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Post by reTrEaD on Feb 10, 2024 9:53:50 GMT -5
There is a group of three people. There is one, and only one, person of each type, in this group. Types:- Truthteller - Always tells the truth.
- Liar - Always tells a lie.
- Spy - Can tell the truth or a lie.
Each of them will make one statement regarding what kind of person they are not. - Charlie says: "I am not a Liar."
- Bob says: "I am not a Spy."
- Alice says: I am not a Truthteller."
What type of person is Charlie?- Charlie is a Truthteller.
- Charlie is a Liar.
- Charlie is a Spy.
- There is not enough information to know.
Please put your answer in a spoiler, so as not to affect others playing the game.. My Answer: Let's test each statement and see if that tells us what type of person Charlie is. Charlie says: "I am not a Liar". - Charlie could be a Truthteller, telling the truth.
- Charlie could be a Liar, telling a lie.
- Charlie could be a Spy, telling the truth.
Well that was no help!
- Bob says: "I am not a Spy."
Bob could be a Truthteller, telling the truth.
- Bob can NOT be a Liar, telling the truth.
- Bob could be a Spy, telling a lie.
Bob is either a Truthteller or a Spy.
Alice says: I am not a Truthteller." - Alice can NOT be a Truthteller, telling a lie.
- Alice can NOT be a Liar, telling the truth.
- Alice could be a Spy, telling a lie, and since she can't be either of the other types ...
- Alice must be the Spy.
- Bob must be the Truthteller. (He can't be a Spy because Alice is the Spy and we learned earlier that Bob can't be a Liar.)
- Charlie must be the Liar. (The other two types of people are determined to be Alice and Bob.)
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Post by asmith on Feb 10, 2024 15:04:35 GMT -5
I enjoy these. Thanks for posting this. Alice can't be the Truthteller. If she was, she'd have to be telling the truth that she's not the Truthteller.
Alice can't be the Liar. If she was, she'd be lying that she's not the Truthteller, making her both the Liar and the Truthteller.
Since Alice can't be the Truthteller or the Liar, she must be the Spy. As the Spy, she's telling the truth that she's not the Truthteller.
Bob can't be lying. If he was, he'd be lying about not being the Spy, and he'd be the Spy. However, Alice is the Spy. Therefore, Bob's telling the truth. Thus, he can't be the Liar. He must therefore be the Truthteller.
Charlie is left as the Liar. He's lying that he isn't the Liar. |
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Post by JohnH on Feb 10, 2024 16:11:44 GMT -5
Alice says she's not a truth teller, which is true because if she was then she wouldn't say she wasn't. But she's not a liar or else she wouldn't have said such truth. Alice is a Spy.
Bob says he's not a spy, and he's right because Alice is the spy, so Bob is the truth teller
Charlie is a dirty LIAR, so obviously he denies it.
I never liked Charlie....
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Post by newey on Feb 11, 2024 15:35:56 GMT -5
I came at this a bit differently. Charlie can only be the liar because, if he is not, he would be telling the truth when he says he's not the liar. Once we nail Charlie, the others just fall into place- Alice can't be th etruthteller if she says she's not, so she's the spy and Bob is the truthteller by process of elimination. |
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Post by reTrEaD on Feb 12, 2024 19:26:49 GMT -5
I came at this a bit differently. Charlie can only be the liar because, if he is not, he would be telling the truth when he says he's not the liar. Once we nail Charlie, the others just fall into place- Alice can't be th etruthteller if she says she's not, so she's the spy and Bob is the truthteller by process of elimination. About that ... You came to the right conclusion about who is who, but you should reconsider your methodology. Your first step was an incorrect inference. Charlie could be a Liar, saying he is not a liar. However, if he was telling the truth, he could be one of the other types. Charlie could be a Truthteller, saying he is not a liar. Charlie could be a Spy, saying he is not a liar. It's only by the process of elimination, that we eventually determine Charlie must be the liar. Just for fun, if we change ONLY Bob's statement, the roles of Bob and Charlie will reverse. - Charlie says: "I am not a Liar."
- Bob says: "I am
not a Spy."
- Alice says: I am not a Truthteller."
Alice's statement is definitive. It can only be made by a Spy. Bob's new statement could be made by a Spy or a Liar. And since Alice is the Spy, Bob must be the liar. Charlie is now the Truthteller, truthfully stating he is not a Liar. Charlie's role changed, even though his statement remained the same! |
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Post by newey on Feb 12, 2024 21:15:57 GMT -5
Forget Charlie and just focus on the Liar, who has to be one of the three. If the Liar were to state "I am not the truthteller", that would be a true statement, but the Liar always lies. So, the Liar cannot have stated he was a truthteller.
If the Liar says "I am not the spy", that is also a true statement becuase the Liar always lies while the spy is sometimes truthful, so the Liar also cannot make that statement.
If the Liar says "I am not the Liar", that is a lie, and so is the only consistent statement the Liar could make.
Therefore, whoever says they are not the liar is, in fact, the Liar. And we are told that Charlie was the one who said that. Ergo, Charlie is the Liar.
The other two then follow via process of elimination, as you noted. |
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Post by reTrEaD on Feb 13, 2024 19:22:02 GMT -5
Forget Charlie and just focus on the Liar, who has to be one of the three. If the Liar were to state "I am not the truthteller", that would be a true statement, but the Liar always lies. So, the Liar cannot have stated he was a truthteller.
If the Liar says "I am not the spy", that is also a true statement becuase the Liar always lies while the spy is sometimes truthful, so the Liar also cannot make that statement.
If the Liar says "I am not the Liar", that is a lie, and so is the only consistent statement the Liar could make.
Therefore, whoever says they are not the liar is, in fact, the Liar. And we are told that Charlie was the one who said that. Ergo, Charlie is the Liar.
The other two then follow via process of elimination, as you noted. oic My apologies for not understanding what you meant, earlier. You're testing all three statements that were made and have found in this case, two of the statements can NOT have been made by the Liar. That's rather clever and adds another dimension to the expression 'negative logic'.
| Truthteller | Liar | Spy | | "I am not a Liar." |
| (Yes) |
| | "I am not a Spy." |
| No |
| | "I am not a Truthteller." |
| No |
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Since we've determined the statement made by the Liar is exclusive to the person (Charlie) who made it, we can eliminate that as a possibility for the other two.
| Truthteller | Liar | Spy | | "I am not a Liar." | X | (Yes) | X | | "I am not a Spy." |
| No |
| | "I am not a Truthteller." |
| No |
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If we move immediately to the last statement (by Alice), we can discern the only type of person who can make this statement and remain in-character, is the Spy.
| Truthteller | Liar | Spy | | "I am not a Liar." | X | (Yes) | X | | "I am not a Spy." |
| No |
| | "I am not a Truthteller." | (No) | No | Yes |
Since we've determined the role of Spy is filled, we can remove that possibility for anyone else.
| Truthteller | Liar | Spy | | "I am not a Liar." | X | (Yes) | X | | "I am not a Spy." |
| No | X | | "I am not a Truthteller." | (No) | No | Yes |
That leaves only one possibility remaining for (Bob) the person who stated "I am not a Spy. He must be the Truthteller. |
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Post by newey on Feb 13, 2024 20:15:35 GMT -5
Yours is the more thorough disquisition, I did it short-hand and clarity clearly suffered.  |
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Post by reTrEaD on Feb 13, 2024 21:41:44 GMT -5
I had to look that up. I'll add it to my eloquence vocabulary list. |
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