Of Al, Ben and Cal, only one man is smart.

Al says truthfully:
    1. If I am not smart, I will not pass Physics.
    2. If I am smart, I will pass Chemistry.

Ben says truthfully:
    1. If I am not smart, I will not pass Chemistry.
    2. If I am smart, I will pass Physics.

Cal says truthfully:
    1. If I am not smart, I will not pass Physics.
    2. If I am smart, I will pass Physics.

It is known that:

   I. The smart man is the only man to pass one 
particular subject.
   II. The smart man is also the only man to fail 
the other particular subject.

Which one of the three men is smart and why?

Since the smart man is the only man to pass one subject and fail the other subject, the two people that are not smart both pass one subject and fail the other subject. Therefore, they pass the same subject and fail the same subject. If neither Al nor Ben is smart, then Al fails physics and Ben fails chemistry. Since they fail different subjects, that is a contradiction, so either Al or Ben is smart. If neither Ben nor Cal is smart, then Ben fails chemistry and Cal fails physics. That is another contradiction, so either Ben or Cal is smart. Therefore, Ben is the smart man. He passes physics and fails chemistry. Al and Cal pass chemistry and fail physics.

Posted by Math Man on 2013-10-18 08:52:54