# Math problems: logic

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Four suspects of a crime made the following statements to the police:

Andy: Carl did it. Bob: I did it. Carl: Dave did it. Dave: Carl lied when he said i did it.

1.) given that one of them "did it" and that exactly one of them told the truth, who did it?

2.) given that one of them "did it" and that exactly one of the statements was false, who did it?

3.) If exactly two answers were true, who could have done it?

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Carl: Dave did it. Dave: Carl lied when he said I did it. Therefore: Dave = I

1. If Andy did it, then Dave is the only person who told the truth. The same goes for Bob. If Carl did it, Andy and Dave told the truth. If Dave did it, Carl and Bob told the truth.

However, Bob: I did it. Therefore I = Bob = Dave

If Bob did it, then he and Dave told the truth.

So Andy did it.

...

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correction i = Dave and I= Bob ... its late... Andy did it ....

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1) Only Carl speaks the truth and dave did it

2) Impossible. For if atmost one is false then atleast two of Carl,Bob and dave ought to have done it, which is contradictory to the fact that only one person did it.

3) 2 possibilities : a) Andy and Dave tell the truth and Carl did it

b) Bob and Dave tell the truth and Bob did it

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1. If Carl lied, then Dave is telling the truth. If Dave lied, then Carl is telling the truth. Since exactly one of them told the truth, Andy and Bob are liars. Hence Dave "did it".

2. Seems impossible if Carl, Bob, Andy and Dave are distinct persons.

3. If what Andy and Dave said is true, then Carl did it.

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Four suspects of a crime made the following statements to the police:

Andy: Carl did it. Bob: I did it. Carl: Dave did it. Dave: Carl lied when he said i did it.

1.) given that one of them "did it" and that exactly one of them told the truth, who did it?

2.) given that one of them "did it" and that exactly one of the statements was false, who did it?

3.) If exactly two answers were true, who could have done it?

1. Dave said, "Carl lied when he said i did it," but whom is referred to as "the variable" i? Well, all you have to do is look at what Carl had said. Carl said, "Dave did it." So i must refer to Dave. But, there is also an ambiguity in Bob's statement in the case of i. Bob said, "I did it." Does Bob mean himself, Dave, or can it be interpreted as either Bob or Dave? If this ambiguity is considered, Andy is the only one who could have "done it", with Dave telling the truth, and everyone else lying.

2. The only two statements which are specific, meaning that they identify the culprit by name, would be from Andy and Carl. They should be the focus of our attention, rather than the statements of Bob and Dave. The only solution would then be that Dave had done it, Andy lied, and everyone else told the truth (with the ambiguity of I). It won't work out if you switch the roles of Carl and Andy as either telling the truth or lying.

3. Finally, Bob is the culprit. Bob and Dave both tell the truth, while Andy and Carl are both lying through their teeth.

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maybe dave did it for part three, with Bob and Carl telling the truth...

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