perplexus.info :: Liars and Knights : Who stole the candy bar?

Who stole the candy bar? (Posted on 2005-02-03)

During lunch hour at school, a group of five boys from Miss Jones' home room visited a nearby lunch wagon. One of the five boys took a candy bar without paying for it. When the boys were questioned by the school principal, they made the following statements in respective order:

1. Rex: "Neither Earl nor I did it."

2. Jack: "It was Rex or Abe."

3. Abe: "Both Rex and Jack are liars."

4. Dan: "Abe's statement is not true; one of them is lying and the other is speaking the truth."

5. Earl: "What Dan said is wrong."

When Miss Jones was consulted, she said, "Three of these boys are knights, but two are liars." Assuming that Miss Jones is correct, can you determine who took the candy bar?

See The Solution Submitted by Jane Doe

Rating: 3.0000 (5 votes)

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Solution

| Comment 17 of 38 |

As stated many times, Rex, Jack, and Earl being Knights is the only viable solution. The question of Dan's statement being a problem for that situation is solved by looking at it this way; If Dan is lying, then only part of his statement has to be false to make him a liar. Place the statement in an If->Then form. If abe's statement is not true, then one of them is lying and the other is telling the truth. If the first half is true and the second half is false, the entire statement is still considered false. Using that helps to solve this problem.

Posted by Nate on 2005-03-27 17:53:08

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