A challenge I intend to put somewhere in a story (possibly)

As a test, I'd like to see someone else solving it.

Here it is:

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 portals and a robot.

You know a few things about this room:

1- Two of the portals 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. It is not possible to discover which portal is the good one without the help of the robot (you can choose randomly, but that wouldn't really solve the challenge).

2- This robot knows everything that can be known 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.

However, it also has one major bug: 50% of the time, it swaps the output (and only the output) answer. When it happens, something that would be answered as "true" becomes "false" and vice-versa. The processed values remain the same, though. The robot KNOWS when this happens and when it will happen, but can't avoid it.

You must discover one statement or series of connected statements which, based on the robot's judgement, determines which portal 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 portal. 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.

That's it. There was an easier version without the bug, but this one is better. If people solve it too quickly, I'll probably make it even harder. I have one possible answer in a .txt file (there are infinite possibilities).

Edit: THE ROBOT CAN'T POINT ANYWHERE. It can only say "true" or "false".

Edit 2: You can't give orders to the robot, only tell him about the labels you gave to each door and make your statement.

edited 9th Mar '12 8:31:10 PM by Teraus

If you experience an error, point towards the good door, if you don't, point towards the bad door.

Easy

Here's another: If you experience an error, point towards the bad door, if you don't, point towards the good door.

edited 3rd Oct '11 6:25:27 PM by deathjavu

Wait, this robot can point? God dammit.

• Head explodes* The only winning move is not to play. How about a nice game of chess?

I think the error occurs or doesn't occur during the output step, after the calculation has already been made. Thus, you can't make 'whether an error occurred during this calculation' one of the inputs.

With that interpretation, then I think it's impossible, so maybe I'm wrong.

Use the right door.

Ugh, and I thought I was clear enough...

Hmm, no. The robot can't point anywhere. It can only say true or false.

Also, it's supposed to be a statement, an affirmation, not an order.

Also, even if he could point somewhere, it still wouldn't work for every case. There are three portals, not two.

Must I add another emphasis to the word "knows" in the first post?

edited 4th Oct '11 8:07:16 AM by Teraus

It is possible to solve it without looking for subterfuges.

Will the robot do anything (go kaput!) if I ask a self-referential question regarding its output; like the sentence is false?

"This door is the fun door OR you have outputted a sentence that is true to the input?"

edited 3rd Oct '11 8:02:28 PM by QQQQQ

That's all the robot does.

Edit: will read your answer now

"This door is the fun door OR you have outputted a sentence that is true to the input?"

Sorry, but that doesn't solve it.

Let's assume that the portal 1 is the good one and that the bug is not happening.

He will say "true" regardless of which portal you're pointing at.

If the bug is happening, however, he will say false, true and true, depending whether you are pointing at portal 1, 2 or 3 respectively. You can't conclude anything from his answers like this.

edited 3rd Oct '11 8:08:08 PM by Teraus

If the door is not a fun door, but the input is true - I imagine the robot will be confounded how to express this truth. True, will he say? It isn't a fun door, and the robot wouldn't contradict that the door isn't fun with its true output, saying True. Will the robot say False instead?

False - the door isn't fun, but it contradicts having a truthful output that its output is True. (It cannot really say false, because of the condition of having a true output being satisfied.) I imagine it may be tongue-tied like this.

edited 3rd Oct '11 8:13:08 PM by QQQQQ

Actually, only one statement needs to be true when you connect two statements with an "or". He will say true when the bug is not happening, always (for your statement).

If you swap the "or" for an "and", it will be like this:

True, false, false if the bug is not happening.

True, true, true if the bug is happening (remember that, in this case, "true" means "false").

edited 3rd Oct '11 8:18:38 PM by Teraus

I think the "50% of the time" phrase in your challenge is not necessary, since as you said, the robot only has enough power to give out one answer, therefore knowing the bug occurs only half the time on full power will not give the reader any useful information. You could just say: "You will not know whether the robot is giving you the right answer or not."

It could be 1% of the time, I just thought it looked better.

edited 4th Oct '11 8:08:43 AM by Teraus

I do not understand how the puzzle is solvable when the robot's final answer is unreliable and he gives no further information.

Trust me, it's solvable with pure logic. It's not trivial, though, and you need to play close attention to the first post. If people start giving up, I'll give more hints.

Well, try to solve it without the bug, first.

edited 4th Oct '11 8:44:45 AM by Teraus

this.

edited 4th Oct '11 8:42:22 AM by TheEmeraldDragon

So... Give up? I'm telling you it's solvable...

edited 4th Oct '11 8:45:43 AM by Teraus

Sure.

Are you being sarcastic or do you believe it but don't care? Well, don't solve it if you don't want to.

edited 4th Oct '11 9:16:24 AM by Teraus

I'm saying sure to giving up, dude.

I see. Well, let's wait for the others.

edited 4th Oct '11 8:51:26 AM by Teraus

...damn this is hard. The bug is easily avoided, but I'm stuck at the question. How can you find the right portal when you can only get two different answers? The bad portals are identical, yes, but still.

Ughh. This will take time.

...is the solution related to the Monty Hall Problem?

Never heard of it. I just read about it in Wikipedia, It's interesting...

But, no. It has no relation to the solution of my challenge whatsoever.