[rookie1ja]

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?

Spoiler for Solution:

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.

Spoiler for old wording:

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?

[larryhl]

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

oh wait, that wouldn't work lol.

[dhuraal]

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

[larryhl]

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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...

[imtcb]

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

[shashank929]

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....

[Naruki]

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..."

[bonanova]

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.

[xandarr]

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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.

[judo_val]

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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.