different meanings for "true" and "false" than what is originally intended by default, which also contradicts rule 4.

Well if you can call a door a mammal why the heck can't I redefine what true and false imply? lol jk

I see what you mean though since I would have to hack the computer in order to redefine what the output values would entail. It was fun to try and attempt it with no in-depth experience in logical pathways/truth statements though.

[Zaevod]

Originally Posted by Dynam0

Well if you can call a door a mammal why the heck can't I redefine what true and false imply? lol jk

I see what you mean though since I would have to hack the computer in order to redefine what the output values would entail. It was fun to try and attempt it with no in-depth experience in logical pathways/truth statements though.

XP
Well, the label thing was specified in the first post.

[Nullifidian]

Originally Posted by Zaevod

The statements themselves are redundant ("door three is correct" means the same as "door one and two are not correct"), but, anyway, let's see...

I didn't originally consider the possibility of many unanswerable statements input separately, but let's consider this anyway: What's unanswerable about these statements? They seem to be either true or false 100% of the time, so I'm not sure what you're getting into :/

By including all three doors instead of say, two doors you prevent the computer from answering a statement it could answer which would mean you could be none the wiser if it does answer and you'd have wasted your only possibility on an answer.

Say you pick the statement:
Door 1 is correct, door 2 is not, door 3 is not
Outcomes:
False, True, False = no answer
False, False, True = no answer
False, False, False = impossible to get an answer, because at least one of the incorrect doors need to be true in order for door 1 to be false
False, True, True = impossible to get an answer, because that would mean there is no correct door.
True, True, False = impossible to get an answer, because that would mean 2 doors are correct.
True, False, True = impossible to get an answer, because that would mean 2 doors are correct.
True, False, False = impossible to get an answer, because that would mean all doors are correct.
True, True, True = answer, meaning your statement is correct regardless of the bug because it answered. Even if the computer's response says False because of the bug, the reply alone means that it's true.


edit: Err, I guess if the computer only outputs based on the entire statement as a whole, then this wouldn't apply.. If it gets something like False, True, False, it would see that entire statement as false because there's incorrect info in it. damn it.

[PaperclipGames]

Originally Posted by Zaevod

For those who missed it: PaperclipGames already solved it in the previous page.

(sun)

The solution you provided is quite marvellous. The trick that is used is that you specify a label, which entails many concepts (that is, many different animals), so that door 3 does point at door 1 and door 2... but both at once. Pretty clever.

My solution was more-or-less brute force: start with a statement and expand it to satisfy more conditions.

[Choofers]

Originally Posted by Reincarnate

there is malt liquor on my monitor, HELP