First, see the original post. Then, here are your answers:
1. I am Daniel. This could be Daniel telling the truth, or Henrik lying. We cannot determine which brother is speaking, but we can conclude that Henrik is the liar.
2. My brother is Daniel. The reverse of #1; this could be Henrik telling the truth, or Daniel lying. Either way, we know that Daniel is the liar.
3. Henrik tells the truth. This could be Henrik telling the truth, or Henrik lying. Either way, we know that Henrik is speaking (in the third person).
4. Henrik lies. The reverse of #3; this could be Daniel telling the truth, or Daniel lying. Either way, we know that Daniel is speaking.
5. Henrik would never say these words. Could this be Henrik telling the truth? Clearly not. Could it be Henrik lying? Sure. Could it be Daniel lying? No, because then Henrik would be the truth-teller — which would make the statement accurate. Could it be Daniel telling the truth? Again, no, because then Henrik would be the liar — which would make the statement inaccurate. Thus, Henrik is speaking, and is lying.
6. Only Henrik can say these words. Could this be Henrik telling the truth? No, because the liar Daniel would happily say the same words. Could this be Henrik lying? No, because the truth-teller Daniel really wouldn’t say the words, making the lie no longer a lie. Could this be Daniel telling the truth? Clearly not. That leaves just one option (and you can check that it works): Daniel is speaking, and is lying.
7. Daniel would call me honest. This could be Daniel telling the truth. Or it could be Henrik lying. But it can’t be Daniel lying (the liar Daniel really *would* call himself honest!) and it can’t be Henrik telling the truth (because the liar Daniel *wouldn’t* call him honest). So we don’t know who is speaking, but we know Daniel is the truth-teller.
8. Daniel would call me a liar. This could be Henrik telling the truth. Or it could be Daniel lying (because he’d actually call himself honest). But it can’t be Henrik lying (because truth-teller Daniel *would* call him honest) and it can’t be Daniel telling the truth (because he wouldn’t call himself a liar). So we don’t know who is speaking, but we know Daniel is the liar.
9. My brother would say I’m Daniel. Could this be Daniel telling the truth? No, because liar Henrik wouldn’t identify his brother so truthfully. Could this be Daniel lying? No, because truth-teller Henrik really would identify Daniel as such. Could this be Henrik telling the truth? Yes. Could this be Henrik lying? Yes. So Henrik is speaking, but we don’t know if he’s lying.
10. My brother would say Daniel lies. Could this be Daniel telling the truth? Yes. Could this be Daniel lying? No, because truth-teller Henrik really *would* say that Daniel lies. Could this be Henrik telling the truth? No, because liar Daniel wouldn’t admit to lying. Could this be Henrik lying? Yes, because truth-teller Daniel wouldn’t describe himself as a liar. So this is either Daniel telling the truth or Henrik lying; either way, we conclude that Daniel is the truth-teller.
11. Both of us claim to be Henrik. If Henrik is the truth-teller, then this is true, so we’re listening to Henrik. But if Henrik is the liar, then this is false, so again, we’re listening to Henrik. Either way, Henrik is speaking.
12. Suppose Daniel is the truthteller. Can you think of something he might say that would reveal *both* that he is Daniel, *and* that he is telling the truth? Here’s one solution: “Daniel is capable of uttering these words.” A truth-telling Daniel could easily say such a thing — which means that a lying Henrik would never. Meanwhile, a lying Daniel could not say those words, because in uttering them, he would make them true — and since Daniel can’t say them, a truth-telling Henrik cannot claim that he can. In the end, only one possibility works: Daniel speaks, and is telling the truth.
I am not a truth-teller named Henrik.
Oh yeah, that’s nice!
“Would your brother say that Henrik lies?”
I reversed the answer for “My brother would say I’m Daniel.” I interpreted it to mean:
My brother would say “I’m Daniel”.
Another answer to the riddle is “I’m Daniel or I’m a liar.”
Oops, didn’t think of that ambiguity! Will maybe edit to say “my brother would say *that* I’m Daniel.”
And I like your solution! (Although a *very* sneaky lying Daniel might utter the same words, using the conversational “or” to mean the logical xor…)
Clearly, the statement needs to use “and/or” instead of “or”, since “and/or” is common parlance and is unambiguously logical OR, while “or” could mean OR or XOR.
Is there a common parlance word that’s unambiguously XOR? I don’t think I’ve heard one.
> Is there a common parlance word that’s unambiguously XOR? I don’t think I’ve heard one.
“or else”
I think I have a different solution for 5 and 6. For item 5, I have no doubts that Henrik is lying, but I don’t think its possible to deduce whether Henrik or Daniel is the speaker. Here’s why I think so:
To determine who is speaking, we should determine the truth value of the statement “Henrik would never say these words.”
Let’s assume the statement P = “Henrik would never say these words.” is a false statement. P being false means Henrik would say the statement P. This is consistent; because Henrik is lying, he should be able to say any false statement, which includes P. Henrik being the speaker is a consistent possibility.
On the other hand, let’s assume the statement P = “Henrik would never say these words.” is a true statement. P being true means Henrik would never say P. This is consistent too; because Henrik is lying, he would never say any true statement, so he would never say P. This means Daniel being the speaker is also a consistent possibility.
This means the statement “Henrik would never say these words.” could be both either true or false, and neither case leads to any contradiction.
The same logic can be applied to item 6 too. Daniel is the liar, but determining who speaks that statement depends on the truth value of “Only Henrik can say these words.”
This reminds me of an anti-paradox: “This sentence is true.” It can be both either true or false, and we can’t determine its truth value.
I asked my brother wether is lying and he said “idk, but you’re lying.”. Now is this true or just nonsense?