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# Who lies and who tells the truth?

## Question

This is a puzzle from an Usborne puzzle books called Logic Puzzles, and though it gives the correct answer, the method for how it reaches that answer eludes me. I’m posting it here to see if anyone can explain the logical steps to reach the answer (I’ll refrain from posting the answer for now if people with to try and solve it. The puzzle goes as follows:

There is a troupe of five mummers: a drummer, a dancing bear, a piper, a juggler, and a jester. One always tells the truth, one always tells lies, and the remaining three tell a mixture of truth and lies. To find out who tells what, the following clues are presented:

Drummer: I always tell a mixture of truth and lies.

Juggler: That is not true.

Jester: If the bear is always truthful, the juggler tells nothing but lies.

Bear: That is false.

Piper: The drummer always tells the truth.

Jester: The piper tells nothing but lies.

Can you figure out who tells what based on this information, and how?

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I agree with harey. As was said earlier, you can rule out the Drummer from being the Truth teller because he said he tells truth and lies, and you can rule out the Piper as being the Truth teller because he says someone else always tells the truth and there's only one Truth teller. So there are three possible Truth tellers.

(1) If the Jester is the Truth teller then the Piper must be the Liar, as Babysnoot said, but that's not enough to rule out other possible truth tellers.

(2) If the Juggler is the Truth teller then you know the Drummer must be the Liar. Since the Drummer can't be the Truth teller, and the Truth teller said his statement that he tells both truths and lies is false, the only thing the Drummer could be is the Liar. This kind of works against Babysnoot's argument.

(3) If the Bear is the Truth teller, then we know the Juggler isn't the Liar but I can't narrow it down more than that.

I also considered the possibility that the statement that the other three "tell a mixture of truth and lies" means that there must be both some true statements and some false statements among the three, but that still doesn't help. If the Drummer and Juggler are mixes then the Drummer's statement is True and the Juggler's statement is False, so any solution excluding them as Truth teller and Liar would work. And for the Drummer = Liar / Juggler = Truth teller scenario, you would have the Jester's first statement be True and the Piper's statement be False, so that doesn't rule anything out.

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Drummer : Mix

Juggler : Mix

Jester : Truth

Bear : Mix

Piper : Liar

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Yes.

We know the drummer doesn’t always tell the truth because they claim they tell a mixture of truth and lies, making it a false statement. So because we know that, the piper also can’t be telling the full truth.

So drummer cant be truth and neither can the piper. So let’s run through each one of the others in that spot.

Bear: When you mark the bear as the one who tells the truth, there isn’t enough info to figure it out. So it cannot be them.

Juggler: Once again, there really isn’t enough information to figure it out if the juggler was it.

Jester: The jester however, does have enough info for it to be the one who tells the truth, because they say the piper tells nothing but lies. That checks out, because the drummer doesn’t always tell the truth. And because the bear doesn’t always tell the truth, the juggler is a mix, as well as the rest.

So, Jester always tells the truth, the piper always lies, and the bear, the drummer, and the juggler tells a mix of truths and lies. I hope that makes sense!

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I fear there are multiple solutions.

Babysnoot is correct, just the only reason to proclaim Jester truthteller is that there is no further contradiction in the system.

For Bear=truthteller, Drummer=liar, others=mix (it does not matter whether what they say is true or false), there is no contradiction in the system, neither.

Does someone agree?

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