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
No solution! by kyju)
Hmmm, that is interesting...
I think it depends on how exactly one defines what constitutes a "liar"
and a "knight", because, at least in the only solution put forth so
far, Dan makes one statement that is true and one that is false. In the
context of the problem, each individual is either a liar or a knight.
If every proposition an
individual says must be false for him to be a liar, then I'd say you're
right; there is no solution. On the other hand, if only one proposition
an individual says must be false for him to be a liar, then the
solution already stated (Abe and Dan liars; Rex, Jack and Earl knights;
Abe the robber) appears to be correct, because the assumption that Dan
is a liar would not lead to the conclusion that Abe is a knight.
Likewise, the assumption that Abe is a liar would not lead to the
conclusion that Dan is a knight.
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Posted by yocko
on 2005-02-08 14:30:10 |
re: No solution!
