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?
Abe has to be a liar, because if his statement is true, then rex and jack are liars. However, this cannot work because Dan would then speak the truth, which would mean Abe couldn't also be telling truth. Now that he know that Abe is a liar, we know that Dan's statement is true and thus we've reached a paradox, because now we have two liars, as Dan says there is a second in either Rex or Jack, but there would have to be a third in Earl, who contradicts Dan.
If we scratch this paradox by assuming that Dan's full statement is not entirely true, then we can call dan the second liar. Now everyone else is speaking truth and since we know the culprits were either Rex or Abe, and Rex is protected by his knight's honor, Abe is the one who stole the candy bar.
Actually, I did it.
solution
