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?

the first thing that comes to mind when I looked at this problem was where do I start.  I saw Abe's comment and realized that if he were telling the truth then both Dan And Earl were also telling the truth.  In which case Dan would be both right and wrong.  Since this can not happen I imediately said the Abe was a liar.

The next thing that I considered was that since Dan says Abe's statement is not true, Then Dan would be telling the truth and Earl would be lying.  If Dan's statement were entirely true then either Jack or Rex would be lying, thus leaving me with three liars, which is not possible.  So therefore Dan is lying.

Since Dan is lying Earl, Rex and Jack must be telling the truth.

Rex-Knight

Jack-Knight

Abe-Liar

Dan Liar

Earl-Knight

Since Rex is a knight we can eliminate Rex and Earl from being the thieves.  Also since Jack is a knight we know the thieve is either Rex or Abe.  Since we already eliminated Rex. Abe is the thief.