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# Logic Problems at the Court III.

## 30 posts in this topic

Logic Problems at the Court III. - Back to the Logic Problems

You live on an island where there are only two kinds of people: the ones who always tell the truth (truth tellers) and those who always lie (liars). You are accused of crime and brought before the court, where you are allowed to speak only one sentence in your defense. What do you say in each of the following situations?

1. If you were a liar (the court does not know that) and you were innocent. And it is an established fact that a liar committed the crime.

2. Same situation as above, but you are the one who committed the crime.

3. If you were a truth teller (the court does not know that) and you were innocent. And it is an established fact that a truth teller committed the crime.

4. If you were innocent and it is an established fact that the crime was not committed by a “normal” person. Normal people are that new immigrant group who sometimes lie and sometimes speak the truth. What sentence, no matter whether you were a truth teller, liar, or normal, can prove your innocence?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.

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Logic Problems at the Court III. - solution

1. „I did it – I am guilty.“

2. There is no such sentence.

3. „I am innocent.“

4. „Either I am an honestant and innocent, or I am a swindlecant and guilty.“ = „I am either an innocent honestant, or a guilty swindlecant.“ The court could think this way:

4.1 If he is an honestant, then his statement is true and he is innocent.

4.2 If he is a swindlecant, then his statement is a lie and he is neither an innocent honestant nor a guilty swindlecant. This means that he is an innocent swindlecant.

4.3 If he is normal, then he is innocent since a normal man couldn’t have done that.

This time you are one of the inhabitants of the island. There was crime committed and people think you did it. At the court you can say only one sentence to save your life. So what do you say?

1. If you were a swindlecant (the court does not know that) and you were innocent. It is known that a swindlecant did it.

2. The same situation but you are guilty.

3. If you were an honestant (the court does not know that) and you were innocent. It is known that an honestant did it.

4. If you were innocent and everybody knows that the one who did it is not normal. Normal people sometimes lie and sometimes speak the truth. What sentence, no matter if you were an honestant, a swindlecant or normal can prove your innocence?

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for the second situation, what about "i am an honestant and i am innocent."

oh wait, that wouldn't work lol.

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For 1 and 2 if you say "I am a swindlecant" it makes it impossible for them to find you guilty.

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For 1 and 2 if you say "I am a swindlecant" it makes it impossible for them to find you guilty.

Uhh, it's also impossible for either the honestants or swindlecants to say that...

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For #2 - "Joe Swindlecant is guilty"

Remember that the court does not know if the accused is Honestant or Swindlecant:

If he is an Honestant, that statement is true and Joe is guilty.

If he is a Swindlecant Joe is innocent.

Reasonable doubt. I walk on technicality. =-D

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for 1st...what about "I am not a swindlecant"

because only an honestant can say that and so his truth will prove that he is an honestant..........

a swindlecant cannot say that because if he'd say that then his lie will prove him an honestant which is a conflict....

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There are 4 scenarios presented, but 2 desired outcomes requested:

A) say 1 sentence to save your life, OR

B) say 1 sentence to prove your innocence.

These are not the same thing.

Outcome B, for example, cannot work with scenario 2.

So only outcome A can be applied to all the scenarios. Thus, I would say something along the lines of:

"There is a nuclear device hidden on this island set to explode if I stop breathing or the signal is lost..."

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Use the shorthand notation IH IS IN GH GS GN for the 6 cases of

[innocent Guilty] [Honestant Swindlecant Normal].

Craft statements that distinguish you from the perpetrator [P] for 4 different scenarios:

[1] You are an IS. The court knows P is a GS. They don't know whether you are H or S.

[2] You are a GS. The court knows P is a GS. They don't know whether you are H or S.

[3] You are an IH. The court knows P is a GH. They don't know whether you are H or S.

[4] You are IH IS or IN [innocent, unspecified]. The court knows P is GH or GS [Guilty, but not Normal].

[1] Distinguish yourself [an IS] from P [a GS].

Create a statement that anyone but a GS can make.

It must be true for a GS [can't] or any H [can] and false for IS [can].

i.e. the statement must be false iff the speaker is IS.

"I am not an Innocent Swindlecant."

What the court can conclude is this:

If you were a GS [and fit P's known profile] this statement would be true and you couldn't make it.

If you were an IS it would be false, and that's ok.

If you were any flavor of H the statement would be true and you could make it; but no H is a GS.

Thus, only an innocent person can make this statement.

P cannot, and anyone else can. You could be anybody but P.

Go home.

[2] Distinguish yourself [a GS] from P [a GS].

You can't. You're cooked. Too bad.

There is no statement that distinguishes a GS from a GS.

Please report to the gas chamber.

[3] Distinguish yourself [an IH] from P [a GH].

Create a statement that anybody but a GH could make.

It must be true for an IH, false for a GH and false for any flavor of S.

i.e. the statement must be true iff the speaker is IH

"I am an innocent honestant."

You're free to go.

[4] Distinguish yourself [you are IH IN or IS] from P [a GH or GS].

Create a statement that any I can make, but neither a GH nor a GS can make.

Cases and Truth requirements.

IH - statement must be T

IN - doesn't matter: N's can say T or F as they choose.

IS - must be F

GH - must be F

GN - doesn't matter: such people do not exist. P is known not to be a GN.

GS - must be T

Taking the cases that do matter, the statement must be true iff the speaker is IH or GS.

"I am either an innocent honestant or a guilty swindlecant"

What the court can conclude is this:

If you were an IH the statement would be true and you can make it.

If you were an IN you could say anything you like, so you could say this.

If you were an IS, the statement would be false, and you could make it.

So you could be any flavor of Innocent.

Further,

If you were a GH the statement would be false and you could not make it.

If you were a GS the statement would be true and you could not make it.

You can't be a GN: P is known not to be N. GN's don't exist.

So you could not be any flavor of Guilty

All charges are dropped. You're free to go.

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Logic Problems at the Court III. - Back to the Logic Problems

This time you are one of the inhabitants of the island. There was crime committed and people think you did it. At the court you can say only one sentence to save your life. So what do you say?

1. If you were a swindlecant (the court does not know that) and you were innocent. It is known that a swindlecant did it.

2. The same situation but you are guilty.

3. If you were an honestant (the court does not know that) and you were innocent. It is known that an honestant did it.

4. If you were innocent and everybody knows that the one who did it is not normal. Normal people sometimes lie and sometimes speak the truth. What sentence, no matter if you were an honestant, a swindlecant or normal can prove your innocence?

It's already been established that there is no solution for situation #2, however, when I was pondering these puzzles, I came up with one statement that I believe would work for all 3 other situations.

My main concern was that the court does not know whether I am an honestant or swindlecant, and so I would need a statement that exonerates me regardless of which I was, and also regardless of who did it.

The statement is: "If you ask me if I am innocent, my answer will be 'yes'."

1. If I am an innocent swindlecant, the logic is as follows:

a. I cannot say that I am innocent, because that is the truth.

b. If you ask me if I am innocent, I must lie and answer 'no'.

c. However, since I am the one making the above statement, I must lie about what my true answer would be. Thus I must say that my answer would be 'yes'.

d. The courts, being logical, would know that only a swindlecant who is innocent could make the above statement, and thus would have to release me if I am a swindlecant.

2. Conversely, a guilty swindlecant could not make the above statement. He's still up the creek.

3. If I am an innocent honestant, the above statement is true, and therefore I am innocent. A guilty honestant could not make the above statement. Thus the courts would have to release me if I am an honestant.

4. Neither a guilty swindlecant nor a guilty honestant could make the above statement. A guilty "normal" can, but we know that the guilty party is not normal. Anyone else who makes this statement must therefore be innocent.

One solution for all 3 solvable puzzles. Not bad for 3am.

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Logic Problems at the Court III. - Back to the Logic Problems

This time you are one of the inhabitants of the island. There was crime committed and people think you did it. At the court you can say only one sentence to save your life. So what do you say?

1. If you were a swindlecant (the court does not know that) and you were innocent. It is known that a swindlecant did it.

2. The same situation but you are guilty.

3. If you were an honestant (the court does not know that) and you were innocent. It is known that an honestant did it.

4. If you were innocent and everybody knows that the one who did it is not normal. Normal people sometimes lie and sometimes speak the truth. What sentence, no matter if you were an honestant, a swindlecant or normal can prove your innocence?

For the case of the guilty swin.(#2)= Could a GS not say something like, "I deserve to be punished."?

If one were an innocent Swin, the statement would be false, and their innocence would be proven.

If one were a guilty swin, the statement would be false (who really thinks they deserve punishment?!) and would make people think they were innocent as well.

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For the case of the guilty swin.(#2)= Could a GS not say something like, "I deserve to be punished."?

If one were an innocent Swin, the statement would be false, and their innocence would be proven.

If one were a guilty swin, the statement would be false (who really thinks they deserve punishment?!) and would make people think they were innocent as well.

Hmm, I think that may work (assuming that this swindlecant really thinks his crime deserves no punishment and the court believes that even a swindlecant would believe that this crime deserves punishment). Very clever, judo_val!

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I think that the answer for the 4th question will simply be... "I am a swindlecat"...

because and honestant will never say that...

neither will a swindlecat...

so obviously... the person saying that is a normal... and he is Innocent!!!!!

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I think that the answer for the 4th question will simply be... "I am a swindlecat"...

because and honestant will never say that...

neither will a swindlecat...

so obviously... the person saying that is a normal... and he is Innocent!!!!!

The fourth problem is looking for a statement that you can say no matter if you were an honestant, a swindlecant or normal. Swindlecants and honestants obviously can't say "I am a swindlecant".

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For solution #1, simply stating your are guilty does not prove you are a swindlecant. It says the court does not know you are a swindlecant. If you were to simply say I am guilty, they might assume you were an honestant.

edit: Nevermind, I see that the court knows a swindlecant did it. But if the court knows a swindlecant did it, how do they not know you are a swindlecant?

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For solution #1, simply stating your are guilty does not prove you are a swindlecant. It says the court does not know you are a swindlecant. If you were to simply say I am guilty, they might assume you were an honestant.

edit: Nevermind, I see that the court knows a swindlecant did it. But if the court knows a swindlecant did it, how do they not know you are a swindlecant?

They know he is a swindlecant because an honestant could not say he is guilty because that would be a lie (remember, the court KNOWS a swindlecant committed the crime). He must therefore be a swindlecant who is lying about being guilty.

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for 1st...what about "I am not a swindlecant"

because only an honestant can say that and so his truth will prove that he is an honestant..........

a swindlecant cannot say that because if he'd say that then his lie will prove him an honestant which is a conflict....

Sorry, nice try, but it is flawed...

Why wouldn't a swindlecant be able to tell this lie? Swindlecants lie all the time! So this statement doesn't prove to which side you belong either way, because EVERYONE can and will say it.

It's actually the other way around: NOBODY on the island would be able to say simply "I'm a swindlecant", because if a swindlecant said it, he would speak the truth - which he can't -, and if an honestant said it, he would be lying - which he can't. The only way they could ever use this, is in combination with another statement IN THE SAME SENTENCE.

BoilingOil

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It's already been established that there is no solution for situation #2, however, when I was pondering these puzzles, I came up with one statement that I believe would work for all 3 other situations.

My main concern was that the court does not know whether I am an honestant or swindlecant, and so I would need a statement that exonerates me regardless of which I was, and also regardless of who did it.

The statement is: "If you ask me if I am innocent, my answer will be 'yes'."

1. If I am an innocent swindlecant, the logic is as follows:

a. I cannot say that I am innocent, because that is the truth.

b. If you ask me if I am innocent, I must lie and answer 'no'.

c. However, since I am the one making the above statement, I must lie about what my true answer would be. Thus I must say that my answer would be 'yes'.

d. The courts, being logical, would know that only a swindlecant who is innocent could make the above statement, and thus would have to release me if I am a swindlecant.

2. Conversely, a guilty swindlecant could not make the above statement. He's still up the creek.

3. If I am an innocent honestant, the above statement is true, and therefore I am innocent. A guilty honestant could not make the above statement. Thus the courts would have to release me if I am an honestant.

4. Neither a guilty swindlecant nor a guilty honestant could make the above statement. A guilty "normal" can, but we know that the guilty party is not normal. Anyone else who makes this statement must therefore be innocent.

One solution for all 3 solvable puzzles. Not bad for 3am.

Now, THAT IS impressive! At first I would not have believed this could be done, but I can not find any holes in your logic. To me it seems to be absolutely airtight! Chapeau for xandarr!

BoilingOil

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There is an answer for #2:

"Nothing I say can save myself"

The reasoning is:

I cannot be telling the truth because it would cause a paradox, so I must be lying.

So if I am lying there IS something I can say to save myself: I have just said it.

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in the first case the jury wud consider d accused as a swindelant(at first sight) nd later if he says " i am guilty" he would surely be pardoned.but actually there is ambiguity n nobody knows whether he is an honestsnt or a swindelant, nd if he repeats the same sentence he might be punished....i m confused....

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here is what i got

1. state random common knoledge untruthfully so the court knows you are either Swindlecant or innocent and normal, then state that you are guilty(untruthfully). and if you a swindlecant you would be lying and saying your innocent

2.

3.state random common knoledge truthfully so the court knows you are either honastant or innocent and normal, then state your innocence. and if you a honestant you would be telling the truth and saying you innocent

4.i tell lies

(an honestant cannot say this because it would be lying and a swindlecant cannot say it becaus it would be truthful)

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Logic Problems at the Court III. - Back to the Logic Problems

This time you are one of the inhabitants of the island. There was crime committed and people think you did it. At the court you can say only one sentence to save your life. So what do you say?

1. If you were a swindlecant (the court does not know that) and you were innocent. It is known that a swindlecant did it.

"If you were to ask me if I committed this crime, I would tell you 'no'."

If you are an Honestant, this is an obvious statement of innocence. If you are a Swindlecant, you must be lying about your purported response -- which in turn would mean that, if asked, you would actually admit to having done it, a lie.

2. The same situation but you are guilty.

Logically, no statement could exonerate you, whether or not people knew your identity.

3. If you were an honestant (the court does not know that) and you were innocent. It is known that an honestant did it.

Same as #1.

4. If you were innocent and everybody knows that the one who did it is not normal. Normal people sometimes lie and sometimes speak the truth. What sentence, no matter if you were an honestant, a swindlecant or normal can prove your innocence?

Same as #1.

Of course, if the suspect pool includes Normals, no statement can exonerate anyone not already known to be an Honestant or a Swindlecant.

Logic Problems at the Court III. - solution

1. „I did it – I am guilty.“

No, this would not work. If they thought you were an Honestant, they would condemn you.

2. There is no such sentence.

Agreed.

3. „I am innocent.“

Again, this would not work. If they thought you were a Swindlecant, they would condemn you.

4. „Either I am an honestant and innocent, or I am a swindlecant and guilty.“ = „I am either an innocent honestant, or a guilty swindlecant.“

This is a perfect example of why compound statements ought not be allowed in these logic problems. They make the solutions too easy, even trivial. For example, #1 could be solved by saying:

"I am a Swindlecant and I did it."

Whoop-de-do. What fun is that?

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For #2, i think you could say:"i will be sentenced to death." now to keep you a swindlecant, the judge has to release you.

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2. There is no such sentence.

I spent a good deal of time under the impression that there was an answer for this.. lol.. that's just mean.

4. „Either I am an honestant and innocent, or I am a swindlecant and guilty.“ = „I am either an innocent honestant, or a guilty swindlecant.“ The court could think this way:

• 4.1 If he is an honestant, then his statement is true and he is innocent.

• 4.2 If he is a swindlecant, then his statement is a lie and he is neither an innocent honestant nor a guilty swindlecant. This means that he is an innocent swindlecant.

4.3 If he is normal, then he is innocent since a normal man couldn’t have done that.

4. If you were innocent and everybody knows that the one who did it is not normal. Normal people sometimes lie and sometimes speak the truth. What sentence, no matter if you were an honestant, a swindlecant or normal can prove your innocence?

You ask what sentence (singular) could I say no matter what my type was. This nullifies your answer for 4, as you have 3 different statements depending on your type, whereas the question leads one to search for a universal answer that any of the three could use to prove their innocence. The format of the fourth question leaves room for no other interpretation, and should be clarified.

That aside, for the solution of the Normal person, the jury doesn't know he's a Normal. So how could the simple fact that he is save his butt when the jury doesn't even know that, and he's one sentence away from execution? He would need a good sentence, such as: I am a Normal, and guilty.

Also, an earlier poster had a point when stating his displeasure at the answer format, as these types of questions don't usually accept compound sentences for answers. You could demolish the one sentence rule by simply constructing one giant run on sentence; or the defendant could decide never to sleep or end his sentence, and continue talking until he died of thirst.

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You ask what sentence (singular) could I say no matter what my type was. This nullifies your answer for 4, as you have 3 different statements depending on your type, whereas the question leads one to search for a universal answer that any of the three could use to prove their innocence. The format of the fourth question leaves room for no other interpretation, and should be clarified.

The sentence I was looking for is: „I am either an innocent honestant, or a guilty swindlecant.“ What is wrong with that?

That aside, for the solution of the Normal person, the jury doesn't know he's a Normal. So how could the simple fact that he is save his butt when the jury doesn't even know that, and he's one sentence away from execution? He would need a good sentence, such as: I am a Normal, and guilty.

As mentioned in the puzzle: "... everybody knows that the one who did it is not normal ..."

Also, an earlier poster had a point when stating his displeasure at the answer format, as these types of questions don't usually accept compound sentences for answers. You could demolish the one sentence rule by simply constructing one giant run on sentence; or the defendant could decide never to sleep or end his sentence, and continue talking until he died of thirst.

So how exactly does the sentence presented by me fail to work? I would say: „I am either an innocent honestant, or a guilty swindlecant.“

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There are 4 scenarios presented, but 2 desired outcomes requested:

A) say 1 sentence to save your life, OR

B) say 1 sentence to prove your innocence.

These are not the same thing.

Outcome B, for example, cannot work with scenario 2.

So only outcome A can be applied to all the scenarios. Thus, I would say something along the lines of:

"There is a nuclear device hidden on this island set to explode if I stop breathing or the signal is lost..."

You, my sir, are what make life so delicious. So very witty