Contrived scenarios as logic problems

[D'kian]

We're all familiar with the contrived, highly unlikely or outright fantastic scenarios meant to expose ethical contradictions. Well, there are some that do well as logic problems. I suppose many here know them, neverhteless here go two:

1) You need to extract an important piece of information from an individual named Zathras, let us say he knows whether the price of a stock will go up or down. The thing is Zathras will lie once in every interrogation, but only once. You can ask him two questions. What would you ask? (this is a very easy one).

2) You face a chioce between two doors, labeled A and B. One leads to freedom, the other leads to a dungeon. Naturally you don't know which is which. Each door has a guard. One guard always lies, the other always tells the truth. Again you don't know which is which. You are allowed only one question to either guard (one question total). What do you ask? Hint: it doesn't matter which guard you choose, whether the liar or the other, the question works for both.

Answers later, assuming no one knows it already or figures it out.

[EC]

I figured out the answer's, but I don't see how these are similar to the scenario's meant to expose ethical contradictions. In the ethical scenario's the people that are posing the questions simply don't understand (or choose to evade) that a proper ethical foundation doesn't include emergency situations. But these just seem like exercises to hone one's use of logic, like sodoku puzzles, etc.

[D'kian]

The similarity is in the contrived, unlikely and fantastic nature of the scenarios. The logic problems can be fun to figure out and they do excercise logical thinking. That's it.

edited to add: They're like math problems. Here's one, BTW. what's the highest number you can build using the numerals 1, 1, 1 and 1 and any mathematical notations or symbols? Example 11+11=22, 11*11=121, 11^11=285,311,670,611. You musy use all the numerals.

Edited June 24, 2008 by D'kian

[JMeganSnow]

1. Is your name Zathras? Will the stock go up?

If he answers "yes" to the first one, you know that his answer to the next question is a lie. If he answers "no", you know that his answer to the next question is the truth.

2. Ask one of the guards (it doesn't matter which one) "Which door would the other guard tell me to go through?" then take the opposite of the answer.

[athena glaukopis]

The second one is used in the movie Labyrinth ^^ O the memories!!

[eriatarka]

1. Is your name Zathras? Will the stock go up?

If he answers "yes" to the first one, you know that his answer to the next question is a lie. If he answers "no", you know that his answer to the next question is the truth.

2. Ask one of the guards (it doesn't matter which one) "Which door would the other guard tell me to go through?" then take the opposite of the answer.

Applying your second answer to the first problem, surely you only need to ask Zathras one question rather than two ("if my next question is 'will the stock go up?' then what will you tell me?').

Edited June 24, 2008 by eriatarka

[eriatarka]

edited to add: They're like math problems. Here's one, BTW. what's the highest number you can build using the numerals 1, 1, 1 and 1 and any mathematical notations or symbols? Example 11+11=22, 11*11=121, 11^11=285,311,670,611. You musy use all the numerals.

11 ↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑(etc) 11 where the ↑ is the Knuth Up Arrow?

Its a bit of an ambiguous question though because theres a lot of pretty obscure math things you could use if 'symbols' allows pre-defined functions. A(11,11) where A is the Ackermann function for instance. Or B(1111) where B is Busy Beaver

Edited June 24, 2008 by eriatarka

[D'kian]

11 || 11 where the '|' is the Knuth Up Arrow?

Its a bit of an ambiguous question though because theres a lot of pretty obscure math things you could use. A(11,11) where A is the Ackermann function for instance.

Before my head explodes, the largest number is infinity. You get at it thus:

((((((1,111!)!)!)!)!)!.....!) Where 1,111!= 1,111*1,110*1,109*1,108.*...11*10*9*8*7*6*5*4*3*2*1 The second parenthesis would be something like (1.6185630726417858745547823350912e+2903)! which is already ridiculously high

[Matus1976]

1. Is your name Zathras? Will the stock go up?

If he answers "yes" to the first one, you know that his answer to the next question is a lie.

He would answer "NO, its ZaathhruUus, not ZaAathhruus" which to the interregator would sound exactly the same, thus diffusing the logical trap! (Babylon 5 reference)

[D'kian]

He would answer "NO, its ZaathhruUus, not ZaAathhruus" which to the interregator would sound exactly the same, thus diffusing the logical trap! (Babylon 5 reference)

Actually he'd say "It's un-stock in time."

Now pardon me while I take cover.

[Benpercent]

He would answer "NO, its ZaathhruUus, not ZaAathhruus" which to the interregator would sound exactly the same, thus diffusing the logical trap! (Babylon 5 reference)

Then there's an easy fix to the problem: "Is your name Billy?"

[JMeganSnow]

Applying your second answer to the first problem, surely you only need to ask Zathras one question rather than two ("if my next question is 'will the stock go up?' then what will you tell me?').

It specified two questions. Actually, if you ask him only one question you KNOW he's going to lie (since he lies once and only once in any given interview).

[D'kian]

2. Ask one of the guards (it doesn't matter which one) "Which door would the other guard tell me to go through?" then take the opposite of the answer.

I'm a bit confused. Does it matter where the guards want you to go? If the liar wants you to go free, he'd tell you to go through the dungeon door, right? If he doesn't, he'd tell you to use the freedom door. If you do the opposite, you wind up in jail.

Since the answer from either guard must be a lie, aren't you better off seeking factual information rather than the guard's desire?

I'll go away now...

[DragonMaci]

Since the answer from either guard must be a lie

How is that the case? The original post said, "One guard always lies, the other always tells the truth" Sounds to be like only what one says is a lie and what the other says is the truth.

[D'kian]

How is that the case? The original post said, "One guard always lies, the other always tells the truth" Sounds to be like only what one says is a lie and what the other says is the truth.

Let's call the guards A and B. Let's say A always tell the truth and B always lies.

So you ask A "What would B say if I asked him what color is the sky?" Since A always tells the truth, he can answer the question truthfully by telling you what B would say. He knows B would lie, therefore his answer would be, let us say, "yellow."

Now suppose you ask B what would A answer to the same question. He knows A would tell the truth. But B always lies. So he will lie about what A would answer. He'd tell you "Yellow."

See, the answer to that form of a question will always be a lie.

[JMeganSnow]

Christ on a crutch. The wording can vary but the question you have to ask is basically "which choice would the *other* guard tell me to make?"

Why? Because if you ask the truth-telling guard, he will truthfully tell you what the other guard would say, which is a falsehood. If you ask the lying guard, he will untruthfully tell you what the other guard would say, which is ALSO a falsehood.

Or, alternately, you can do this.

[D'kian]

Or, alternately, you can do this.

I did disassemble many a Rubik's Cube