## Friday, August 31, 2007

### We got a thing goin' on

Last night's final question:

During the lunch hour at school, five boys from Mrs. Jones's homeroom visited a nearby lunch wagon. One of the boys took a candy bar without paying for it. When the boys were questioned by the principal, they made the following statements, in order:

1. Rex: "Neither Earl nor I did it."
2. Jack: "It was either Rex or Abe."
3. Abe: "Both Rex and Jack are lying."
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 Mrs. Jones was consulted, she said, "Three of the boys are always truthful, but everything the other two say will be a lie." Assuming that Mrs. Jones is correct, who stole the candy bar?

Don't those boys have excellent grammar and speaking skills?
Where are they going to school that they have an open campus and nearby lunch trucks?
Couldn't Mrs. Jones be a bit more helpful in identifying the rascals in her class?

anne57 said...

Maybe Mrs. Jones is an accessory after the fact. I bet she got half the candy bar to dissemble and throw off the investigater...

My guess is Abe. If Abe is telling the truth, then Jack and Rex are the liars and Dan and Earl would also be telling the truth. However, if Dan tells the truth, Abe can't be. So Abe lies. If Dan is telling the truth, then either Rex or Jack is the second liar. But then Earl would be correct that Dan is wrong. If Earl is lying, Dan would be correct that either Rex or Jack is lying...resulting in 3 liars. So Dan must be lying because Dan cannot be right and Earl wrong and still have two liars and three truth tellers. Therefore, Rex, Jack, and Earl are telling the truth. Rex exonerates himself, removing one option from Jack's statement: Abe. Hopefully this makes sense and is right.

J. Bowman said...

Correct! And, that's at least as good an explanation as I could give.

Leo said...

Did Rex, Abe or Jack have anything to say about your running diary? :)