Who Is The Thief?

There is only one truth teller, but Alice and Evelyn both claim to be innocent, so one of them must be the thief.

If Evelyn is innocent and telling the truth, then Alice would be the thief. However, then Bob would also be telling the truth, which contradicts that there is only one person telling the truth.

Thus, Evelyn must be guilty (and lying, whereas Alice is telling the truth and Bob/Carly/Dave are lying).

You have only one case with only one thief.

Case 1 when Alice say the truth : only Evelyn is the thief.

Case 2 when Bob say the truth : Alice and Evelyn are the thief.

Case 3 when Carly say the truth : Carly and Evelyn are the thief.

Case 4 when Dave say the truth : Carly and Evelyn are the thief.

Case 5 when Evelyn say the truth : Nobody is the thief becaus Alice "I am not the thief" is not true but Bob "Alice is the thief" is not true either.

The only case who make sens when we know that it have only one thief is the case number 1.

Evelyn is the Thief

While it may not be significantly faster than the other solutions offered here, I feel somewhat compelled to point out that you need only examine two (mutually exclusive / disjoint) cases:

We are given the following [translated to formal logic:]

$\text{Let:} \; [ ( \exists T, \, \forall x \in \{ \text{A:E} \} ) \: T(x) = \text{x is the Thief}] \; \& \; [ (\exists t, \, \forall x \in \{\text{A:E} \} ) \: t(x) = \text{Statement from x is True} ]$

We know: $[ \exists^{!1} x \: | \: \text{T}(x) ] \; \& \; [ \exists^{!1} x \: | \: t(x) ]$

Alice says: "I am not the thief" $[ \neg T(A) ]$

Bob says: "Alice is the thief" $[ T(A) ]$

Since we know that Alice can only be the thief or not be the thief (i.e. they are mutually exclusive) $[ T(A) \, \lor \, \neg T(A) ]$ , we can infer that (at least) one of them is telling the truth; moreover, we can infer that Alice cannot be both the thief and not the thief $[ ( T(A) \, \lor \, \neg T(A) ) \iff \neg ( T(A) \, \& \, \neg T(x) ) ]$ ; thus, we know exactly one of either Alice of Bob is the (only person) telling the truth $[ \exists (y \in \{ \text{A:E} \} ) \: | \: ( t(y) \implies (y \in \{ A, B \} ) ) \iff ( (y \notin \{ A, B \} ) \implies \neg t(y) ) ]$ .

From this point, it is simply a matter of seeing which assertion $[ t(A) \lor t(B) ]$ conflicts with the remaining propositions, assuming they are (all) false:

Carly says: "I am the thief." $[ T(C) ] \implies [ \neg T(C) ]$

Dave says, "Carly is the thief." $[ T(C) ] \implies [ \neg T(C) ]$

Evelyn says, "I am not the thief." $[ \neg T(E) ] \implies [ T(E) ]$

Thus, we know (without a full trial & error outcome set) which person is the thief.

(And, of course, that Alice is the one person telling the truth--and that Bob obviously has it out for her; and while we're not quite sure what Carly & Dave are up to, we should definitely be suspicious...)

I found the answer by simply looking at the top two. Both of those CAN'T be lies, because they would contradict each other. As a result:

*Either Alice is telling the truth (that she isn't the thief) or *Bob is telling the truth (that she is).

So one of them has to be telling the truth.

The bad news is that based on just those two we don't have enough information to determine who is telling the truth... but the good news is that since one of them is, we know for a fact that the other three statements have to be lies (since only one is telling the truth).

So Carly can't be the thief (since both her and David are lying). And since Evelyn claimed not to be the thief (but also lied), she must be the thief.

Using that piece of information, we can also know that Alice couldn't be the thief (since Evelyn was), so she was the one telling the truth.

QED

Alice cannot be both thief and not thief, so either Alice or Bob tell the truth. Others, among them Evelyn are lying, so Evelyn is a thief.

The most straight forward way to solving this logic riddle was to assume 1 person's statement as true and consider it's effect on the rest of the statements till they stop being a contradiction, if we start off with Alice, we know Alice is yelling the truth so Alice isn't the thief, Now Bob, Carly, Dave And Evelyn all will be lying, while Bob, Carly and Dave all lie, none of them denies themselves from being a theif clearly, Bob lies about Alice which satisfies our conditions and prevents a contradiction, Dave and Carly both are lying so Carly is definitely not the theif, despite Bob and Dave's statements cause us to believe that there might be a possibility they really are the theif, but since Evelyn's statement is already a lie, we take it as when she says " I am not a theif" we assume she's lying so the true statement would therefore be " I am the theif", Evelyn clearly announces her innocence and given the condition that she's lying she actually announces herself to be the culprit

You can do it by looking at each person in turn , assume they are truthful and see if fits .Or you may realise that the only candidates are A & E since they can't both be telling the truth - and see who fits with the rest, Not a difficult one this I don't think.

Carly confessed and Dave accused Carly of the theft, but they can't both be right from the statement of "the detectives know that one of them is the thief and that only one of them tells the truth", so Carly must be innocent and they both lied.

Alice and Bob gave conflicting statements, so our sole honest suspect is between these two and Evelyn must have lied. She deceptively claimed to be innocent, so the truth is she's the guilty thief.

Statements:

Alice says, "I am not the thief."

Bob says, "Alice is the thief."

Carly says, "I am the thief."

Dave says, "Carly is the thief."

Evelyn says, "I am not the thief."

Carly and Dave's statements are informationally the same, stating that "Carly is the thief". As only one of the 5 statements is true, Carly and Dave's statements cannot be both true, so they both must be false.

Alice and Bob's statements are both about Alice, but are opposite in meaning, therefore one of the statements must be true (they can't both be false or both be true as they are opposite in meaning). As only one of the 5 statements is true, and it is either Alice or Bob's statements, Evelyn's statement must therefore be false, meaning she is the thief. Another way of finding out who is the thief after proving Carly and Dave's statements are false: In order for Bob's statement to be true, Evelyn's statement must be true as well, so Bob's statement is clearly false (as only one statement can be true, but Evelyn's statement could still be true with the reasoning of the previous statement). Therefore Alice cannot be the thief, therefore Alice's statement is true and Evelyn's statement is false, and therefore Evelyn is the thief.

Remember, only ONE is telling the truth. Lets go it like this. A=Alice, B=Bob, C=Carly D=Dave and E=Evelyn. If D is telling the truth that he thinks C is the thief, D=True but C would also be true. It cannot be C or D. If B was telling the truth, Alice is the thief, B=True and A=False... but E would then be true. Cannot be A or B. If E however was telling the truth, she says she isn't the thief, E=True, then C=True, D=True, B=True and A=True! We already can tell it was E without the statement above, but we can prove it with that. And one more proof. If E is lying, E is the thief, D and C would be lying too, A wouldn't and therefore B would be lying. Sorry if this isn't clear, i'm not exactly a genius at logic or maths.

So I started by following out the situation if Alice is telling the truth(I flipped everyone else's to make them true); Alice: I am not the thief Bob: Alice is not the thief Carly: I am not the thief Dave: Carly is not the thief Evelyn: I am the thief

Since nobody's statement contradict one another, this must be the answer. Evelyn is the thief.

• C cannot be true, because that would mean A and E are true; therefore C cannot be the thief, and is one of the four liars.

• Because C is not the thief, D is one of the liars (though he could be the thief).

But none of that is really necessary, because:

• The thief MUST be either A or E, because both say they are innocent, and only one can be telling the truth (and only one can be lying).

• Either A or B is telling the truth, but not both.

• Either A or E is telling the truth, but not both.

Therefore, A is telling the truth, B and E are lying, and E is the thief.

-x means x claims to not be the thief

y means y admits to being the thief

x + z means z accuses x to be the thief

There can only be 1 liar and 1 honestly person

Assuming that all claims are given equal weightage of 1

1) -A + B = 0

2) -C + D =0

3) -E = -1

If we say E is the liar and A as the honest one we get

1) -(-A) + B = A + B =2

3-(-E) = 1

If we say C is the liar and E is the honest one we get

2) -(-C) + D =2

3) -E = -1

...

(Continue with all possible equations)

Since the equation involving the thief must equal to a odd number ( since the waitage of one response is 1).

Regardless of who is assumed to be the liar or honest person, E will always equal +/- 1 which is a odd number. Since there is only one equation involving E and there are no other subjects in that equation, E is the thief.

I am thinking about Alice and Charlie, but I know that neither of them do this. And I see Evelyn. I press that field and I was surprised. It's correct.

Since there is only one truthful person 4 of the statements are lies. Thus reverse all the statements and 4 are true and only 1 lie. It is rhe evident that evelyn is the only uncontradicted statement and she is the thief.

Conditions / restrictions:

• honest count: 1
• thief ... count: 1

Cases:
....................... initial: ...................... inferred:
Alice .. honest not ( Alice.is thief ) .. not ( Alice.is thief )
Bob ... liar ..... ( Alice.is thief ) ........ not ( Alice.is thief )
Carly . liar ..... ( Carly.is thief ) ........ not ( Carly.is thief )
Dave . liar ..... ( Carly.is thief ) ........ not ( Carly.is thief )
Evelyn liar .... not ( Evelyn.is thief ) ( Evelyn.is thief )
thief count: 1

Alice liar not ( Alice.is thief ) ( Alice.is thief )
Bob honest ( Alice.is thief ) ( Alice.is thief )
Carly liar ( Carly.is thief ) not ( Carly.is thief )
Dave liar ( Carly.is thief ) not ( Carly.is thief )
Evelyn liar not ( Evelyn.is thief ) ( Evelyn.is thief )
thief count: 2

Alice liar not ( Alice.is thief ) ( Alice.is thief )
Bob liar ( Alice.is thief ) not ( Alice.is thief ) <- contradiction
Carly honest ( Carly.is thief ) ( Carly.is thief )
Dave liar ( Carly.is thief ) not ( Carly.is thief ) <- contradiction
Evelyn liar not ( Evelyn.is thief ) ( Evelyn.is thief )
thief count: 1

Alice liar not ( Alice.is thief ) ( Alice.is thief )
Bob liar ( Alice.is thief ) not ( Alice.is thief ) <- contradiction
Carly liar ( Carly.is thief ) not ( Carly.is thief )
Dave honest ( Carly.is thief ) ( Carly.is thief ) <- contradiction
Evelyn liar not ( Evelyn.is thief ) ( Evelyn.is thief )
thief count: 1

Alice liar not ( Alice.is thief ) ( Alice.is thief )
Bob liar ( Alice.is thief ) not ( Alice.is thief ) <- contradiction
Carly liar ( Carly.is thief ) not ( Carly.is thief )
Dave liar ( Carly.is thief ) not ( Carly.is thief )
Evelyn honest not ( Evelyn.is thief ) not ( Evelyn.is thief )
thief count: 0

Set up a sketch of a table. Column headings are A, B, C, D, E, each of which is a candidate for being the thief. Each row is for the statement being True or False in each cell if the person the column stands for were the thief. The only column with four Falses and one True (Alice's statement) is "E", Evelyn-as-Thief, column.

when ever somebody said "I am not the theif", somebody said back that "they are the thief!'" but when Evelyn said "I am not the thief", nobody replied back

The solution revolves around Alice and Evelyn. They can't both be lying - that would mean that they are both the thief! And, because there is only one person telling the truth, it means that Bob is lying, implying that Alice is not the thief. That leaves Evelyn as the thief.

Since there is only one truth teller, so considering one of the statement true we can solve the problem. Evelyan is correct.

Forget all these mathematical solutions. Carly (Simon) is the thief. She stole my heart.

First assume Alice is telling the truth which means everyone else has to be lying. Let's examine each of their comments.

Alice says, "I am not the thief." Ok. Fine. Alice is not the thief. Bob says, "Alice is the thief." Since Alice is not the thief, then Bob is lying and we're fine with this comment given our first assumption. Carly says, "I am the thief." Again. This is still possible should Carly be lying. Dave says, "Carly is the thief." Dave is lying and Carly is not the thief. Still ok. This matches our previous comment. Evelyn says, "I am not the thief" Evelyn is lying and she is the thief.

So now we have one possible outcome in which Evelyn is the thief and Alice is the only one that tells the truth.

Now lets assume Bob is the one telling the truth. Alice says, "I am not the thief." Alice is lying and that means that she is the thief. Evelyn says, "I am not the thief" Evelyn is also lying and that would mean she is a thief as well. This is not possible so Bob cannot be the one telling the truth.

Now lets assume Carly is telling the truth. Carly says, "I am the thief." Ok. Carly is the thief and tells the truth. Dave says, "Carly is the thief." But Dave lies, so this does not match the previous statement.

Now lets assume Dave tells the truth. Dave says, "Carly is the thief." So Carly is the thief given this assumption. Alice says, "I am not the thief." Alice would be a lier and this would mean that she is also a thief. Not possible.

Finally lets assume Evelyn is the one telling the truth. Evelyn says, "I am not the thief" Evelyn is the thief then. Alice says, "I am not the thief." Again, Alice would be a lier and this would mean that she is also a thief. Not possible.

The only situation that satisfies all the conditions is the first set. Alice tells the truth and Evelyn is the thief.

Brute force solution: Assume Alice is the thief. Then see if each person's statement is truth or lie, based on that assumption. Repeat the process for each person. The thief is the person for whom only one person is telling the truth. In all the other cases, two people will be telling the truth, which contradicts the premise.