[NT] Riddles!

[Mycroft]

I thought it would be interesting to start a thread devoted to posing and dissecting riddles and brainteasers. Yeah, so I'm a pretty huge nerd.

You can most likely find the solution to any of the riddles and brainteasers people post here on the Internet, but that sort of ruins the fun now doesn't it? The first two riddles I will post here I came across surfing the Internet, matter a'fact, but you have my solemn oath I've not looked at the solutions, nor will I look for the solutions to any riddles subsequently posted in this thread before commenting upon them. Let's make that the code of conduct for this thread. Anyone who is clearly in violation of this code of conduct will have to live knowing that strangers on the Internet think he's a real fat jerk, so there.

To begin:

The Monty Hall Problem:

Suppose you're on a game show and you're given the choice of three doors. Behind one door is a car; behind the others, goats. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?

The solution is here. See how closely your thinking matches!

Next is a riddle I found on an IQ test of somewhat questionable validity:

Bob is locked in a crappy dungeon with three doors, all with signs posted on them. He knows that behind one of the doors is freedom, and behind the other two doors are dragons (which will brutally maul him, because that's what they do). He also knows that at least one of the signs is telling the truth, and that at least one of the signs is lying. The signs read:

Door 1: Freedom is not behind this door.
Door 2: Freedom is not behind this door.
Door 3: Freedom is not behind the blue door.

He thinks for a second and then leaves through door number 3. Which is the blue door?

Taking this riddle at face value, it can be solved pretty quickly, but it has one rather large flaw. In order to test whether or not my thinking is solid, I'm curious to see if other members spot the same flaw.

Edit: in the name of fairness, I'll confess that people may find my issue with this riddle to be either flippant or pedantic, depending upon their assessment of my character.

Finally, the classic two guards riddle:

You stand at a fork in the road. Next to each of the two forks, there stands a guard. You know the following things: 1. One path leads to Paradise, the other to Death. From where you stand, you cannot distinguish between the two paths. Worse, once you start down a path, you cannot turn back. 2. One of the two guards always tells the truth. The other guard always lies. Unfortunately, it is impossible for you to distinguish between the two guards.

You have permission to ask one guard one question to ascertain which path leads to Paradise. Remember that you do not know which guard you're asking -- the truth-teller or the liar -- and that this single question determines whether you live or die. The question is: What one question asked of one guard guarantees that you are led onto the path to Paradise, regardless of which guard you happen to ask?

Many people are likely familiar with the proper answer, but to make this more of a challenge: imagine that you are only allowed to ask one guard one yes or no question only.

 

[Chris_in_Orbit]

Taking this riddle at face value, it can be solved pretty quickly, but it has one rather large flaw. In order to test whether or not my thinking is solid, I'm curious to see if other members spot the same flaw.

They don't define what freedom is, thats what the flaw is. Death to some people is freedom right?

 

[BlackOp]

Finally, the classic two guards riddle:



Many people are likely familiar with the proper answer, but to make this more of a challenge: imagine that you are only allowed to ask one guard one yes or no question only.

I'd ask them the same question.... If they had ever taken a dump. I would just turn away then.....paradise is for suckers blinded by fantasy. Either path would be hell.

Reminds me of the time two Mormons came to my door. They said if I "accepted" Jesus I would get into heaven....gave me a pamphlet. It was a crudely drawn cartoon of the afterlife...had some kid petting a lion. I told them if I were "creator of the universe".....I would strike them down for such crappy illustration work. I then asked them if they would would be there (in heaven)....they said "yes". I said "fuck that".

 

[ygolo]

I think it is quite reasonable to question the rationality and reasoning ability of Bob.

 

[ragashree]

Two guards riddle:

This rings a vague bell even though I don't generally do such things... In any case it doesn't seem that hard:

*point to one road or the other*

*ask guard of choice "Would the other guard say that road led to heaven?"

if answer = yes the road will always lead to hell
if answer = no the road will always lead to heaven

or was this a trick question somehow?

 

[ed111]

Blue door? 3?

Guards: Ask one if the other tells the truth.

 

[Mycroft]

Two guards riddle:

This rings a vague bell even though I don't generally do such things... In any case it doesn't seem that hard:

*point to one road or the other*

*ask guard of choice "Would the other guard say that road led to heaven?"

if answer = yes the road will always lead to hell
if answer = no the road will always lead to heaven

or was this a trick question somehow?

When you say "the road", are you referring to the road you're pointing at or the road behind the guard you're questioning?

And no, no trick questions. Riddles with "answers" that reveal the riddle to be a trick question are by and for the sort of people who are interested enough in appearing clever to bother with such nonsense but not adequately clever to make or solve proper riddles.

I think it is quite reasonable to question the rationality and reasoning ability of Bob.

Yes, exactly! The line ought to read, "He thinks for a second and then, choosing correctly, leaves through door number 3."

As long as you take for granted that Bob isn't an imbecile, the riddle is pretty straightforward, but if you don't know that for certain it's unsolvable.

 

[ragashree]

When you say "the road", are you referring to the road you're pointing at or the road behind the guard you're questioning?.

That doesn't seem to materially affect the outcome... I suppose it would make more sense for it to be the one behind the guard, however.

And no, no trick questions. Riddles with "answers" that reveal the riddle to be a trick question are by and for the sort of people who are interested enough in appearing clever to bother with such nonsense but not adequately clever to make or solve proper riddles.?.

Heh, try telling that to an ENTP, I dare you!

Yes, exactly! The line ought to read, "He thinks for a second and then, choosing correctly, leaves through door number 3."

As long as you take for granted that Bob isn't an imbecile, the riddle is pretty straightforward, but if you don't know that for certain it's unsolvable.

This seems like a badly worded question, I agree, but as it is the only possible solution I suppose it has to be taken as the one intended. I presume the person who came up with it was too busy thinking of the process to be too concerned with context. It is pretty sloppy actually...

 

[kyuuei]

Next is a riddle I found on an IQ test of somewhat questionable validity:

blah blah Door stuff here.

Taking this riddle at face value, it can be solved pretty quickly, but it has one rather large flaw. In order to test whether or not my thinking is solid, I'm curious to see if other members spot the same flaw.

Uhm.. They're both (1&2) blue? I've never heard the first two riddles before.. the third I vaguely remember from the Labyrinth.

 

[The_Liquid_Laser]

Riddle1: This has been discussed to death in another thread a few months ago.

Riddle2: As has already been stated we're going to assume that Bob chose correcty. Here is the solution:

Since we are assuming that Bob chose correctly, then let's look at the three cases for which door is blue.

Door1: If this door is blue then all three doors are telling the truth. We know that at least one is lying, so this door cannot be blue.

Door2: Same logic as Door1.

Door3: If this door is blue, then the first two doors are telling the truth and the third door is lying. Therefore this is the blue door.


Riddle3: Anyone who has seen the movie Labyrinth should be able to answer this.

 

[Mycroft]

Liquid Laser, actually:

If door number one is the blue door, the door to freedom could be either door number one or door number two. Only door number three is impossible. To wit:

Scenario one: door one is blue and it is the path to paradise:

Freedom is not behind this door = false
Freedom is not behind this door = true
Freedom is not behind the blue door = false

At least one of the doors is correct and at least one is false. Criteria met.

Scenario two: door one is the blue door and door two is the path to paradise:

Freedom is not behind this door = true
Freedom is not behind this door = false
Freedom is not behind the blue door = true

Again, criteria met.

Scenario three: door one is the blue door and door three is the path to paradise:

Freedom is not behind this door = true
Freedom is not behind this door = true
Freedom is not behind the blue door = true

Criteria are not met. Hence, door three is impossible.

This holds true if either of the first two doors is the blue door. In short, if either of the first two doors is the blue door, the door to freedom could be either of the first two doors and the criteria would be met. However, if the blue door is either of the first two doors, door three cannot be the door to freedom.

Edit: actually, this doesn't contradict what you said at all. Apologies!

 

[Mycroft]

Ragashree:

Your solution is nice, if I understand correctly. I believe you mean such:

Walk up to, say, the left guard. Point to the guard on the right. Ask him, "Would the other guard say that road leads to heaven?" Here, making it evident you are asking about the road behind the guard you are not talking to. If the guard response in the affirmative, this means one of two things:

1.) He is the truth-telling guard and, as such, is telling you truthfully that the lying guard to the right, being a liar, would lie and say his road lead to heaven even though it leads to destruction (or Hell or whatever.) You should enter the road of the guard you are querying.

2.) He is the lying guard and, accordingly, is lying: the other, truth-telling guard, were you to ask him, would tell you truthfully that the road behind him leads to hell. In this case, as well, you should enter the road of the guard you are querying.

It works in the reverse. So, yeah, very nice!

Another possible solution: ask if the lying guard is the one guarding the door to paradise.

Heh, try telling that to an ENTP, I dare you!

Accusing someone of being an ENTP and of doing something merely for the sake of appearing intelligent would be redundant!

OH but I kid!

...70%

 

[INTJMom]

Ragashree:


It works in the reverse. So, yeah, very nice!

.




Accusing someone of being an ENTP and of doing something merely for the sake of appearing intelligent would be redundant!

OH but I kid!

...70%

Does the ability to do all that convoluted thinking come from Ti?
If not, which function is it?

 

[G-Virus]

Riddle 2 is a classic Logic game you will find in most critical thinking/logic books.

 

[G-Virus]

Adam is a man-slut (or playa for some) that has two girlfriends he likes equally. Each Saturday afternoon he visits one of them, and in hopes of not having to decide, he used his logic and knowledge of limits to infinity. Since both of them live on the same train line but in opposite directions from his train station, he simply strolls right into the station and hops on the first train to come. If the eastbound train arrives first, he visits Jackie, and if the westbound train comes first, he visits Donna. Since there is an equal number of eastbound and wesbound trains, Adam reasons that in the long run he will visit them with more or less equal frequency. After a few months, he realizes the he is visiting Jackie four times more often than he is visiting Donna. What is Adam' mistake?

(Hint, think of the P and Q values of the random walk and remember that the probability in a gaussian distribution should always equal 1).

 

[BlackOp]

After a few months, he realizes the he is visiting Jackie four times more often than he is visiting Sarah. What is Adam' mistake?

(Hint, think of the P and Q values of the random walk and remember that the probability in a gaussian distribution should always equal 1).

Poor Donna....odd woman out. Sarah must have bigger breasts....but Jackie reminds him of his mother.

*edit* Hey, you changed the question. I thought that was the puzzle......

 

[ragashree]

Yes, Mycroft, that was it, thanks. I was a bit drunk when I first answered and altogether too lazy to type it out in more detail after doing a couple of other long posts, sorry I wasn't clearer.

Does the ability to do all that convoluted thinking come from Ti?
If not, which function is it?

If you meant me (I presume you did), it was good old inferior Te, I suppose. It's quite good for solving concrete problems in combination with a healthy dose of secondary Ne (should tell you what type I am with a bit of problem solving deduction) but isn't so much use for the more abstract and theoretical kinds of reasoning such as those used in higher mathematics. At least not in my case, but then it is meant to be my inferior function if MBTI actually does what it says on the can! My understanding is that Te works better when it can focus on concrete external matters, wheras Ti seeks to build a private internal system of understanding and is comfortable with building this understanding on theories which may have no immediate practical application or association with concrete objects.

Despite my putative natural disadvantage, I really didn't have much trouble with either questions 2 or 3, though as I had had a few drinks before reading the thread I was a bit unsure about whether I was missing something. Question 1 is a horrible counter-intuitive thing, I remember, however, coming across it in a novel I read a couple of years ago called "The Curious Incident of the Dog in the Nighttime" where it was solved by the protagonist, an autistic teenager. It would have been cheating to try to answer it as I remembered the original (not sure I'd have got it on my own though!). However, I simply don't know the kind of maths that seems to be needed to properly answer such a question as the one just posted above, though I can make a reasonable guess. I imagine that question will most likely be solved by an INTP, or maybe an ENTP, as they have the strongest combination of openness to the necessary theory in Ti and and Ne to do the actual mental leap necessary to solve the problem. But maybe I'll be wrong

 

[G-Virus]

Hi Rag, you don't need anything but a good set of inferior Te (J/k) to solve the above problem. I was just giving the gaussian and random walk stuff as a hint for those who took stats or quantum mechanics because they should know the answer in a heartbeat.

Really, if you can do fractions, then you have all the math skills you need.

 

[Mycroft]

Adam is a man-slut (or playa for some) that has two girlfriends he likes equally. Each Saturday afternoon he visits one of them, and in hopes of not having to decide, he used his logic and knowledge of limits to infinity. Since both of them live on the same train line but in opposite directions from his train station, he simply strolls right into the station and hops on the first train to come. If the eastbound train arrives first, he visits Jackie, and if the westbound train comes first, he visits Donna. Since there is an equal number of eastbound and wesbound trains, Adam reasons that in the long run he will visit them with more or less equal frequency. After a few months, he realizes the he is visiting Jackie four times more often than he is visiting Donna. What is Adam' mistake?

(Hint, think of the P and Q values of the random walk and remember that the probability in a gaussian distribution should always equal 1).

Do the trains run nonstop 24 hours a day all days of the week?

 

[G-Virus]

sure All day all the time 24/7

Just to let you guys know, this riddle involves no word play or any of that clever mumbo jumbo, what you see is what you get.