A little challenge I created

[Teraus]

Hi. You don't know me.

You have entered a room. The door you passed through was automatically closed and will never be opened again.
In this room, there are three other absolutely identical doors and a robot.

You know a few things about this room:

1- Two of the doors will take you to a place of eternal boredom and one of them will take you to an awesome place. You don't know which, obviously. They also automatically close when you pass through.

2- This robot knows everything that can be known, has no programming quirks or bugs and makes calculations with infinite precision (no approximations). However, he can only give two possible answers: true or false (if possible to answer). He has enough energy left for only one answer.

You must discover one statement which, based on the robot's judgement, determines which door takes you to the cool place. This statement must work for 100% of the cases.

Useful information:

You can use logical operators like and, or, nor, etc., as long as there is only one final answer.

You can give labels to each door. However, you can't ask the robot to assign the values "true" or "false" to things. Every answer must depend on the robot's previous knowledge.


It might seem ridiculously easy at first, but it might also seem impossible. It's neither. If it takes too long, I can give hints.

[emulord]

Define the doors to be named Left, middle and right, for the left, middle and right doors respectively.
Define a function G as follows:
{Left} -> {True}
{Middle}->{False}
{Right}->{No answer}

What is G()?

[YoshL]

Originally Posted by emulord

Define the doors to be named Left, middle and right, for the left, middle and right doors respectively.
Define a function G as follows:
{Left} -> {True}
{Middle}->{False}
{Right}->{No answer}

What is G()?

bahahahahahahaha nicely done.

[Mans0n]

Emulord pretty much wrecced this game haha.

[Teraus]

Hmm... Okay, I need to specify things a bit more.

Originally Posted by emulord

Define the doors to be named Left, middle and right, for the left, middle and right doors respectively.
Define a function G as follows:
{Left} -> {True}
{Middle}->{False}
{Right}->{No answer}

What is G()?

If we consider that, the statement "G(true door) is true" solves the problem. However, you cannot ask the robot to assign true and false values to things, as every answer must depend on the robot's previous knowledge (true and false must refer to actual facts only). You can only give him names or numbers for each door. So you are supposed to know what G is.

But it's my fault, I'll make this clear in the description.

[hcmushroom]

how about this

left door= 1
middle door= 2
right door= -1

is the square root of the correct path 1?
true/false/error

[MarioNintendo]

Originally Posted by hcmushroom

how about this

left door= 1
middle door= 2
right door= -1

is the square root of the correct path 1?
true/false/error

That question can't be answered either by true, false, or error... Only by yes or no, which don't solve the problem. But I believe we're going somewhere with this.

EDIT: How about putting it like this:

left door = (-1)
middle door = 0
right door = 1

f(x) = (x)^(1/2)

f(door #) = (door #)^(1/2) < f(correct path #) = (correct path #)^1/2

What would the robot reply?

... But, sigh, if the correct path = (-1), the result would be f'ed up...

[LongGone]

Took awhile to think about

Since there are 3 scenarios (3 cases of each door being the cool door) and three possible answers, we must make each case count. We need a statement that the robot will answer e.g. True if its door 1, False if its door 2 and -noreply- if its door 3.

Making the robot(assume its a he) say True is easy, just say the statement "Door 1 is the cool door". If door 1 is the cool door, he will say "True". We can then link this statement with an OR, "Door 1 is the cool door OR ______", for the remainder of the statement.

Now, how do we make a "False" answer useful? The robot will say "False" if the statement I said is false (obvious, but how to implement it?). More difficult, how do we make a robot unable to answer? We can use a statement like "This statement is false". If I said "(This statement is false) AND 1+1=2", the robot will not answer because 1+1 is two, but (This statement is false) is undefined. If I said "(This statement is false) AND 1+1=3" the robot will answer false, because 1+1 is not 3 and regardless of the other statement, ____ AND 1+1=3 is always false. Hence we have three possible answers we can milk from the robot, so we mix the statements together using an OR and we get

"(Door 1 is the cool door) OR (This statement is false AND door 2 is the cool door)"

3 Cases:
If Door 1 is the cool door, he will say True, and we are done.
If Door 2 is the cool door, (This statement is false AND door 2 is the cool door) will be the deciding statement, but the robot can't answer because the statement simplifies to "This statement is false". Hence he will not answer.
If Door 3 is the cool door, everything is false; Door 1 is not the cool door, (__) AND door 2 is not the cool door. Hence he will say False

[Teraus]

Originally Posted by hcmushroom

how about this

left door= 1
middle door= 2
right door= -1

is the square root of the correct path 1?
true/false/error

I guess he would use complex numbers by default (since it's the only way he can get an answer for the right door). But, even if he didn't, it would still be true/false/false.

Originally Posted by LongGone

"(Door 1 is the cool door) OR (This statement is false AND door 2 is the cool door)"

3 Cases:
If Door 1 is the cool door, he will say True, and we are done.
If Door 2 is the cool door, (This statement is false AND door 2 is the cool door) will be the deciding statement, but the robot can't answer because the statement simplifies to "This statement is false". Hence he will not answer.
If Door 3 is the cool door, everything is false; Door 1 is not the cool door, (__) AND door 2 is not the cool door. Hence he will say False

Very good. That really does work, congrats.

I chose a more mathematical path for my solution:

Label the left, middle and right doors 1, 2 and 3 respectively and make the following statement, with n=number of the cool door:

"1/(n-1)<1"

If the cool door is 3, he will say true, since 1/(3-1)=0.5.
If the cool door is 2, he will say false, since 1/(2-1)=1.
If the cool door is 1, he won't be able to answer, since 1/(1-1) is NaN (or even if you tried to count infinity as a number, it could be either positive or negative, so...).

But there are infinite solutions, of course.

[MarioNintendo]

Originally Posted by Teraus

"1/(n-1)<1"

Gah... I had it on the tip of my tongue. :P

[Teraus]

Originally Posted by MarioNintendo

Gah... I had it on the tip of my tongue. :P

Dividing by 0 is useful. XD
I also thought of an answer that didn't involve numbers:

Label the doors, from left to right, "Apples", "solid fire" and "something that cannot be perceived".

Make the statement "The thing which the cool door's label refers to in the real world exists."
This one is a bit more complicated, though.