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?

(In reply to

answer by K Sengupta)

Since precisely three of these boys are knights, but two are

liars, we examine each of the five cases wherein each of the

five individuals in turn are guilty, and verify whether

the respective number of liars and knights in each of those

five situations conform to the given conditions.

These five situations are now examined in terms of the

following table:

Situation Conclusion Remarks

Rex is Guilty Abe, Rex and Earl Contradiction

are liars,and Jack

and Dan are knights

Jack is Guilty Jack, Abe and Earl Contradiction

are liars and Rex

and Dan are knights

Dan is Guilty Jack, Abe and Dan Contradiction

are liars,and Rex

and Dan are knights

Earl is Guilty Rex, Jack and Dan Contradiction

are liars,and Abe

and Earl are knights

Abe is Guilty Abe and Dan are Conform to the

liars,and Rex, Jack given conditions

and Earl are

knights

Consequently, Abe took the candy bar.

*Edited on ***June 11, 2008, 4:45 pm**