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
Puzzle Solution
