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Smart Man (Posted on 2013-10-17) Difficulty: 3 of 5
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?

See The Solution Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Possible solution | Comment 1 of 3

      I believe that direct contradictions can be found to supply a unique solution. Number the stipulations as follows:

 A. Al says truthfully:        
     1. If I am (not smart), I will not pass Physics.        
     2. If I am smart, I will pass Chemistry.        
         
 B. Ben says truthfully:        
     1. If I am (not smart), I will not pass Chemistry.        
     2. If I am smart, I will pass Physics.        
         
 C. Cal says truthfully:        
     1. If I am (not smart), I will not pass Physics.        
     2. If I am smart, I will pass Physics.        
         
 D1. Either 2 pass Physics, and smart passes Chemistry, or        
 D2. 2 pass Chemistry, and smart passes Physics.        
         

Case D1. We just need to consider Cal's case.       
 Assume Cal is (not smart): contradiction between C1 and D1        
 Now assume that Cal is smart: contradiction between C2 and D1.        
         
Case D2. This time Cal is flexible.     
 Assume Cal is (not smart): no contradiction.        
 Now assume that Cal is smart: still no contradiction.        
 As to Al's case, assume that Al is smart: contradiction between A2 and D2        
 Now assume that Al is not smart: no contradiction.        
 As to Ben's case, assume that Ben is smart: no contradiction        
 Now assume that Ben is not smart: contradiction between B1 and D2.        
         
 So Ben must be smart, Al must be (not smart) , and by elimination, Cal is (not smart) also. 

Edited on October 17, 2013, 11:30 am
  Posted by broll on 2013-10-17 11:26:59

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